UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO PROGRAMA DE MAESTRÍA Y DOCTORADO EN INGENIERÍA INGENIERÍA ELÉCTRICA – TELECOMUNICACIONES IMPLEMENTATION OF MACHINE LEARNING TECHNIQUES TO OPTIMIZE THE GROUND SEGMENT FOR HIGH THROUGHPUT SATELLITE SYSTEMS IN Q/V BAND T E S I S QUE PARA OPTAR POR EL GRADO DE: DOCTOR EN INGENIERÍA PRESENTA: IVÁN ANDRÉS CORNEJO GAIBOR TUTORES PRINCIPALES DR. SALVADOR LANDEROS AYALA, FI-UNAM DR. JOSÉ MARÍA MATÍAS MARURI, FI-UNAM COMITÉ TUTOR DR. VÍCTOR RANGEL LICEA, FI-UNAM DR. RAMÓN MARTÍNEZ RODRÍGUEZ-OSORIO, GR-UPM CIUDAD DE MÉXICO, NOVIEMBRE 2020 UNAM – Dirección General de Bibliotecas Tesis Digitales Restricciones de uso DERECHOS RESERVADOS © PROHIBIDA SU REPRODUCCIÓN TOTAL O PARCIAL Todo el material contenido en esta tesis esta protegido por la Ley Federal del Derecho de Autor (LFDA) de los Estados Unidos Mexicanos (México). El uso de imágenes, fragmentos de videos, y demás material que sea objeto de protección de los derechos de autor, será exclusivamente para fines educativos e informativos y deberá citar la fuente donde la obtuvo mencionando el autor o autores. Cualquier uso distinto como el lucro, reproducción, edición o modificación, será perseguido y sancionado por el respectivo titular de los Derechos de Autor. JURADO ASIGNADO: Presidente: Dr. Víctor Rangel Licea Secretario: Dr. Miguel Moctezuma Flores 1er. Vocal: Dr. José María Matías Maruri 2do. Vocal: Dr. Salvador Landeros Ayala 3er. Vocal: Dr. Ramón Martínez Rodriguez-Osorio Lugar donde se realizó la tesis: FACULTAD DE INGENIERÍA, UNAM. TUTOR DE TESIS: DR. SALVADOR LANDEROS AYALA -------------------------------------------------- FIRMA To my parents, Iván and Lourdes, for their endless love and encouragement. To my loving wife, María Fernanda, for her support and patience. Thank you for making it possible. Acknowledgements My deepest thanks to my tutor and supervisor, Dr. Salvador Landeros-Ayala, for sharing his knowledge and his support during my Ph.D study, whose guide and advice were essentials in the development of this thesis. Also, he was always aware of me and my family in Mexico. I am very grateful to him for allowing me the opportunity to pursue my Ph.D at Universidad Nacional Autonoma de Mexico, UNAM. It has been a privilege and an honor to work with him and learn from him. I wish to thank my co-tutor and co-supervisor, Dr. Jose Maria Matias Maruri, for his patience and his linking-up in my research work. During my Ph.D thesis, he always supported me all-the-time. We had several meetings to discuss different topics of my research, administrative issues at UNAM, and my residence in Mexico. I wish also to express my gratitude to Dr. Ramon Martinez and his work-team at Universidad Politecnica de Madrid, UPM, in Madrid, Spain, where I performed my studies as a visiting student. We exchanged several criteria for my research and gave me excellent feedback in order to improve some aspects of my thesis. I am eternally grateful for all his comments and advice. I would also like to thank Dr. Victor Rangel-Licea, he is a member of the tutoring committee of this thesis and Head of the Telecommunications Engineering Department at DIE, UNAM. Through his support and management, it was possible to attend different events to enrich my knowledge in the telecommunications field. I want to thank Dr. Miguel Moctezuma Flores for agreeing to be part of my Ph.D committee member and review my research. A special thanks to Mtra. Susana Kolb Cadwell. She is the coordinator at DGECI, UNAM. DGECI has a great program in academic writing that I was part of this program as a student, learned a lot from her as well as her work-group. I am grateful to Consejo Nacional de Ciencia y Tecnologia, CONACYT, for granting me a scholarship to study my Ph.D at Universidad Nacional Autonoma de Mexico, UNAM, CVU/Scholarship number: 559998/298954, and the CONACYT International Mobility Grant, 291250, to attend to Universidad Politecnica de Madrid, UPM, in Madrid, Spain. At last but not least, I must express my endless gratitude to my parents. They have always supported my studies and have stayed with me in my life decisions. To my grandmother, for her eternal blessings. I am grateful to my wife Fernanda for her love and encouragement every time, in all good and bad moments. To my friends and colleagues in Mexico, Spain, and Ecuador, thank you all. ii Abstract Rain attenuation events are one of the most important drawbacks in satellite communications, impairing directly on satellite link availability. For this reason, it is necessary to foresee rain events in order to avoid an outage of the satellite link. However, the lack of rainfall database hinders the development of a reliable prediction method. In this thesis, we implement an alternative method to generate rain attenuation time-series in the Q/V band for a specific geographic location based on the recommendation of the International Telecommunication Union. With the computed rain-attenuation data, we propose and develop a method to predict rain attenuation events based on deep learning techniques without appealing to complex mathematical models. To be specific, we implement the Long-short term memory network, which is a Machine Learning technique based on supervised learning. Each model is trained and validated by computational experiments, employing statistical metrics to find the most accurate and reliable models. The outcomes of the prediction model are employed and discussed to compare with other related methods and models. In addition to the evaluation of the proposed method, we find that our method could be notably able to improve mechanisms for switching either data traffic or satellite links in order to increase the satellite-link availability. For this purpose, two methods were proposed to optimize the ground network by the implementation of the deep learning method as well as another method based on the Markov chain. The smart-predictive method is based on the developed deep learning model, where the predictions of the rain attenuation and the carrier-to-noise and interference time series are able to detect, in advance, when one or more gateway feeder uplinks are going to be affected by the rain, so that the smart method can foresee the switching between the affected nominal gateway and an available redundant gateway. This mechanism is applied to all gateways of the ground network so that it is possible to find the number of nominal and redundant gateways needed for outperforming the minimum required availability of 99.9%. The second method, in essence, employs the same principle but using the Markov chain to find a stationary distribution, which allows us to know the time spent of each state according to its nominal gateway or redundant gateways in the process, in addition to the switching probability between them. The obtained results are discussed and compared with another well-known method to define the ground network scheme, finding a ground network more efficient, lower complexity, and with a lower number of gateways, that take part in the data managing of the satellite system. iii Contents Acknowledgements ii Abstract iii Mathematical Notation xi Nomenclature and Units xiii Abbreviations and Acronyms xix 1 Introduction 1 1.1 Traditional Broadband Satellite Systems . . . . . . . . . . . . . . . . 1 1.2 Multiple Spot Beam Satellite Systems . . . . . . . . . . . . . . . . . . 3 1.3 Evolution of High Throughput Satellite Systems . . . . . . . . . . . . 4 1.4 State-of-art in current HTS systems . . . . . . . . . . . . . . . . . . . 6 1.4.1 Feeder Link Design in Q/V band . . . . . . . . . . . . . . . . 6 1.4.2 Aggressive Frequency Reuse . . . . . . . . . . . . . . . . . . . 6 1.4.3 Ground Segment Architecture . . . . . . . . . . . . . . . . . . 7 1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.7 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 9 1.8 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 System Models for the Ground Segment 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Feeder Uplink Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Parameters of the Feeder Uplink . . . . . . . . . . . . . . . . . 13 2.3 Spatial Correlation Model . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 The Dynamic Rain Attenuation Model . . . . . . . . . . . . . . . . . 15 2.4.1 Procedure to Synthesize the Rain Attenuation Time-series . . 17 2.5 N + P Diversity Model on Ground Segment . . . . . . . . . . . . . . 18 3 Quantification of Multiple Spot Beams for HTS Systems in Ka and Q/V bands 21 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Connectivity in Latin America: A Review . . . . . . . . . . . . . . . 21 iv CONTENTS v 3.3 Available Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3.1 Ka-band Radio Regulations . . . . . . . . . . . . . . . . . . . 23 3.3.2 Q/V band Radio Regulations . . . . . . . . . . . . . . . . . . 24 3.4 Satellite Link Design in Ka and Q/V bands . . . . . . . . . . . . . . 26 3.5 Radio Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.6 Methods to Calculate the Performance of Satellite Antennas . . . . . 28 3.6.1 First Method: Antenna Size Evaluation . . . . . . . . . . . . . 29 3.6.2 Second Method: Calculations for Antenna Gain and EIRP . . 29 3.7 Analysis and Quantification of Multiple Spot Beams for HTS Systems in Ka and Q/V bands: Numerical Results and Discussion . . . . . . . 30 3.7.1 Orbital Position Analysis . . . . . . . . . . . . . . . . . . . . . 31 3.7.2 Quantification of Multiple Spot Beams . . . . . . . . . . . . . 32 3.8 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 37 4 Interference Evaluations in Frequency Reuse by Using Offset- Parabolic-Reflector Antennas 38 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Geometric Design of an Offset-Parabolic-Reflector Antenna . . . . . . 38 4.3 Multiple Spot Beams Antenna for HTS Systems . . . . . . . . . . . . 41 4.3.1 Multiple Spot Beams: Design and Analysis . . . . . . . . . . . 42 4.3.2 Spot Beam Pattern: Model Analysis . . . . . . . . . . . . . . 43 4.4 Carrier-to-Interference: Evaluation Model . . . . . . . . . . . . . . . 44 4.5 Offset-Parabolic-Reflector Antennas: Numerical Results . . . . . . . . 45 4.5.1 Offset-Parabolic-Reflector Antenna: Geometric Parameters . . 45 4.5.2 Sizing of Spot Beams over the Coverage Area . . . . . . . . . 48 4.5.3 CIR Evaluation Results . . . . . . . . . . . . . . . . . . . . . 49 4.5.4 Link Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.6 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 52 5 Method of Rain Attenuation Prediction Based On Long-Short Term Memory Network 55 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2 Implementation of the Proposed Deep Learning Method Based on LSTM Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2.1 Deep Learning Network: Model Architecture . . . . . . . . . . 56 5.2.2 Deep Learning Network: Model Description . . . . . . . . . . 63 5.3 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3.1 Experiment 1: Training and validation subsets partitioning, 70/30 73 5.3.2 Experiment 2: Training and validation subsets partitioning, 90/10 74 5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.6 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 90 CONTENTS vi 6 Ground Segment Optimization by Using Smart Strategies of Switching Between Gateway Stations 91 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2 Proposed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.2.1 Sizing of Nominal Gateways, NGWs . . . . . . . . . . . . . . . 92 6.2.2 Smart Method for Forecasting Rain Attenuation and CNIR at each GW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2.3 Method to Decide the Best NGWs . . . . . . . . . . . . . . . . 93 6.2.4 A Strategy to Allocate the Best PGWs . . . . . . . . . . . . . 94 6.3 The 1 + P̄ Scheme Analyzed by a Markov Chain . . . . . . . . . . . . 95 6.3.1 Method to Calculate the Probability of Rain, P0 . . . . . . . . 96 6.3.2 The Switching Strategy, 1+P̄ , from the perspective of a Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.6 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 115 7 Conclusions, Future Work, and Contributions 116 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.3 Contributions and Production . . . . . . . . . . . . . . . . . . . . . . 118 Appendix A List of Geographic Coordinates for Gateway (GW) Locations 120 A.1 List of Geographic Coordinates for Gateway (GW) Locations, Chapter 3120 A.2 List of Geographic Coordinates for Gateway (GW) Locations, Chapter 5120 A.3 Distance Matrix Between Pairs of Locations, Chapter 6 . . . . . . . . 120 Bibliography 125 List of Figures 1.1 Architecture of a broadband satellite system. . . . . . . . . . . . . . . . 2 1.2 Architecture of a multiple spot beams satellite system with 4-color frequency reuse scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Capacity Evolution of HTS systems. . . . . . . . . . . . . . . . . . . . . 5 2.1 The correlation coefficient, ⇢a, between two sites separated by a distance of D km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Block diagram of the rain attenuation time series synthesizer, ITU-R P.1853. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Gateway diversity scheme with a redundant GW. . . . . . . . . . . . 20 3.1 Percentage of households with Internet access per country [40]. . . . . . . 22 3.2 Percentage of households with Internet access per geographical zone [40]. . 23 3.3 Es/N0 for each feeder uplink using the Monte Carlo Method. . . . . . . . 32 3.4 Normal distribution of the orbital-position observations. . . . . . . . . . . 33 3.5 Comparison of the obtained number of beams using DVB-S2X and DVB-S2 standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.6 The number of carriers in the feeder downlink. . . . . . . . . . . . . . . . 34 3.7 Total capacity comparison between different data traffic ratios. . . . . . . 35 3.8 The number of beams and carriers using both 3F1P and 3F2P schemes. 36 3.9 The number of beams and carriers using both 4F1P and 4F2P schemes. 37 4.1 The geometry for the offset-parabolic-reflector antenna. . . . . . . . . . . 40 4.2 The hexagonal-grid layouts of both 3-cell and 4-cell for frequency reuse, illustrating the beam parameters. . . . . . . . . . . . . . . . . . . . . . 42 4.3 The interference geometry of the downlink. . . . . . . . . . . . . . . . . 46 4.4 Normalized pattern of the offset-parabolic-reflector antenna, 40 GHz. . . . 48 4.5 Spot beams of feeder downlinks over the Latin America region. . . . . . . 50 4.6 The 3-color frequency-reuse schemes over the Mexico region with 4 different beamwidths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 The 4-color frequency-reuse schemes over the Mexico region with 4 different beamwidths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.8 Forward link margin vs. co-channel CIR. . . . . . . . . . . . . . . . . . . 54 5.1 A single LSTM cell diagram [78]. . . . . . . . . . . . . . . . . . . . . . . 57 5.2 The architecture of an LSTM layer [77]. . . . . . . . . . . . . . . . . . . 59 vii LIST OF FIGURES viii 5.3 The architecture of an LSTM multi-layer [80]. . . . . . . . . . . . . . . . 60 5.4 The architecture of the proposed LSTM layer. . . . . . . . . . . . . . . . 61 5.5 The architecture of the proposed deep learning network. . . . . . . . . . . 62 5.6 Sigmoid activation function. . . . . . . . . . . . . . . . . . . . . . . . . 64 5.7 Hyperbolic tangent activation function. . . . . . . . . . . . . . . . . . . 65 5.8 Rectifier-Linear-Unit activation function. . . . . . . . . . . . . . . . . . . 66 5.9 Scaled-Exponential-Linear-Unit activation function. . . . . . . . . . . . . 66 5.10 Block diagram of the proposed method based on the deep learning network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.11 RMSE scores for training subsets. . . . . . . . . . . . . . . . . . . . . . 76 5.12 RMSE scores for validation subsets. . . . . . . . . . . . . . . . . . . . . 76 5.13 MAE scores for training subsets. . . . . . . . . . . . . . . . . . . . . . . 77 5.14 MAE scores for validation subsets. . . . . . . . . . . . . . . . . . . . . . 77 5.15 The training rain-attenuation subsets obtained from deep learning models. 78 5.15 The training rain-attenuation subsets obtained from deep learning models (cont.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.16 The validation rain-attenuation subsets obtained from deep learning models. 80 5.16 The validation rain-attenuation subsets obtained from deep learning models (cont.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.17 R2 for training subsets. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.18 R2 for validation subsets. . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.19 Model performance results: measured vs. predicted rain-attenuation values for validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.19 Model performance results: measured vs. predicted rain-attenuation values for validation (cont.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.20 The higher R-Squared, R2 = 0.9224 at Tuxtla, Gtz. . . . . . . . . . . . . 85 5.21 The lower R-Squared, R2 = 0.7265 at Cd. Juarez. . . . . . . . . . . . . . 85 5.22 Training and validation loss functions for each rain-attenuation time series. 86 5.22 Training and validation loss functions for each rain-attenuation time series (cont.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.23 Comparison between predictive models. . . . . . . . . . . . . . . . . . 89 6.1 Flowchart of the multiple 1 + P̄ switching strategy. . . . . . . . . . . . . 96 6.2 The 1 + P̄ strategy represented by a Markov Chain graph. . . . . . . . . . 99 6.3 Unavailability percentage per year, for all N̄ configuration schemes. . . . . 102 6.4 System availability vs. the feeder uplink capacity, on average, by ranging the CNIR threshold, ⇠th. . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.5 Performance of the N̄ + P̄ schemes, as a function of system unavailability and the number of P̄ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.6 Performance of the N̄ + P̄ schemes, as a function of system outage probability, Pout, and the number of P̄ . . . . . . . . . . . . . . . . . . . 113 6.7 N̄+P̄ configuration schemes obtained from the three aforementioned methods.114 List of Tables 2.1 Basic Propagation Parameters . . . . . . . . . . . . . . . . . . . . . . 13 3.1 Frequency Allocations for Satellite Downlink in Ka-band, ITU Region R2 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Frequency Allocations for Satellite Uplink in Ka-band, ITU Region R2 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Frequency Allocations for Satellite Downlink in Q band, ITU Region R2 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Frequency Allocations for Satellite Uplink in V band, ITU Region R2 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.5 Frequency Reuse and Polarization Schemes [18]. . . . . . . . . . . . . 27 3.6 Maximum Spectral Efficiencies . . . . . . . . . . . . . . . . . . . . . . 28 3.7 Feeder Uplink Parameters . . . . . . . . . . . . . . . . . . . . . . . . 32 3.8 Throughput Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1 Geometric Parameters of the Offset-Parabolic-Reflector Antenna . . . 47 4.2 Spherical Spread Losses and Edges illuminations with a Symmetric Gaussian Radiation Pattern . . . . . . . . . . . . . . . . . . . . . . . 47 4.3 Spherical Spread Losses and Edges illuminations, f = 34.71 . . . . 47 4.4 Cross-polar isolation XPiso for both feeder and user downlinks. . . . . 48 4.5 The Number of Spot Beams (Nbmin /Nb) for the Latin American Regions. 49 4.6 The CIR Evaluation for Feeder Downlink, 40 GHz. . . . . . . . . . . 49 4.7 The CIR Evaluation for the 3-color Frequency-reuse Scheme. . . . . . 51 4.8 The CIR Evaluation for the 4-color Frequency-reuse Scheme. . . . . . 53 4.9 The CNIR Values for the Forward Link. . . . . . . . . . . . . . . . . 53 5.1 Hyperparameters for Experiment 1 . . . . . . . . . . . . . . . . . . . 74 5.2 Hyperparameters for Experiment 2 . . . . . . . . . . . . . . . . . . . 75 6.1 Month Numbers and Number of Days . . . . . . . . . . . . . . . . . . 97 6.2 The Inbound and Total Capacity of the Ground Network Segment. . 101 6.3 Gateway Availabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.4 The Number of Outages of Each NGW for the 4 + P̄ Scheme. . . . . 104 6.5 The System Availability for the 4 + P̄ Scheme. . . . . . . . . . . . . . 104 6.6 The Number of Outages of Each NGW for the 8 + P̄ Scheme. . . . . 104 6.7 The System Availability for the 8 + P̄ Scheme. . . . . . . . . . . . . . 104 ix LIST OF TABLES x 6.8 The Number of Outages of Each NGW for the 12 + P̄ Scheme. . . . . 105 6.9 The System Availability for the 12 + P̄ Scheme. . . . . . . . . . . . . 105 6.10 The Number of Outages of Each NGW for the 16 + P̄ Scheme. . . . . 106 6.11 The System Availability for the 16 + P̄ Scheme. . . . . . . . . . . . . 107 6.12 The Operation Probability of Gateways. . . . . . . . . . . . . . . . . 108 6.13 The Stationary Distribution of Each NGW for the 4 + P̄ Scheme. . . 109 6.14 The System Operation Probabilities for the 4 + P̄ Scheme. . . . . . . 109 6.15 The Stationary Distribution of Each NGW for the 8 + P̄ Scheme. . . 110 6.16 The System Operation Probabilities for the 8 + P̄ Scheme. . . . . . . 110 6.17 The Stationary Distribution of Each NGW for the 12 + P̄ Scheme. . . 111 6.18 The System Operation Probabilities for the 12 + P̄ Scheme. . . . . . 111 6.19 The Stationary Distribution of Each NGW for the 16 + P̄ Scheme. . . 112 6.20 The System Operation Probabilities for the 16 + P̄ Scheme. . . . . . 112 A.1 List of Geographic Coordinates for GW Locations, Chapter 3 . . . . . 121 A.2 List of Geographic Coordinates for GW Locations, Chapter 5 . . . . . 122 Mathematical Notation Note: the vectors are denoted by bold lowercase letters whereas the matrices are expressed by bold uppercase letters. [N ] the set {1, 2, . . . , N} x a dataset ^ logical conjunction, if statement bxc the floor of a scalar x _ logical disjunction R the set of real numbers U an interval [0, 1] E{·} the mathematical expectation of a random variable X a Matrix x a vector x y the Hadamard product (element-wise product of either vectors or matrices) x(i) the i-th example (input) of a dataset XT the transpose of matrix X X:,i the column i of matrix X, (a column vector) Xi,: the row i of matrix X, (a row vector) Var{·} the variance of a set of data, 2 | x | absolute value of a scalar x rXy the matrix derivatives of y with respect to X rxy the gradient of y with respect to x ±U an interval [1, 1] xi MATHEMATICAL NOTATION xii Pr{·} the probability of a random event ! prepositional logic, if ... then ... {·} the standard deviation of a set of data {0, 1} the set containing 0 and 1 f(·) the general form of the mathematical function Jn(·) the Bessel function of the n kind m{·} the mean of a set of data Q complementary cumulative normal distribution Q1 inverse complementary cumulative normal distribution s(t) continuous signal, where t is the independent variable s[k] discrete signal, where k is the independent variable x a scalar (real or integer) xi the element i of a vector x, with indexing starting at 1 Xi,j the element i, j of matrix X Nomenclature and Units Ac the coverage area, [km2] Ah the area of the hexagon cell, [km2] Ai the rain attenuation in the i-th site Aoffset the parameter that adjusts the time-series to match the probability rain, [dB] BWT total-bandwidth available, [Hz] Cpi the capacity of the satellite link, b/s CpT total-capacity available, [b/s] D distance, [km] DL the download traffic, [b/s] Dant the diameter of satellite antenna, [m] E the signal’s average power EIRPsat the effective isotropic radiated power from satellite antenna, [dBW] Es/N0 the energy per symbol to noise power spectral density, [dB] F the focal length of the parabolic-reflector-antenna, [m] FreqsE the frequency on the space-Earth (s-E) path, [Hz] G/T antenna gain-to-noise-temperature, [dB/K] Gr(✓) the relative gain of the antenna, [dB] GTX the transmitter-antenna gain, [dBi] H the offset of the parabolic-reflector-antenna center, [m] HPAsat the high power amplifier of the satellite in Ka-band, [W] K the total number of samples, the K-dimensional Euclidean space xiii Nomenclature and Units xiv LNA low noise amplifier, [W] MTii the monthly mean total rainfall data, [mm] N number of GWs on the Ground Segment Nb the number of the beams Np the potential for polarization reuse Nii the number of days of each month Nsb the number of the frequency sub-bands PL the path loss from either s-E or E-s, [dB] Pa conditional joint probability that the attenuations exceed a1 and a2, respectively Pi the probability of occurrence in the i-th site P rain i the annual probability of rain (%) in the i-th site, a.k.a P0i Pr joint probability that it is raining at both sites P0ii the monthly probability of rain, [%] Pout the total probability of a system outage Psw the switching probability R the range between HTS and GW, [km] Ri solution of P rain i for the i-th site Rp the rainfall rate exceeded for the desired probability of exceedance, [mm/h] R0.01 the annual rainfall rate data exceeded for 0.01% of an average year, [mm/hr] Rsw the switching rate Savail the total available spectrum, [Hz] Seff the spectral efficiency, [b/s/Hz] Ts the time interval between samples Tii the monthly mean surfaces temperatures, [K] Tsw the interval between switching instants UL the upload traffic, [b/s] Γk,i the k-th value of CNR matrix, Γ, according to the i-th feeder link of GW Nomenclature and Units xv ↵ the learning rate ↵i phase component of the communication channel for the i-th GW feeder link N̄ number of nominal gateways on the Ground Segment P̄ number of redundant gateways on the Ground Segment the parameter that describes the time dynamics, [s1] 1 the linear decay factor 2 the quadratic decay factor ` the number of iteration ✏ the small constant in order to avoid division by zero csi clear sky CNR for the i-th GW feeder link  Boltzmann’s constant, 1.380 649⇥ 1023 [J/m] the wavelength of the frequency band used in a specific satellite link, [m] Ct the collection of all cell state at time step t D the distance matrix between pair of locations Ht the collection of all hidden state at time step t P the state transition matrix Wd the weights matrix of the dense layer Wh the recurrent weights matrix, Whf ,Whi,Who Wx the input weights matrix, Wxf ,Wxi,Wxo ΘD the concatenation matrix of the dense layer (weights and biases) ΘL the concatenation matrix of the LSTM layer (weights and biases) bd the bias vector of the dense layer b the bias vector of the LSTM layer, bf ,bi,bo ct the stacked cell states at time step t ht the stacked hidden states at time step t D the mathematical function of a dense layer F the deep learning model Nomenclature and Units xvi Ii() the function that describes the nature of the interference at the i-th beam, [dB] LU the mathematical function of a LSTM layer L the mathematical function of a single LSTM cell Ni the noise variance at satellite interface for the i-th GW feeder link S the mathematical function of a LSTM multi-layer ⌫ the system availability, where ⌫i is the feeder uplink availability of each NGW ! the angle that ranges from 0 (beam center) to ✓BW/2 (beam edge), [deg] the angle between the point T and the center of the i-th beam, [deg] B the bisector angle of parabolic-reflector-antenna, [deg] C the f aims to the aperture center at the point C, [deg] L the lower angle of parabolic-reflector-antenna, [deg] P the angle from the lower edge of dish to feed pointing direction, [deg] U the upper angle of parabolic-reflector-antenna, [deg] f the angle of feed-antenna-pattern, [deg] s the half of the angle subtended of parabolic-reflector-antenna, [deg] ⇢a the correlation factor for the conditional joint probability ⇢r the correlation factor for the joint probability g the gate function activation based on the sigmoid function ✓0 the beam diameter at the triple beam crossover, [km] ✓c the closest spacing between beam centers reusing the same frequency, [km] ✓r the closest spacing between the reuse-beam edges, [km] ✓s the spacing between adjacent-beam centers, [km] ✓3dB the angle subtended by the half-power points of the main lobe, [deg] ✓BW Beamwidth in degrees, [deg] ⇠th the CNIR threshold ⇣ the value of the carrier-to-interference, [dB] ai the attenuation threshold in the i-th site, [dB] Nomenclature and Units xvii ct the cell state at time step t cu the cell candidate of the LSTM block d0 GEO distance of 35786 [km] above Earth’s surface fg the forget gate of the LSTM block h the offset distance of the parabolic-reflector-antenna, [m] hi[k] the kth value of the communication channel for the i-th GW feeder link ht the hidden state at time step t ig the input gate of the LSTM block ii the month numbers k index of each sample m the number of dataset’s examples n the integer number n(t) the white gaussian noise process og the output gate of the LSTM block p the probability of the rain pd the desired average annual probability of exceedance rc the coverage radius of spot beam, [km] ro roll-off parameter, [%] tii the monthly mean surfaces temperatures, [C] v` the moving average Ξk,i the k-th value of CNIR matrix, Ξ, according to the i-th feeder link of GW t time in seconds, 1 [s] b/s rate in bit per second, 1 [b/s] dB decibels, 1 [dB] Gb/s giga bit per second, 1⇥ 109 [b/s] GHz giga Hertz, 1⇥ 109 [Hz] Nomenclature and Units xviii Hz frequency in hertz, 1 [Hz] km kilometers, 1⇥ 103 [m] km2 square kilometers, 1⇥ 106 [m2] m distance in meters, 1 [m] Mb/s mega bit per second, 1⇥ 106 [b/s] MHz mega Hertz, 1⇥ 106 [Hz] mm millimeters, 1⇥ 103 [m] mW milli watts, 1⇥ 103 [W] Tb/s tera bit per second, 1⇥ 1012 [b/s] W power in watts, 1 [W] Abbreviations and Acronyms 5G Fifth generation wireless technology for digital cellular networks a.m.s.l. Height above mean sea level ACI Adjacent Carrier Isolation factor ACM Adaptive Coding and Modulation ADAM Adaptive Moment Estimation Optimizer ARIMA Autoregressive Integrated Moving Average BRASILSAT Brazilian communications satellite BSS Broadcast Satellite Service CIR Carrier-to-interference ratio CNIR Carrier-to-noise and interference ratio CNR Carrier-to-noise ratio DVB Digital Video Broadcasting DVB-RCS2 DVB - Return Channel Satellite, Second Generation DVB-S2X DVB - Second Generation, Extensions E-s Earth-to-space satellite communication link EHF Extremely high frequency EI the edge illuminations which can be both upper and lower, [dB] EIRP Effective Isotropic Radiated Power EoC the beam End-of-Coverage EUTELSAT European Telecommunications Satellite Organization xix Abbreviations and Acronyms xx FMT Fade Mitigation Technique FRF Frequency Reuse Factor FS Fixed Service FSL Free Space Loss FSS Fixed Satellite Service FT the feed edge tapers which can be both upper and lower, [dB] GEO Geostationary Orbit GPU Graphics Processor Units GS Ground Segment GW Gateway Station HD High Definition Video HDFSS High-Density application in the Fixed Satellite Services HPA the High Power Amplifier HTS High Throughput Satellite i.i.d Independent and identically distributed random variables IDU Indoor Unit IoT Internet of Things ITU International Telecommunication Union LDPC Low-Density Parity-Check LHCP Left Hand Circularly Polarized LSTM Long Short-Term Memory M-APSK M-ary Amplitud and Phase-Shift Keying modulation M-PSK M-ary Phase-Shift Keying modulation M-QAM M-ary Quadrature Amplitude Modulation M2M Machine-to-machine communication MAE Mean Absolute Error Abbreviations and Acronyms xxi MBA Multiple Beam Antenna MF-TDMA Multiple-Frequency Time Division Multiple Access MODCOD Modulation and Coding Scheme modem Modulator and Demodulator device MS Mobile Service MSS Mobile Satellite Service NCC Network Control Center NGSO Non-geostationary-satellite orbit systems NGW Nominal Gateway ODU Outdoor Unit PGW Redundant or Backup Gateway QoS Quality of Service R-Squared Coefficient of determination, R2 R2 ITU Region 2 ReLU Rectifier-Linear-Unit Activation Function RF Radio Frequency RHCP Right Hand Circularly Polarized RMSE Root Mean Squared Error RMSProp Root Mean Square Propagation s-E space-to-Earth satellite communication link SaaS Software as a Service SatCom Satellite Communication SELU Scaled-Exponential-Linear-Unit Activation Function SFTSS Standard Frequency and Time Signal-Satellite SGD Smart Gateway Diversity SNN Self-Normalizing Neural Networks Abbreviations and Acronyms xxii SSL Spherical Spreading Loss, [dB] TDMA Time Division Multiple Access TPU Tensor Processor Units UHTS Ultra High Throughput Satellite Systems ULPC Uplink Power Control UT User Terminal VSAT Very Small Aperture Terminal XPiso Cross-Polar Isolation factor Chapter 1 Introduction The thesis is focused on the performance analysis of the ground segment (GS) architecture for a new generation of satellite communications (SatCom) systems. Nowadays, the current requirements of throughput and broadband to users are huge so that the traditional communication infrastructures need to expand their resources and capabilities to cover the service demand. This main idea is also applied to SatCom systems in order to increase their capacity and to become an efficient solution to carry data traffic. Thus, new technological challenges emerge, providing an important research frame for the network architecture on GS. This chapter presents the state-of-the-art related to the problems arisen with the new satellite technology, specifically in areas involved in the feeder link design, multiple beam satellite systems, the frequency reuse, interference evaluations, availability, and reliability. Further, the chapter also brings out the main objectives of the thesis to study the aforementioned areas. 1.1 Traditional Broadband Satellite Systems A traditional broadband satellite system provides communication services in remote areas wherein the terrestrial infrastructures do not reach them, especially in rural areas. The services offered by a broadband satellite system range from Internet access to multimedia services [1, 2]. Figure 1.1 depicts the architecture of a traditional broadband satellite system. Each network component accomplishes a specific role in the broadband satellite architecture. However, the satellite GS network has not undergone a major change in its architecture, but there are some parameters to take into account which are explained in the following subsections in detail [3]. • Satellite: The broadband satellite is placed in a geostationary orbit (GEO) in order to cover a wider area. Also, the GEO satellite is able to connect a gateway station (GW) to the user terminals (UTs) using radio frequency (RF) links (feeder and user links). This link connection is also known as bent-pipe satellite architecture, however, it is important to note that the amplification and frequency translations are only executed by satellite onboard processing. 1 CHAPTER 1. INTRODUCTION 2 Forward Link Return Link Satellite GEO Gateway Station, GW User Terminals, UT Feeder Link User Link Figure 1.1: Architecture of a broadband satellite system. • Gateway Station: The gateway (GW) station is capable of transmitting and receiving data. That is, the GW is responsible for controlling, managing and operating data traffic to and from user terminals (UT), via satellite links. In satellite networks, GWs are also known as gateway earth stations. Further, the GS network architecture can be made up of multiple GWs when the gateway diversity is considered necessary. • User Terminal: The user terminal (UT), also referred to as user earth station, is a two-way broadband terminal, i.e., the UT can both transmit and receive data to and from the satellite employing a very small aperture terminal (VSAT). Moreover, the UT is a device that consists of two main units, the indoor unit (IDU) and the outdoor unit (ODU) [1]. The ODU is made up of the antenna, the RF transmitter, and one or more RF receivers. Meanwhile, the IDU contains the modulator and demodulator (modem), and the interface to the local network. • Feeder Link: It is a RF link between the GW and satellite. The feeder link consists of both uplink and downlink. Currently, feeder links work in Ka-band1 for broadband satellite systems. • User Link: The RF link between the satellite and UTs is also known as the user link, which is made up of both uplink and downlink. It is important to mention that time division multiple access (TDMA) [1] and multi-frequency time division multiple access (MF-TDMA) [1, 5] are employed to access from satellite to UTs and vise versa. Not only do the feeder link uses Ka-band but also the user link. 1The Ka-band is a frequency band of millimeter waves ranges from 17.70–21.20 GHz for downlink, whereas from 24.75–30.00 GHz for uplink. Both frequency ranges are available for ITU Region 2 (R2), [4]. CHAPTER 1. INTRODUCTION 3 • Forward Link: The link from GW towards UTs is described as the forward link. The forward link is also called the end-to-end link, which includes uplink of the feeder link, satellite, and downlink of the user link. Therefore, a GW transmits data to the UTs via the forward link. In this work, the digital video broadcasting (DVB), with its standard (DVB-S2X), is employed by the forward link to communicate from GW to UT [6]. • Return Link: On the other hand, the link from UT towards the GW is named as return link, which is made up of the uplink of the user link, satellite, and downlink of the feeder link. The UT transmits RF signals to the GW by using the DVB-RCS2 standard, which has the specification for the return link where the data traffic flow from UT to GW [7]. 1.2 Multiple Spot Beam Satellite Systems Satellite systems have been an efficient solution to cover remote and rural areas due to their ubiquitous links. Nevertheless, it is very tough to compete with terrestrial communications because the transmitted bit has a high cost so that it is necessary to reduce the cost by increasing the total capacity of the satellite systems [8]. Most of the satellite systems solely cover a large area by using a single beam, especially in L2 , C3 and Ku4 bands. Although the area is entirely covered by a single beam, the system capacity is limited as well as its efficiency. Currently, modern SatCom systems have multiple spot beams which increase the system capacity by using frequency reuse among beams. This architecture is also known as multiple beam architecture which is inspired by traditional cellular networks. Therefore, the inter-beam interference must be maintained within the typical values and admissible limits in order to achieve high spectral efficiency on the satellite link. It is important to note that the latest satellite systems are at the technological cutting edge to cover a region by generating multiple spot beams. This means that satellites have multiple beam antennas (MBA). Reflector MBAs are usually used for SatComs due to their excellent RF performance in terms of coverage gain and the carrier-to-interference ratio (CIR), payload simplicity, reduced cost, and mature technology. These MBAs are classified into three types: (a) single reflector with a single feed per beam, (b) single reflector with over-lapping feed clusters, and (c) 2The L band is a frequency band in the radio spectrum from 1–2 GHz. The mobile satellite services use L band carriers where the downlink ranges from 1518.0–1559.0 MHz, 2180.0–2200.0 MHz, and 2483.5–2500.0 MHz, whereas the uplink ranges from 1610.0–1660.5 MHz, 1668.0–1675.0 MHz, and 2000.0–2025.0 MHz, [4]. 3The C band in communication satellites uses the frequency band from 3.40–4.20 GHz and 4.50–4.80 GHz for the downlink, whereas the uplink ranges from 5.091–5.250 GHz and 5.850–7.075 GHz. Both frequency ranges are available for ITU region 2 (R2), [4]. 4The Ku band in communication satellites uses the frequency band from 10.70–12.70 GHz for the downlink, whereas the uplink ranges from 12.70–13.25 GHz, 13.75–14.80 GHz, and 15.43–15.63 GHz. Both frequency ranges are available for ITU region 2 (R2), [4]. CHAPTER 1. INTRODUCTION 4 multiple reflectors with a single element per beam, [9]. In particular, the reflectors are generally offset-fed parabolic reflectors where the feed elements are horns. Thus, Type (a) MBA has a straightforward architecture, where the reflector is illuminated by a dedicated feed in order to generate a beam pattern due to radiating the radio waves reflected from the antenna. This technique offers both good isolation and high radiation efficiency between the different beams. Type (b) MBA design needs low-level beamforming networks to provide element sharing among beams and beam combining functions. In fact, Type (b) antenna is usually used for mobile satellite services at low frequencies such as L-band and S-band5. Finally, Type (c) MBA is made up of multiple reflectors where each reflector is illuminated with its own feed array. These apertures are either 3 or 4 units, which are independent of each other. Here, each feed horn generates a single beam, therefore, the feed is able to provide optimal illumination on the reflector. Type (c) MBAs are often used at frequency bands such as the Ku band, Ka-band, and Extremely High Frequency (EHF) band. At the satellite, each beam is generated by a specific feed horn, where the beams with the same frequency sub-bands are radiated from the same reflector. That is, each frequency sub-band corresponds to a segment (also known as a color), consequently, the frequency-reuse scheme in the MBA is usually known as either three-color or four-color schemes. Figure 1.2 details the architecture of a satellite system with a 4-color frequency-reuse scheme. Particularly, a 4-color scheme is defined by partitioning the available frequency and polarization resources into four segments (colors), i.e, each color belongs to half the available bandwidth and one polarization. It is important to mention that frequency-reuse schemes employ the circular polarization, i.e., right hand circularly polarized (RHCP) and left hand circularly polarized (LHCP), therefore, it is available 2 polarization resources. Currently, these modern SatComs are also known as high throughput satellite (HTS) systems. 1.3 Evolution of High Throughput Satellite Systems The evolution of HTS systems has outperformed many stages since the appearance of the first broadband satellite system in 2005 [10], improving impressively its capacity in order to increase both the coverage area and the quality of service (QoS) requirements of the end-user. Figure 1.3 compares the capacity of some HTS systems in different years. For instance, Spaceway 3 with 24 spot beams has a capacity of 10 Gb/s. Echostar XVII has 60 spot beams and a capacity of 120 Gb/s, whereas Echostar XIX has 120 spot beams and a capacity of 200 Gb/s. Spaceway 3, Echostar XVII, and XIX are part of the Hughes® HTS constellation which has the latest JupiterTM System technology for broadband satellite access [11,12]. KA-SAT is part of the EUTELSAT fleet which has a capacity of 90 Gb/s and 82 spot beams [13]. By 2021 the Echostar 5The S-band is part of the microwave band in the electromagnetic spectrum, whose frequency band ranges from 2.0–4.0 GHz [4]. CHAPTER 1. INTRODUCTION 5 Figure 1.2: Architecture of a multiple spot beams satellite system with 4-color frequency reuse scheme. XXIV will have been launching with a capacity up to 500 Gb/s and multiple spot beams in Ka-band. G ig ab it p er s ec o n d [ G b /s ] 0 100 200 300 400 500 600 HTS Generations HTS, Spaceway 3, year: 2007 HTS, KA-SAT, year: 2010 HTS, Echostar XVII, year: 2012 HTS, Echostar XIX, year: 2016 HTS, Echostar XXIV, year: 2021 500 200 120 90 10 HTS, Spaceway 3, year: 2007 HTS, KA-SAT, year: 2010 HTS, Echostar XVII, year: 2012 HTS, Echostar XIX, year: 2016 HTS, Echostar XXIV, year: 2021 Figure 1.3: Capacity Evolution of HTS systems. From 2021 onwards, it is estimated that next-generation HTS systems will require capacity equal to or greater than 1 Tb/s, which will reduce the cost per transmitted bit. However, the bandwidth is limited due to the lack of available spectrum in the Ka-band. In the following section, three alternatives are detailed in order to overcome the spectrum constraint and technical limitations, which are given an excellent background for this research. CHAPTER 1. INTRODUCTION 6 1.4 State-of-art in current HTS systems 1.4.1 Feeder Link Design in Q/V band As stated above in Section 1.3, the capacity of HTS systems is continually increasing due to the demand for data traffic. Therefore, it is necessary to design a reliable feeder link in terms of higher bandwidth and frequency bands. A first alternative is to move the feeder link from the Ka-band to the Q/V band6 whose bandwidths are available for satellite communications [4, 8, 14]. It is important to mention that the feeder link needs more available spectrum, for this reason, up to 5 GHz are available for both feeder uplink and feeder downlink, respectively. As a result, the whole Ka-band spectrum is feasible for the user link, i.e., 3.50 GHz are available for both user uplink and user downlink, respectively. Indeed, it is a very important solution for satellite operators, however, the feeder link turns into a very susceptible link due to the heavy rain attenuation [8, 15]. Although the fade mitigation technique (FMT) is used as an uplink power control (ULPC), it can only compensate a few decibels (dB) during short-term fades. For this reason, it is necessary to design a Q/V band feeder link with availability in excess of 99.9% [16]. Thus, multiple GWs are used by using transmit diversity in order to achieve the required availability [13,14]. This design of feeder links must be reliable so that each feeder link can operate in its corresponding GW, therefore, it is a key-feature in the development of this research. 1.4.2 Aggressive Frequency Reuse As already mentioned, current HTS systems use a 4-color multiple spot beam structure in order to increase the total capacity in the satellite system. Nevertheless, each beam utilizes only 1/4 of the total resources in terms of frequency and polarization, therefore, it is not an efficient scheme. Nowadays, a lot of research aims to improve the conventional 4-color frequency-reuse scheme in order to achieve full frequency reuse with advanced systems [14, 17–19]. Although the main idea is that each beam can utilize the whole available resources, this leads to an increase in the inter-beam interference among the adjacent beams. In fact, it has been explored 3-color and 4-color frequency reuse scheme with both simple and double polarization [18], as well as the incidence in the interference among user and feeder links. To sum up, it is important to know the affectation of these interferences in the Q/V band feeder link in order to guarantee communication from/to the HTS system. 6Q/V band ranges from 37.50–42.50 GHz for the downlink (Q band), whereas the uplink (V band) ranges from 42.50–51.40, GHz. These frequency bands are within the EHF band for ITU region 2 (R2), [4]. CHAPTER 1. INTRODUCTION 7 1.4.3 Ground Segment Architecture In Section 1.4.1, it was mentioned that the transmit diversity was necessary to achieve an availability greater than 99.9% on the feeder link. That is, the ground segment architecture is made up of a number of GWs, which are interconnected by terrestrial links in order to generate an ease routing of feeder link data. Therefore, this architecture is used in diversity way in order to mitigate fades on the feeder link of each GW. The main advantage of this mechanism is when a GW experiences either feeder link outage or reduced capacity, then an available GW receives all data traffic by using terrestrial links [14]. Consequently, some diversity scheme models have been studied by several researchers, one of them has been the 1 + 1 diversity scheme [20, 21], where a nominal GW was backed up by another redundant GW. Although this architecture is acceptable for low/medium throughput systems, it is not efficient for HTS systems, where high capacities and tens of GWs are necessary. Further, another transmit diversity scheme is also known as the N + P scheme, which has been studied in [8, 14, 22–26]. This scheme is made up of N active or nominal gateways (NGW), and P idle or redundant gateways (PGW). Whether one of the NGWs is in outage, whole the traffic from the affected NGW is rerouted to one of the PGWs by a switching mechanism. Furthermore, the smart gateway diversity (SGD) is another scheme that has been studied in [22, 26]. The main difference between the SGD and the N + P scheme diversity is that the SGD does not need redundant PGWs, but its disadvantage is when one or more NGWs are in outage, that is, the throughput of users served is reduced by either the GW or GWs affected. However, this disadvantage can be overcome by adding more capacity for each GW in order to support other GWs in case of an outage. Therefore, GWs need to be oversized in terms of capacity. Moreover, the user terminals require a level of intelligence, increasing the complexity of the network. In this thesis, the research is only focused on the N + P scheme, therefore, the contributions are associated with this scenario. 1.5 Objectives The objectives of this thesis are to design, allocate, develop and optimize the GS by cutting edge techniques for HTS systems. That is, the main focus on this thesis is related to an adequate design of the Q/V band feeder uplink, allocating properly the GW sites on the GS, and developing techniques to optimize the network architecture on the GS. In this section, a brief description of specific objectives are given as follows, • Q/V band Feeder Uplink Design: As already mentioned, the Q/V band is very susceptible to both rain attenuation and propagation effects. Therefore, the Q/V band feeder uplink must be designed to achieve high reliability in order to provide new broadband services on the user link of an HTS system. Each Q/V band feeder uplink provides a high bandwidth communication to/from the HTS. Therefore, this thesis is focused on the design of a reliable feeder uplink for CHAPTER 1. INTRODUCTION 8 each GW in order to operate over the typical availability of an N +P diversity scheme on the GS. • Allocating GW Sites on Ground Segment: An important part of this research is to analyze if the site for each GW is adequate to be considered in an N + P diversity scheme. The performance of this scheme is assessed by a correlated rain fading channel and its impact on the distance between two or more GWs. For this reason, the GW sites are modeled by implementing a dynamic rain attenuation model. It is important to mention that the rain attenuation model is brought by the recommendations of the International Telecommunication Union (ITU). As a result, the total outage probability is determined by a theoretical analysis for each N + P simulated scenario. Also, the effects of other parameters related to the dynamic rain attenuation model are observed and studied by several N + P simulations. • Optimization Techniques for Ground Segment Architecture: Very few works that studied the N + P scheme were developed by deep mathematical analysis. However, it is very important to develop a rigorous mathematical analysis in order to detect and to find the switching-rate performance between N and P GWs. The switching parameter is a key-feature in the system model, which relates directly to the outage probability in the HTS system. Therefore, the lack of a rigorous analysis taking into account dynamic rain attenuation characteristics, spatial correlation between GWs, and switching rate requirements, it motives strong research on the GS for multiple GWs using the Q/V band. In this context, machine learning techniques are implemented in this study in order to optimize the total number of GWs, which are assured efficient switching with an optimal N + P scheme. 1.6 Methodology In this thesis, the quantitative method is employed by mathematical analysis, statistical data, and computational techniques. The scientific rigor is based on the reliability and validity of data. For this purpose, several models are developed by statistical analysis to later be handled and submitted to an experimental method by advanced computational techniques based on machine learning algorithms. In this context, due to the lack of a historical rainfall database in the gateway locations to be used in this thesis, the ITU Recommendations provides rain attenuation time-series by statistical analysis. Thus, these rain attenuation time-series are employed to develop, generate, train, and validate rain-attenuation models by machine learning algorithms in order to predict rain attenuation events in advance. Currently, computational tools offer up high performance and speed to run and solve complex algorithms. All found data will be collected and their statistical/computational treatment results as well as all relevant results in relation to the research problem of this thesis. These outcomes are also employed to propose, design, and evaluate an efficient CHAPTER 1. INTRODUCTION 9 switching mechanism for sizing and optimizing the ground network segment by smart techniques based on the predictive rain-attenuation models and the Markov process. Finally, all obtained data from this research are depicted and tabulated by figures and tables which explain and show the nature and behavior of the outcomes from each process in more detail. However, all results are discussed in their respective sections by comparative and analytic methods with other models and researches. 1.7 Contributions of the Research The contributions of this thesis include modeling the rain attenuation over satellite feeder links, predictive modeling based on machine learning algorithms, and developing optimization techniques for the Ground network segment. A brief description of each of them is detailed as follows: • The satellite feeder link is modeled in this thesis by mathematical analysis. Further, other models are added to the feeder link model to generate an artificial rain-attenuation dataset for specific geographic locations. This model is essential to find and understand the availability of each gateways station in addition to the ground network availability. • The available electromagnetic spectrum, maximum capacity, and schemes of the frequency reuse of the high throughput satellite system were approached by theoretical and numerical analysis. For this reason, code scripts using Matlab and Python were developed in this thesis in order to find and evaluate the results in these processes. • The rain-attenuation dataset is employed to train and validate predictive models by the implementation of Machine Learning algorithms in order to determine in advance when the feeder link is impaired by the heavy rain. For this purpose, code scripts using Python/Tensorflow were developed in this thesis to find and explain the model outcomes. • Finally, an efficient switching scheme mechanism for the N+P gateway scenario is presented in this thesis. By using predictive rain-attenuation models obtained from Machine Learning algorithms and the Markov Chain process, it is possible to define the number of redundant gateways is necessary to maintain the network availability above 99.9%. These processes optimize the Ground network segment as a function of the number of redundant gateways. 1.8 Thesis Structure This thesis is organized as follows: Chapter 2 explains the main background concepts and system models to implement in this thesis. In Chapter 3, the quantification of multiple spot beams and the total capacity of the HTS system is detailed. Chapter 4 evaluates the interferences in frequency reuse by using offset-parabolic-reflector CHAPTER 1. INTRODUCTION 10 antennas. The deep learning models, developments, implementations, results, and discussions are provided in more detail by Chapter 5. In Chapter 6, the optimization of the Ground Segment is presented and discussed by smart and predictive switching mechanisms. Finally, Chapter 7 concludes this research and its proposals, in addition to remarking about future research studies. Contributions and scientific productions of this thesis are also detailed. Chapter 2 System Models for the Ground Segment 2.1 Introduction In this chapter, system models that are used throughout this thesis are introduced and explained. Systems models were briefly mentioned in Chapter 1, showing a problem statement in each case. Therefore, each system model is described in mathematical detail providing an excellent background to the different objectives of this thesis. The feeder uplink model is presented in Section 2.1, where the mathematical analysis and the main impairments in the feeder uplink are minutely discussed. Moreover, the system parameters are provided to find and discuss the problems that are associated with the Q/V band uplink budget. In Section 2.2, the spatial correlation model is described. This model is based on the ITU-R recommendations, which is used to determine a minimum separation between GWs in order to avoid the rain attenuation in two sites or more at the same time. The dynamic rain attenuation model is presented in Section 2.3, which also is based on an ITU-R recommendation. This model is used to obtain the rain attenuation in each site of the GS. Finally, the N + P diversity model is explained in Section 2.4 which is implemented on the GS by simulated scenarios to understand the behavior of the network. 2.2 Feeder Uplink Model Each gateway station (GW) is distributed and separated from other GWs by a distance of D km on the ground segment (GS). Hence, each satellite feeder uplink belongs to its respective i-th GW, transmitting the signal si(t), where si(t) is a function that varies with time. It is important to mention that i indicates the i-th GW site. In this thesis, the modeled satellite-link is the feeder uplink which is between the i-th GW and the high throughput satellite (HTS). It is worth noting that the feeder uplink operates at the EHF band because there is more available spectrum. The frequency band is ranged from 42.50–51.40 GHz which is also known as the V band. This model is based on the Gharanjik’s feeder link model [21], but with slight 11 CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 12 differences according to the aim of this study. To begin with, the average power of the feeder-uplink signal is defined as Ei = E{|si(t)| 2}, for i = 1, 2, . . . , N, (2.1) where N is the number of GWs on the ground network. Thus, the set of GWs, {1, 2, . . . , N}, can also be represented by the set notation [N ]. The continuous signal si(t) is sampled by measuring the value of the continuous function every Ts seconds or minutes, i.e., it depends on the sampling period to be used. As a result, the sampled signal is given by si[k], where k is the index of each sample, being an integer value, i.e., k = 1, 2, . . . , K, whereas K is the total number of samples, and Ts is the time interval between samples or sampling period. In this case, the numeric value of the k-th number in the sequence is equal to the value of the continuous signal, si(t), at time t = kTs, i.e., si[k] = si(kTs). By using this analysis, the communication channel between an i-th GW and the satellite at t = kTs can be represented by hi[k] = |hi[k]|e j↵i , for i = 1, 2, . . . , N, (2.2) where ↵i is the phase component. Moreover, the channel amplitude |hi[k]| is estimated by a signal beacon from the satellite. The channel expression is obtained from [25], which is explained in more detail. Further, the clear sky carrier-to-noise ratio (CNR) for each feeder uplink at the satellite receiver is expressed as csi = Ci Ni = Ei Ni 1 1 + ro , for i = 1, 2, . . . , N, (2.3) where Ni is the noise variance at satellite interface and ro is the roll-off parameter. Here, the roll-off factor is a measure of the excess bandwidth of the filter, that is, the bandwidth occupies beyond the Nyquist bandwidth. For this purpose, the roll-off value, either 5% or 10%, is obtained from the Digital Video Broadcasting Second Generation with Extensions (DVB-S2X) standard [6]. It is important to note that the DVB-S2X standard is considered as the baseline air interface for the forward link. Based on the previous equations, the actual CNR for the feeder uplink between an i-th GW and the satellite at t = kTs for k = 1, 2, . . . , K, is denoted by Γk,i = |hi[k]| 2Ci Ni = |hi[k]| 2csi , for i = 1, 2, . . . , N, (2.4) where each value of Γk,i can be stored in a column vector Γ :,i for i = 1, 2, . . . , N, which defines a point in a K-dimensional space called Euclidean space denoted by R K , therefore, the matrix of CNR can be expressed by Γ 2 R K⇥N . However, this case is only when the feeder uplink is not affected by either interferences or weather impairments, such as rain, clouds, and fog. Therefore, it is necessary to obtain the carrier-to-noise and interference ratio (CNIR) using both the CNR and the carrier-to-interference ratio (CIR). It is important to mention that CIR is one of the most serious challenges due to the fact that interferences degrades the signal quality, impairing directly to communication system. The CIR can also be represented CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 13 by the symbol ⇣. The total CIR, ⇣T , directly impacts on the feeder uplink, which is made up of the co-channel interference, ⇣co, adjacent channel interference, ⇣adj, and the intermodulation interference, ⇣im, [8]. The ⇣T can be calculated by 1 ⇣T = 1 ⇣co + 1 ⇣adj + 1 ⇣im (2.5) Finally, the CNIR for k = 1, 2, . . . , K is defined as Ξk,i = Γk,i · ⇣T Γk,i + ⇣T , for i = 1, 2, . . . , N, (2.6) where each value of Ξk,i is also stored in a K-dimensional column vector, Ξ:,i 2 R K for i = 1, 2, . . . , N . The matrix of CNIR is given by Ξ 2 R K⇥N . To sum up, the signal quality is defined by the CNIR value for each k-th sample, therefore, this is a good measure to know whether the feeder uplink can be able to transmit to the satellite receiver, or if the weather conditions affect the feeder link, then it can not transmit the signal to the satellite, degrading the spectral efficiency on the channel. 2.2.1 Parameters of the Feeder Uplink Many parameters are involved in the performance of the Q/V band feeder uplink. Table 2.1 shows the basic propagation parameters for the feeder uplink between a GW station and the HTS system. These parameters were used in link simulations for each GW station of the GS. Currently, the BRASILSAT B4 satellite is positioned at 92.0° West. Although the satellite has exceeded its lifespan (19 years), the orbital position is only used for HTS simulation purposes of HTS systems. Furthermore, the specific parameters of the system and the link budget are detailed in Chapters 3 and 4. Table 2.1: Basic Propagation Parameters Feeder Uplink Values Frequency 50 GHz Orbital Position 92.0°W Orbit GEO, d0 = 35786 km Polarization LHCP, RHCP Boltzmann’s constant =1.380 649⇥ 1023 J/m In order to determine elevation, azimuth, and range between each GW station and the HTS system, it is essential to use geographical coordinates for each site (latitude and longitude) [1,2]. With these parameters, the transmitter antenna of each GW is adequately pointed towards the HTS receiver antenna. It is important to mention that each feeder uplink is also affected by the user downlinks, therefore, each forward link (Feeder Uplink + User Downlink) is analyzed and calculated. Thus, it is assumed as a mixed Ka and Q/V band solution [8,14,18]. CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 14 Although the study of the Ka-band user link is not the aim of this thesis, it is necessary to know its implication in this system. The Ka-band implications are approached in more detail in Chapter 4. 2.3 Spatial Correlation Model Spatial correlation is a measure that analyzes the relationship between near spatial units. For this purpose, the Recommendation ITU-R P.1815 indicates the method to obtain the spatial correlation model, which is able to estimate the correlation of rain rate to determine differential rain attenuation on satellite paths between the HTS and multiple locations on the surface of the Earth [27]. The Recommendation ITU-R P.618 includes the spatial correlation model [28], (See §2.2.4.1), whose objective is generally to calculate propagation data for the design of Earth-space telecommunication systems. Here, a set of ITU Recommendations were neatly employed to implement the obtained spatial-correlation-model for our study [29–35]. It is important to mention that the use of Recommendations ITU-R 1815 and ITU-R 618 are valid for antenna elevations above 10, frequencies up to 55 GHz, and site separations D between 0 and at least 250 km. Log-normal distribution of rain intensity and rain attenuation level are assumed by the differential rain attenuation method [27, 28]. Thus, this method determines the joint probability (%) that the attenuation on the path to the first site is greater than the attenuation threshold (a1) and the attenuation on the path to the second site is greater than the attenuation threshold (a2). The probability is the product of two joint probabilities and is expressed as, Pr{A1 a1, A2 a2} = 100⇥ Pr ⇥ Pa, (2.7) where Pr is the joint probability that it is raining at both sites, Pa is the conditional joint probability that the A1 and A2 attenuations exceed a1 and a2, respectively [27]. In general terms, the attenuation threshold for every i-th site can be denoted as ai. The discrete rain attenuation process and the channel gain, for each i-th site and k = 1, 2, . . . , K, are related as Ai[k] = 10 log10 |hi[k]| 2, for i = 1, 2, . . . , N (2.8) Both probabilities (Pr and Pa) are complementary bivariate normal distributions, which are expressed as Pr = 1 2⇡ p 1 ⇢2r Z 1 R1 Z 1 R2 exp  ✓ r21 2⇢rr1r2 + r22 2(1 ⇢2r) ◆ dr2 dr1, (2.9) Pa = 1 2⇡ p 1 ⇢2a Z 1 ln a1−mlnA1 σlnA1 Z 1 ln a2−mlnA2 σlnA2 exp  ✓ b21 2⇢ab1b2 + b22 2(1 ⇢2a) ◆ db2 db1, (2.10) CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 15 where r1 and r2 are independent variables of the function Pr whereas b1 and b2 are independent variables of the function Pa. The correlation coefficients ⇢r and ⇢a are respectively denoted as ⇢r = 0.7 exp ✓ D 60 ◆ + 0.3 exp ✓ D 700 ◆2⌫ , (2.11) ⇢a = 0.94 exp ✓ D 30 ◆ + 0.06 exp ✓ D 500 ◆2⌫ . (2.12) In Eq. (2.11) and Eq. (2.12), D is the distance between two sites in km, whereas in Eq. (2.9), the thresholds R1 and R2 are the solutions of rain probability (P rain i ) for a particular i location, which is calculated from step 3 of Annex 1 in [29] by the following equation: P rain i = 100⇥Q(Ri) = 100⇥ 1p 2⇡ Z 1 Ri exp ✓ r2 2 ◆ dr, for i = 1, 2 . . . , N. (2.13) Once obtained P rain i (%), it is possible to calculate the threshold Ri using the inverse complementary cumulative normal distribution, Q1, as follows Ri = Q1(P rain i /100). Finally, the parameters mlnA1 , mlnA2 , lnA1 and lnA2 are computed by fitting each i-th site rain attenuation, Ai, versus probability of occurrence, Pi, to the log-normal distribution: Pi = P rain i Q ✓ lnAi mlnAi lnAi ◆ , for i = 1, 2, . . . , N. (2.14) This method is described in §2.2.1.1 from [28]. Nevertheless, the inclusion of spatial correlation makes the analysis very complex so that it is necessary to assume spatially independent and identically distributed (i.i.d) links. Indeed, a typical diversity scheme of multiple gateways has a few tens of GWs dispersed over the GS, where each i-th site is only separated a few tens kilometers from each other. In a sense, the rain attenuation at each i-th site must be uncorrelated to avoid link outages in two or more GWs at the same time. Therefore, applying the correlation coefficient, ⇢a, by Eq. (2.12), it is possible to find uncorrelated distances for ⇢a  0.1 [25]. Figure 2.1 depicts the correlation coefficient ⇢a between two sites, where the correlation drops to 0.1 at a distance of 80 km, therefore, it takes solely a few tens of kilometers to carry through the decorrelation of rain attenuation. 2.4 The Dynamic Rain Attenuation Model In the Q/V band, the link impairment is mainly related to the rain attenuation, which is traditionally modeled and validated by using a log-normal distribution [36]. Eq. (2.8) expresses the relation between the rain attenuation and the channel gain, where hi[k] is the communication channel between a GW and the HTS. However, the rain attenuation is a time-varying process so that it is necessary to model the dynamic CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 16 Figure 2.1: The correlation coefficient, ⇢a, between two sites separated by a distance of D km. behavior of the rain attenuation. Despite that several time-series models to synthesize rain attenuation samples with temporal properties have been studied and proposed, only one model has been stood out [3]. This model was based on the Maseng-Bakken model [37], which was implemented as a new recommendation by the International Telecommunication Union (ITU), ITU-R P.1853 [38]. The ITU Recommendation P.1853 details how the time series synthesis method generates a time series that reproduces the spectral characteristics, fade slope and fade duration statistics of rain attenuation events. Also, the statistics of the inter-fade duration are reproduced but solely within individual events of the rain-attenuation. Figure 2.2 depicts the block diagram of this process, for this purpose, the rain attenuation, A(t), is synthesized from the white-Gaussian-noise discrete process, n(t). Here, it is important to mention that A(t) is a continuous signal. In this model, the white-Gaussian-noise is filtered by a low-pass filter, which is transformed from a normal distribution to a log-normal distribution in a memoryless nonlinearity, in addition to being calibrated to match the desired rain-attenuation statistics [38]. The time-series synthesizer is made up of five features, where m is the mean of the log-normal rain attenuation distribution, is the standard deviation of the log-normal rain attenuation distribution, p is the probability of rain, is the parameter that describes the time dynamics (s1), and the Aoffset that adjusts the time-series to match the probability of rain (dB). This time-series synthesizer is employed in this thesis, therefore, the following procedure is the basis for effective implementation. CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 17 k p+ Low-pass Filter exp (m+ [X(t)]) Memoryless Non-linear Device Aoffset Calibration n(t) White Gaussian Noise X(t) A(t) Rain Attenuation (dB) Figure 2.2: Block diagram of the rain attenuation time series synthesizer, ITU-R P.1853. 2.4.1 Procedure to Synthesize the Rain Attenuation Time-series The following step-by-step method is used to synthesize the attenuation time-series Ai(kTs) for k = 1, 2, . . . , K, and for i = 1, 2, . . . , N , which is based on the ITU Recommendation P.1853 [38]. The suggested method is apportioned as follows: A. Estimation of m and σ The parameters m and are obtained by the cumulative distribution of rain attenuation vs. probability of occurrence. In most cases, the development process is extremely difficult due to the lack of rain attenuation statistics from measured data in situ. However, the ITU Recommendation P.618 [28] provides excellent rain attenuation data prediction for Earth-space paths, which are also known as artificial rain attenuation data. Therefore for the path and frequency of interest, it was performed a log-normal fit of the rain attenuation vs. probability of occurrence by using the ITU Recommendation P.1057, where the step-by-step procedure to approximate a complementary cumulative distribution by a log-normal complementary cumulative distribution is described in detail [39]. As a result of this procedure, it was possible to obtain m and . B. Low-pass filter parameter The parameter is configured as, = 2⇥ 104 s1 C. Attenuation offset The attenuation offset for each i-th site is estimated by Aioffset = exp  m+ Q1 ✓ P rain i 100 ◆ , for i = 1, 2, . . . , N (2.15) CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 18 D. Time-series synthesis The rain attenuation time-series, Ai(kTs), for k = 1, 2, . . . , K, and for i = 1, 2, . . . , N , is synthesized as follows: • Step D1: A white-Gaussian-noise time-series, ni(kTs), is synthesized for each i-th GW site, where k = 1, 2, . . . , K, with m{ni(kTs)} = 0 and Var{ni(kTs)} = 1 at a sampling period, Ts. It is important to mention that the sampling period value can be modified, however, the default value is 1 s. • Step D2: Set X(0) = 0 • Step D3: The noise time-series, ni(kTs), for k = 1, 2, . . . , K, is filtered by a recursive low-pass filter, which is expressed by Xi(kTs) = ⇢X[(k 1)Ts] + ni(kTs) p 1 + ⇢2, for i = 1, 2, . . . , N, (2.16) where ⇢ = exp (Ts). • Step D4: Yi(kTs) for k = 1, 2, . . . , K, and for each i-th GW site, is defined as Yi(kTs) = exp [m+ Xi(kTs)], for i = 1, 2, . . . , N (2.17) • Step D5: The dynamic rain attenuation, Ai(kTs) (dB) for k = 1, 2, . . . , K, and for each i-th GW site, is computed as follows Ai(kTs) = max bYi(kTs) Aioffset , 0c, for i = 1, 2, . . . , N (2.18) • Step D6: The first 200000 samples are discarded from the synthesized time-series which correspond to the filter transient. Here, rain attenuation events are represented by sequences where, for a consecutive number of samples, values are above 0 dB. Consequently, Eq. (2.8) can be replaced by Eq. (2.18) in order to simulate a dynamic rain attenuation. It is necessary to mention that Eq. (2.18) can be expressed as a discrete signal, Ai[k], where each k-element of rain attenuation, Ak,i, can be stacked in a K-dimensional column vector, A:,i 2 R K for i = 1, 2, . . . , N,. Finally, the matrix of rain-attenuation is given by A 2 R K⇥N . 2.5 N + P Diversity Model on Ground Segment As was previously mentioned in Chapter 1, an important drawback was the seriously increased rain attenuation in the Q/V band compared with Ka-band. Therefore, site diversity is introduced in order to mitigate the impact of rain attenuation [22,25,26]. This kind of diversity model uses generally spatial diversity of the feeder links, which has feeder links spatially independent and identically distributed, i.i.d, as already mentioned in Section 2.2. As a result, there is a very small probability that all the CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 19 GWs experience heavy rain fading at the same time. However, if a GW is affected by the rain attenuation, another GW under clear sky conditions can take over the capacity from that affected GW [8,14,18,26]. For this process to be possible, the network must have extra resources, e.g. extra GWs, which are also known as redundant or backup PGWs. In other words, this process is also known as the switching mechanism between NGWs and PGWs. The switching mechanism can be performed if a certain switching threshold is reached, which can be a capacity threshold, a carrier-to-noise and interference ratio (CNIR) threshold or a combination of these two cases. In summary, when the switching threshold is reached, the capacity of the NGW affected is transferred (handover) to another PGW with clear sky or in much better conditions [21,23,24]. Figure 2.3 shows the gateway diversity scheme to be used in this thesis, which is known as the smart gateway diversity technique 3 and is gathered from [26]. When there are good weather conditions, the nominal gateways (NGW1 and NGW2) use the total available bandwidth allowed by the ITU radio regulations [4], as shown in Figure 2.3a. However, when the feeder link of the NGW1 is affected by a rain fading event, that capacity is taken over by the redundant gateway PGW1, as illustrated in Figure 2.3b. Therefore, this model expresses adequately the N + P diversity model, which has the following properties: • from the system aspect: the system capacity does not degrade unless too many gateways are impacted at the same time. It is thus important to carefully select switching thresholds and carefully perform system dimensioning. End-to-end availability is improved; • from the user aspect: user terminals served by the impacted gateway do not need to switch to a different carrier. They experience a short switching time because of switching traffic from one GW to the other [26]. Altogether, the N+P model is used to establish a solid base for this thesis in order to approach from a mathematical point of view to the optimization of this model. CHAPTER 2. SYSTEM MODELS FOR THE GROUND SEGMENT 20 Beam 3 Beam 2 Beam 1 Beam 6 Beam 5 Beam 4 Empty Empty Empty HTS NGW 1 NGW 2 PGW 1 Beam 1 Beam 2 Beam 3 Beam 4 Beam 5 Beam 6 (a) Operation in clear sky conditions HTS NGW 1 NGW 2 PGW 1 Beam 1 Beam 2 Beam 3 Beam 4 Beam 5 Beam 6 N/A N/A N/A Beam 6 Beam 5 Beam 4 Beam 3 Beam 2 Beam 1 (b) Operation under rain conditions Figure 2.3: Gateway diversity scheme with a redundant GW. Chapter 3 Quantification of Multiple Spot Beams for HTS Systems in Ka and Q/V bands 3.1 Introduction In this Chapter, it is proposed a methodology to quantify the necessary number of HTS spot beams in order to achieve a capacity of 1 Tb/s for the Latin America region by using an HTS system under ideal conditions. Firstly, a mix solution is proposed in order to obtain more available spectrum. Therefore, the Q/V band is used by the Feeder link whereas Ka-band is used by the User link. In this sense, two mechanisms are introduced to this system to find the precise number of spot beams for both Feeder and User links respectively. Moreover, traffic configurations are analyzed by simulations in order to project future needs in terms of capacity. The system capacity is important to supply multiple data services to/from UT such as HD streaming, Big Data, IoT, M2M, etc. At the end of this Chapter, it was assured the theoretical capacity for the HTS system in order to face the main challenges by 2021 and beyond. 3.2 Connectivity in Latin America: A Review Latin America is one of the biggest regions in the world either in population or territory, however, there is a strong social, economic, and technological gap, influencing especially in the Internet connectivity in urban and rural areas with noteworthy differences. Based on the above, an HTS system could cover this region, close the current gap, and reach remotes areas where terrestrial infrastructures do not deploy their services due to economic and technological factors. The Internet penetration rate is crucial to size any communication system so that it is also useful in an HTS system. In the last decade, the percentage of inhabitants that use the Internet has increased by 36% on average. In 2016 the 56% of inhabitants accessed to the Internet in Latin America [40]. Moreover, the Latin American region 21 CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .22 is characterized by a high heterogeneity between countries. For instance, the number of households connected to the Internet grown by about 103% between 2010 and 2016, however, more than 50% of total households have no Internet connections. For the sake of brevity, the big economic differences between social classes are the reason for the lack of internet connections in Latin America, however, the thesis does not delve into this topic. Thus, the countries with the highest growth rate of households connected to the Internet in the period 2010–2016 were Nicaragua, Guatemala, Honduras, and Bolivia, which had a lower Internet penetration rate at the beginning of the period. Costa Rica had the highest growth in the total Internet penetration of households (from 24% to 65%), as it is shown in Figure 3.1. There is a lot of difference between urban and P er ce n ta g e o f H o u se h o ld s [% ] 0 5 10 15 20 25 30 35 40 45 50 55 60 65 C R I U R Y C H L A R G B R A P A N C O L M E X V E N E C U P R Y B O L P E R H N D G T M S L V N IC C U B H T I Year 2016 Year 2010 Figure 3.1: Percentage of households with Internet access per country [40]. rural zones in terms of households with an Internet connection. Figure 3.2 illustrates the high inequality between urban and rural households due to social and economic differences in the Latin America region in addition to higher costs of infrastructure deployment in rural areas than urban areas. As a result, there were 18 million rural households without Internet access in the year 2016, whereas by the year 2020 there will be 20 million rural households without Internet access for all Latin America region. For this reason, it is necessary to reduce the social gap between urban and rural zones generating more opportunities in these areas [40]. Based on above analysis, it is convenient to use high throughput satellite (HTS) systems in order to cover remote zones where the terrestrial infrastructure cannot reach them and be able to face to the access demand (getting higher and higher). This satellite infrastructure can be used either as a high-performance backhaul or be part of a non-geostationary (NGSO) satellite fleet. No doubt this leads to new services and markets in satellite communications and other service providers, being mainly integrators of both Shared and 5G networks by the year 2020 [41–48]. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .23 P er ce n ta g e o f H o u se h o ld s [% ] 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 C H L C R I P A N U R Y C O L M E X B R A JA M E C U P R Y P E R S L V B O L Rural zone, year 2015 Urban zone, year 2015 Figure 3.2: Percentage of households with Internet access per geographical zone [40]. 3.3 Available Spectrum Nowadays, the Ku-band does not have sufficient available spectrum for an HTS system, therefore, it is necessary to go to upper bands either the Ka-band or the novel Q/V band, providing enough spectrum in order to achieve a capacity of satellite system above 1 Tb/s. There are some satellite services assigned to the radio spectrum, for instance, Fixed Satellite Service (FSS), Mobile Satellite Service (MSS), Inter-satellite links, Space Research, Radioastronomy, Earth Exploration by Satellite, Standard Frequency and Time Signal-Satellite (SFTSS), and Broadcast Satellite Service (BSS). Also, the satellite services are sharing spectrum with other terrestrial services as Mobile Service (MS) and Fixed Service (FS) [4]. 3.3.1 Ka-band Radio Regulations The current generation of HTS systems is exclusively dedicated to using the Ka-band, where the downlink ranges from 19.70–20.20 GHz and the uplink ranges from 29.50–30.00 GHz. That is, there is an available bandwidth of 2⇥ 500 MHz given by ITU Region 2 (R2) [4]. The rest of the frequency allocations in Ka-band are sharing with other services that depend on regulations in each country and coordination between operators. • Downlink Frequency Bands: This frequency band ranges from 17.70–19.70 GHz and shares services such as FSS, MSS, and BSS, however, in some countries could be different assignments so that it is necessary to have adequate coordination. The frequency band of 20.20–21.20 GHz is assigned to military services, therefore, it could be restricted in some countries. It is important to mention that both frequency bands of 18.30–19.30 GHz and 19.70–20.20 GHz are available for High-Density application in the Fixed Satellite Services (HDFSS), which enables to deploy a large number of earth stations (VSATs). CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .24 Table 3.1 indicates the frequency allocations for satellite downlink in Ka-band given by ITU Region R2 [4]. • Uplink Frequency Bands: In this case, the frequency band ranges from 24.75–25.25 GHz that is exclusively for FSS, therefore, this frequency band is not shared with other services. The frequency band of 27.00–29.50 GHz is shared with other services such as FS, MSS, and Space Exploration. Finally, both frequency bands of 28.35–29.10 GHz and 29.25–30.00 GHz are available for HDFSS. Table 3.2 indicates the frequency allocations for satellite uplink in Ka-band given by ITU Region R2 [4]. 3.3.2 Q/V band Radio Regulations In this case, it does not exist exclusive assignments for FSS services, but it requires coordination for each portion of the spectrum since the ITU suggests that each portion must be assigned to services such as FSS, BSS, MSS, FS, MS, radioastronomy, space research, and exploration. • Downlink Frequency Bands (Q band): This Q band spectrum is divided into two frequency bands, where the first frequency band ranges from 37.50–39.50 GHz, sharing services such as FSS, FS, research, and space exploration. Meanwhile, the frequency band ranges from 40.00–42.50 GHz is sharing services such as FS, FSS, MSS, BSS, research, and space exploration so that this frequency band needs a lot of coordination between regulatory entities in each country. Table 3.3 shows the frequency band portions for satellite downlinks in the Q band for ITU Region R2 [4]. • Uplink Frequency Bands (V band): In contrast to the Q band, the V band is divided into three frequency bands, therefore, the first frequency band ranges from 42.50–43.50 GHz, which is shared by other services such as FSS, FS, and radioastronomy. The second frequency band is assigned to both FSS and FS, which ranges from 47.20–50.20 GHz, however, each regulatory entity could issue restrictions in this frequency band. Finally, the third frequency band ranges from 50.40–51.40 GHz, where its spectrum assignment is similar to the previous frequency band. Table 3.4 denotes the frequency band portions for satellite uplinks in the V band for ITU Region R2 [4]. As a result, in the Ka-band are available of 3.500 GHz of the spectrum for downlink and 3.500 GHz for uplink, whereas in the Q/V band are available 5.000 GHz of the spectrum for downlink and 5.000 GHz for uplink, respectively. In both cases, the availability must be subject to coordination from regulatory entities. As stated above, a mixed solution was proposed in this Thesis, i.e., Ka-band was used for the User Link and the Q/V band was used for the Feeder Link. Nevertheless, it was not possible to use the entire available spectrum, therefore, it was assumed that the analysis was totally theoretical so that 3.000 GHz were available for both CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .25 T ab le 3. 1: F re qu en cy A ll oc at io n s fo r S at el li te D ow n li n k in K a- b an d , IT U R eg io n R 2 [4 ]. K a -b a n d D o w n li n k 17 .7 0 – 17 .8 0 [G H z ] 17 .8 0– 18 .4 0 [G H z ] 18 .4 0– 18 .6 0 [G H z ] 18 .6 0– 18 .8 0 [G H z ] 18 .8 0– 1 9. 3 0 [G H z ] 1 9. 3 0– 1 9. 7 0 [G H z ] 1 9. 7 0 – 2 0. 2 0 [G H z ] 2 0 .2 0– 2 1. 2 0 [G H z ] B W [G H z ] F S S (s -E )/ B S S /F S 0. 10 0 0 .1 0 0 F S S (s -E )/ F S 0. 60 0 0. 20 0 0 .5 0 0 0 .4 0 0 1 .7 0 0 F S S (s -E )/ E ar th E x p . S at ./ F S /M ob il e/ S p ac e R es ea rc h 0 .2 00 0 .2 0 0 F S S (s -E ) 0 .5 0 0 0 .5 0 0 F S S (s -E )/ M S S (s -E )/ S F T S S 1 .0 0 0 1 .0 0 0 A v a il a b le B a n d w id th 3 .5 0 0 N o t e : S o m e ba n d w id th s re qu ir e co o rd in a ti o n w it h o th er se rv ic es , es pe ci a ll y F ix ed S er vi ce s (F S ). T ab le 3. 2: F re qu en cy A ll oc at io n s fo r S at el li te U p li n k in K a- b an d , IT U R eg io n R 2 [4 ]. K a -b a n d U p li n k 24 .7 5 – 25 .2 5 [G H z ] 27 .0 0– 27 .5 0 [G H z ] 27 .5 0– 28 .5 0 [G H z ] 28 .5 0– 29 .1 0 [G H z ] 2 9. 1 0– 2 9. 5 0 [G H z ] 2 9. 5 0– 2 9. 9 0 [G H z ] 2 9. 9 0– 3 0. 0 0 [G H z ] B W [G H z ] F S S (E -s ) 0 .5 00 0. 5 0 0 F S S (E -s )/ F S /I n te r- S at el li te s/ M S S 0 .5 00 0. 5 0 0 F S S (E -s )/ F S /M S S 1. 00 0 1. 0 0 0 F S S (E -s )/ E ar th E x p . S at ./ F S 0. 60 0 0. 4 0 0 1. 0 0 0 F S S (E -s )/ E ar th E x p . S at . 0. 4 0 0 0. 1 0 0 0. 5 0 0 A v a il a b le B a n d w id th 3 .5 0 0 N o t e : S o m e ba n d w id th s re qu ir e co o rd in a ti o n w it h o th er se rv ic es , es pe ci a ll y F ix ed S er vi ce s (F S ). T ab le 3. 3: F re qu en cy A ll oc at io n s fo r S at el li te D ow n li n k in Q b an d , IT U R eg io n R 2 [4 ]. Q b a n d D o w n li n k 37 .5 0– 38 .0 0 [G H z ] 38 .0 0– 39 .5 0 [G H z ] 39 .5 0 – 40 .0 0 [G H z ] 40 .0 0– 4 0 .5 0 [G H z ] 4 0. 5 0– 4 1. 0 0 [G H z ] 4 1. 0 0 – 4 2. 5 0 [G H z ] B W [G H z ] F S S (s -E )/ F S /S p ac e R es ea rc h /M S S /E ar th E x p . S at . 0. 50 0 0 .5 0 0 F S S (s -E )/ F S /M S /E ar th E x p . S at 1. 50 0 1 .5 0 0 F S S (s -E )/ F S // M S /M S S /E ar th E x p . S at . 0. 50 0 0 .5 0 0 F S S (s -E )/ F S // M S /M S S /E ar th E x p . S at ./ S p ac e R es ea rc h 0 .5 0 0 0 .5 0 0 F S S (s -E )/ F S /B S S /M S /M S S 0 .5 0 0 0 .5 0 0 F S S (s -E )/ F S /B S S /M S 1 .5 0 0 1 .5 0 0 A v a il a b le B a n d w id th 5 .0 0 0 N o t e : S o m e ba n d w id th s re qu ir e co o rd in a ti o n w it h o th er se rv ic es , es pe ci a ll y F ix ed S er vi ce s (F S ). CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .26 Table 3.4: Frequency Allocations for Satellite Uplink in V band, ITU Region R2 [4]. V band Uplink 42.50–43.50 [GHz] 47.20–50.20 [GHz] 50.40–51.40 [GHz] BW [GHz] FSS(E-s)/FS/MSS/Radioastronomy 1.000 1.000 FSS(E-s)/FS/MS 3.000 1.000 4.000 Available Bandwidth 5.000 Note: Some bandwidths require coordination with other services, especially Fixed Services (FS). the downlink and uplink in Ka-band, respectively. Finally, the feeder link employed only 4.000 GHz for the uplink (V band) and 4.000 GHz for the downlink (Q band), taking into account that it was an ideal case. 3.4 Satellite Link Design in Ka and Q/V bands The satellite links can be designed and calculated by using traditional satellite-links calculations, i.e., the equations for free space loss (FSL), effective isotropic radiated power (EIRP), Range, CNR, etc., are the same for bands C, Ku, Ka, and Q/V [1,2, 49, 50]. For this satellite link design, it must be taking into account that the sky is in clear conditions. This assumption is necessary to find the maximum limit of the satellite system. However, there are some losses on the path such as attenuation due to fog, clouds, and gases, but without considering the rain attenuation. Moreover, both directions forward link and the return link are analyzed separately and independently. Despite the sky is in clear conditions, there are some losses on the path that affect the satellite link performance. For this reason, the following ITU-R Recommendations are included in this study: • ITU-R P.676: Attenuation by atmospheric gases and related effects [51]. • ITU-R P.834: Effects of tropospheric refraction on radiowave propagation [52]. • ITU-R P.840: Attenuation due to clouds and fog [53]. It is important to mention that the found losses on the Earth-space (E-s) satellite links range from 0.5–4.0 dB, which do not affect strongly to satellite links. For this case, satellite links on the E-s path, i.e., satellite uplinks, operate at the V-band. As a result, the carrier-to-noise ratios (CNR) have reasonable power levels so that it is possible to estimate the carrier-to-noise and interference ratio (CNIR) using the carrier-to-interference ratio (CIR), as a value of 20 dB [18]. An initial estimation of capacity and system configuration can only be based on the bandwidth, spectral efficiency, frequency reuse, and polarization reuse. Therefore, the total bandwidth available (BWT ) and the total capacity (CpT ) are obtained from [18] and are expressed as BWT = NbNp Nsb Savail, (3.1) CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .27 and CpT = BWTSeff , (3.2) where Nb is the number of the beams, Np is the potential for polarization reuse, Nsb is the number of the frequency sub-bands, Savail is the total available spectrum in the chosen direction, and Seff is the spectral efficiency that is obtained from DVB-S2X. Table 3.5: Frequency Reuse and Polarization Schemes [18]. Conf. Nsb Np Comments Scheme 1F2P 1 2 Each spot beam is dual-polarization but it has no frequency reuse. 3F1P 3 1 Beams are single-polarization and 3 frequency sub-bands (3-color scheme). 3F2P 3 2 Beams are dual-polarization and 3 frequency sub-bands (3-color scheme). 4F1P 4 1 Beams are single-polarization and 4 frequency sub-bands (4-color scheme). 4F2P 4 2 Beams are dual-polarization and 4 frequency sub-bands (4-color scheme). Table 3.5 indicates the schemes that use different frequency sub-bands or/and polarizations for multiple spot beams (adjacent beams) on the HTS system. The use of these schemes is popular thereby reducing the interference levels by appropriate filtering and permitting reuse of a sub-band in a non-adjacent beam. The degree of frequency reuse is often described numerically by using a frequency reuse factor (FRF) [18]. It is conventional in frequency reuse to divide the frequency band into several sub-bands, which use different frequencies, usually 3, 4, 7, etc. These frequency sub-bands can be referred to as colors for simplicity, therefore, in this study, the system can have either three or four colors. Moreover, the polarization discrimination between the beams can be used in various patterns. In [18], the author has developed the nomenclature mFnP, who has described the use of m colors and n polarizations, of course, this nomenclature is employed throughout this thesis. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .28 Furthermore, the antenna circular polarization is employed in this study, as a result, the module of the field is constant. It is important to note that circular polarizations are made up of two directions of the rotation field, left (counter-clockwise) and right (clockwise), also known as left hand circularly polarized (LHCP) and right hand circularly polarized (RHCP) respectively. 3.5 Radio Interfaces In order to achieve high capacities for HTS systems, it is essential to have advanced radio interfaces that permit high performance in satellite links. Thereby, the DVB-S2X standard is used on the forward link [6], whereas the DVB-RCS2 standard is used on the return link [7]. The DVB-S2X standard has 39 modulation and coding schemes (MODCOD), whose modulations varying from QPSK (M-ary Phase-Shift Keying, M-PSK) to 256-APSK (M-ary Amplitud and Phase-Shift Keying, M-APSK) with different coding rates. Also, the standard uses Low-Density Parity-Check (LDPC) which is a linear error-correcting code for transmitting a message over a noisy transmission channel [54,55]. The roll-off can be either 5% or 10%, therefore, it is possible to have excellent spectral efficiency, that is, DVB-S2X has a 51.44% more spectral efficiency than the DVB-S2 standard [56]. On the other hand, the DVB-RCS2 standard uses M-ary Quadrature Amplitude Modulation (M-QAM) and M-PSK schemes, i.e., varying from QPSK to 16-QAM with two bursts, short and long. Moreover, the roll-off takes on 4 different values, which are 20%, 25%, 30%, and 35%. It is important to mention that each MODCOD has a particular coding rate and its error-correcting code is based on turbo-codes [57]. Table 3.6 indicates and compares the maximum spectral efficiencies for each DVB standard where both DVB-S2X and DVB-RCS2 MODCODs are used on the forward link and return link respectively. Table 3.6: Maximum Spectral Efficiencies Standard MODCOD Roll-off Spectral Efficiency, [b/s/Hz] DVB-S2X vs. DVB-S2 DVB-S2 32 APSK 9/10 20% 3.7109 – DVB-S2X 256 APSK 3/4 5% 5.6199 +51.44% DVB-RCS2 16 QAM 5/6 20% 2.1417 – 3.6 Methods to Calculate the Performance of Satellite Antennas The trend is to have satellites of large dimensions, especially in communication capacity as well as size and weight. Indeed, in this thesis were implemented two CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .29 methods to calculate the performance of the satellite antenna, aiming to reduce the antenna size, therefore, the antenna is also reduced in weight and assured the desired cover. It is important to mention that if the beamwidth is larger, the power amplifier needs more power and a lower diameter of the antenna. However, the proposal is to use MBAs so that it is possible to reduce the beamwidth and to cover the same region using multiple spot beams. Therefore, there is lower consumption of energy on the satellite’s power subsystem but higher coordination in the onboard processing for managing the satellite spot beams, in addition to higher size antennas. Consequently, the two evaluation methods for antenna performance are presented in the following subsections, where the first method is focused on the antenna size evaluation, whereas the second method is approached in the power amplifier performance in Ka-band. 3.6.1 First Method: Antenna Size Evaluation In this process, the satellite-antenna size (Dant) was numerically calculated by a loop process. The Q band is used in the space-Earth satellite-communication link (s-E), which is denoted by FreqsE. The s-E satellite downlink is established between the HTS and the GW (return link). To begin with the method execution, the Dant was either increased or decreased in steps of 1 mm until to find the desired beamwidth (✓BW ). Here, it was suggested that the ✓BW of the satellite antenna might be defined by a value of 0.20 in direction to GW [18]. As a result, the best diameter of the satellite antenna was fitted in 2.63 m by using the illumination law [19], therefore, it was assured a narrow beamwidth with a coverage radius (rc) about 62.5 km. It is possible to compute rc by using ✓BW and the s-E range (R). Finally, Method 1 is detailed in the pseudocode of the process to size the satellite antenna. This method can be also applied to size the satellite antenna diameter in Ka-band, Dant, which is a function of antenna beamwidth (✓BW ). In this case, the ✓BW must be less than 0.5, therefore, the Dant fluctuates in steps of 1 mm, which is very similar to the calculation process of antenna size in the Q band. In particular, the coverage radius (rc) of the spot beams can be modified from 80–125 km by using different beamwidths that range from 0.26–0.40 according to the ground-segment requirements. 3.6.2 Second Method: Calculations for Antenna Gain and EIRP Here, it is possible to find the transmitter-antenna gain (GTX) and the effective isotropic radiated power (EIRPsat) for each spot beam in Ka-band. For this purpose, High Power Amplifier (HPA) was either increased or decreased by steps of 100 mW until reaching the maximum EIRP as a system threshold, whereas the second option was to modify the Dant by steps of 1 mm until reaching the maximum EIRP allowed. As a result, the diameter of the satellite antenna (Dant) was ranged from 2.62–4.10 m, and the HPA was set in 53.0 W, therefore, it was possible to calculate in different coverage cases and to choose the best option for the proposed system. Method 2 is CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .30 Method 1 Calculation of the Satellite Antenna Diameter Input: Dant, R, FreqsE Output: Dant, rc 1: ✓BW compute(FreqsE, Dant); {For Ka-band:  0.26–0.40} 2: if (✓BW  0.20) then 3: while (✓BW  0.20) do 4: Dant Dant 0.001; 5: ✓BW compute(FreqsE, Dant); 6: end while 7: else 8: while (✓BW 0.20) do 9: Dant Dant + 0.001; 10: ✓BW compute(FreqsE, Dant); 11: end while 12: end if 13: rc compute(R, ✓BW ); 14: return [Dant, rc] detailed in the pseudocode of the process to calculate the satellite antenna size as a function of HPA, EIRP, FreqsE, and ✓BW . Moreover, if the EIRP levels exceed the permitted limit in the Q band, this method can be also implemented for satellite antennas in that frequency band. 3.7 Analysis and Quantification of Multiple Spot Beams for HTS Systems in Ka and Q/V bands: Numerical Results and Discussion Primarily, the analysis to quantify the number of spot beams was based on the bandwidth, spectral efficiency, frequency reuse, polarization, EIRP levels, and data traffic rates. Generally, this first analysis provided a theoretical quantification for the HTS system, however, it was considered neither payload nor power subsystem of the HTS system, since it was not the purpose of this thesis. As stated above, the scheme N + P was implemented on the Ground Segment, also, the mixed solution was proposed where both Ka and Q/V bands were assigned to user and feeder links, respectively. It is important to mention that 1 Tb/s is the maximum capacity for this numerical analysis. Furthermore, the quantification of multiple spot beams was also evaluated by data-traffic-ratio scenarios at the feeder link. The traffic scenarios can be denoted by [DL:UL], where DL is the download traffic and UL is the upload traffic. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .31 Method 2 Calculations for Antenna Gain and EIRP Input: Dant, R, option, FreqsE, EIRPmax, HPAsat Output: Dant, rc, HPAsat 1: GTX compute(Dant, F reqsE); 2: EIRPsat compute(GTX , HPAsat); 3: switch (option) 4: case 1: 5: while (EIRPsat < EIRPmax) do 6: HPAsat HPAsat + 0.1; 7: EIRPsat compute(GTX , HPAsat); 8: end while 9: case 2: 10: while (EIRPsat < EIRPmax) do 11: Dant Dant + 0.001; 12: GTX compute(Dant, F reqsE); 13: EIRPsat compute(GTX , HPAsat); 14: ✓BW compute(FreqeT , Dant); 15: end while 16: default: 17: {This option does not exist} 18: end switch 19: rc compute(R, ✓BW ); 20: return [Dant, rc, HPAsat] 3.7.1 Orbital Position Analysis In this thesis, several GWs were distributed in the Latin America region, that is, Mexico, Central America, The Caribbean, and South America. For this reason, the orbital position for the HTS system was crucial for this evaluation. The list of possible geographic coordinates for GW locations is provided in Appendix A.1. First, the energy per symbol to noise power spectral density (Es/N0) must be calculated for each GW feeder uplink by ranging the orbital position from 0–180 (west longitude). To find the best orbital position, the Monte Carlo Method is employed in this assessment [58], where a domain of possible inputs (window of orbital positions) is used to perform a deterministic computation of the inputs. Thus, each Es/N0 is computed regarding the range of orbital positions. As a result, the best orbital position can be interpreted according to the best power levels, which are represented by a set-theoretic intersection. Table 3.7 shows the parameters used for the feeder uplink calculations which were obtained from [8, 13, 14, 18] in addition to the previously mentioned Methods. In order to obtain the best spectral efficiency for each feeder uplink, the Es/N0 levels must be above 20 dB due to the fact that the best MODCOD (256 APSK 3/4) of the DVB-S2X standard requires 19.57 dB of Es/N0. Furthermore, the found Es/N0 have a positive link margin of 2.5 dB above the reference of 13.5 dB [14]. Figure 3.3 CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .32 Table 3.7: Feeder Uplink Parameters HTS System User Terminal (UT) Gateway Station (GW) Parameter Value Parameter Value Parameter Value Dant (Q band) 2.63 m Dant (Ka-band) 0.75 m Dant (V band) 5 m Dant (Ka-band) 4.10 m LNA (Ka-band) 8.8 W HPA (V band) 16 W HPA (Q band) 15 W G/T 20 dB/K HPA (Ka-band) 53 W depicts the Es/N0 20 dB of each feeder uplink by using the Monte Carlo Method. Therefore, several valid orbital-positions were found from -102.0 to -50.0, but only one orbital-position encompassed the best Es/N0 levels of each feeder uplink. -180 -160 -140 -120 -100 -80 -60 -40 -20 20 22 24 26 28 30 32 Figure 3.3: Es/N0 for each feeder uplink using the Monte Carlo Method. For this purpose, the Central Limit Theorem was applied to the orbital-position observations, which were obtained from the Monte Carlo Method. It is important to mention that each observation does not depend on the values of the other observations, therefore, the central limit theorem says that the distribution of the average is closely approximated by a normal distribution. Figure 3.4 depicts the normal distribution by using the central limit theorem, providing the best orbital position that is -74.1. Even though -74.1 is the best orbital position in this evaluation, the range from -80.0 to -70.0 is also a good option for orbital positions due to the orbital positions are true 68% of the time within the 1- events. Finally, It is worth noting that the orbital positions must be negotiated with regulatory entities, however, these orbital positions are studied for theoretical purposes. All these calculations are made using computer codes, i.e., Matlab and Python scripts. 3.7.2 Quantification of Multiple Spot Beams In order to find the number of spot beams, Eq. 3.1 and Eq. 3.2 were used by taking as reference the total capacity of 1 Tb/s. Thus, the traffic behavior was considered in this analysis where 5 data-traffic-ratio scenarios were proposed and CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .33 Figure 3.4: Normal distribution of the orbital-position observations. studied. Initially, symmetric traffic between forward and return links was assumed as [1 : 1] data traffic ratio, meaning 50% (500 Gb/s) of the data throughput in the outbound and 50% (500 Gb/s) in the inbound. However, a more realistic traffic scenario could be 60%:40% which can be expressed as [3 : 2] data traffic ratio. The other three traffic scenarios employed in this thesis are: [4 : 1] (80%:20%), [7 : 3] (70%:30%), and [9 : 1] (90%:10%). Figure 3.5 shows the results of the number of beams using DVB-S2X and DVB-S2 standards for the feeder uplink. For this purpose, the 1F2P scheme was implemented for both trials, in addition to the satellite links were computed under ideal conditions. Due to the best spectral efficiency, the best results were found by using the DVB-S2X standard, where the number of beams for the feeder uplink is always less than the number of beams using the DVB-S2 standard, for all data traffic scenarios. That is, each feeder uplink beam corresponds to a gateway station (GW) on the ground segment (GS). For this reason, a fewer number of beams are necessary for infrastructure savings on terrestrial segment deployments. Throughout this study, the DVB-S2X standard is used only for assessing and calculating satellite forward links. Figure 3.6 illustrates the results of the number of carriers in the feeder downlink (return link). Each carrier has a bandwidth of 10 MHz [8], hence, whether the return data traffic is greater, there are more carriers on the feeder downlink. Particularly with 50% of data traffic, i.e. [1 : 1] traffic ratio, there are 11664 carriers. On the other hand, with 10% of data traffic, which is [9 : 1] traffic ratio, there are only 2331 carriers. Therefore, the choice of data-traffic-ratio can be either a positive or a negative factor in order to synchronize all data carriers in the satellite return links towards GWs. Figure 3.7 depicts the behavior of total capacity vs. data traffic ratio, where the upper limit of capacity is always 1 Tb/s. Nevertheless, there is a slight increase in total capacity due to the greater number of beams, generally, one more beam in the set of feeder uplinks. Table 3.8 shows the increase in the throughput of feeder uplinks whereas the set of feeder downlinks is easier to fit because each carrier has only a CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .34 N u m b er o f B ea m s 0 7 14 21 28 35 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 31 27 24 21 17 21 18 16 14 12 Feeder Uplink, DVB-S2X [1F2P] Feeder Uplink, DVB-S2 [1F2P] Figure 3.5: Comparison of the obtained number of beams using DVB-S2X and DVB-S2 standards. N u m b er o f C ar ri er s 0 1250 2500 3750 5000 6250 7500 8750 10000 11250 12500 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 2331 4662 6992 9338 11664 Feeder Downlink, DVB-RCS2 [1F2P] Figure 3.6: The number of carriers in the feeder downlink. bandwidth of 10 MHz. That is, each feeder-uplink beam has a theoretical capacity of 44.96 Gb/s and each feeder-downlink carrier has a capacity of 42.83 Mb/s. Figure 3.8 shows the number of beams and carriers in the user link using the 3-color frequency-reuse scheme. Figure 3.8a displays the number of beams using both 3F1P and 3F2P schemes where it is possible to visualize the difference between these two configurations. The number of beams for the 3F1P scheme is approximately twice regarding the 3F2P scheme, for all traffic-ratio cases. However, the theoretical throughput of each user downlink for the 3F2P scheme is twice regarding the 3F1P scheme, that is, 11.24 Gb/s versus 5.62 Gb/s respectively. On the other hand, Figure 3.8b illustrates the number of carriers for both 3-color frequency-reuse schemes. The number of carriers for the 3F1P scheme is approximately two times greater than the 3F2P scheme, for all traffic-ratio cases. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .35 T o ta l C ap ac it y [ T b /s ] 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.100 1.200 1.300 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] Feeder Downlink Traffic, DVB-RCS2 Feeder Uplink Traffic, DVB-S2X Figure 3.7: Total capacity comparison between different data traffic ratios. Table 3.8: Throughput Comparisons Traffic Ratio Feeder Uplink Throughput [Gb/s] Feeder Downlink Throughput [Gb/s] Total Increase [1 : 1] 539.51 499.62 3.9% [3 : 2] 629.43 399.98 2.9% [7 : 3] 719.35 299.50 1.9% [4 : 1] 809.27 199.69 0.9% [9 : 1] 944.14 99.85 4.4% Conversely, the theoretical throughput of each user uplink for the 3F2P scheme is two times greater than the 3F1P scheme, that is, 14.28 Mb/s versus 7.14 Mb/s respectively. It is important to mention that it is tough to manage and to synchronize several user-uplink carriers. For this reason, the sophisticated multiple-frequency time-division multiple access (MF-TDMA) is a great choice in order to manage adequately user traffic, in addition to increasing the number of users on the GS [5]. The analysis for 4-color schemes is similar to 3-color schemes, thus, Figure 3.9 shows the number of beams and carriers using both 4F1P and 4F2P schemes. The common factor between the number of beams for both 4-color schemes was about 2.0 due to the double polarization antenna, reducing the number of beams by a factor of 2.0 but increasing the throughput in the same proportion. Figure 3.9a describes the number of beams in both 4-color schemes where the throughput of the 4F1P scheme is about 4.21 Gb/s and 8.42 Gb/s for the 4F2P scheme in all data traffic cases. Figure 3.9b illustrates the number of carriers for the user uplink in all data traffic cases, where 4F1P schemes have a number of carriers greater than 4F2P schemes by a factor about 2.0. Finally, the throughput of carrier uplinks for 4F2P schemes is about 10.70 Mb/s whereas the throughput of carrier uplinks for 4F1P schemes is about 5.35 Gb/s. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .36 N u m b er o f B ea m s 0 19 38 57 76 95 114 133 152 171 190 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 81 72 63 54 45 161 143 125 107 89 User Downlink, DVB-S2X [3F1P] User Downlink, DVB-S2X [3F2P] (a) The number of beams in the user downlink for the 3-color schemes. N u m b er o f C ar ri er s 0 7500 15000 22500 30000 37500 45000 52500 60000 67500 75000 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 6,966 13,968 20,979 27,972 35,010 14,007 27,885 42,000 55,961 69,954 User Uplink, DVB-RCS2 [3F1P] User Uplink, DVB-RCS2 [3F2P] (b) The number of carriers in the user uplink for the 3-color schemes. Figure 3.8: The number of beams and carriers using both 3F1P and 3F2P schemes. To sum up, the sizing of the number of beams depends on the coverage area and the data traffic ratio, that is, to find an adequate beamwidth size in order to fit in the desired coverage area. Moreover, it is important to understand the data traffic behavior for each user so that it can choose properly the data traffic scenario. This last parameter is essential to design the throughput in both beams and carriers for the HTS system and to be able to size the right capacity for the end-user. At last but not least, the rain attenuation was not considered in this initial study, however, a complete analysis of rain attenuation and interferences sources are taken into account in the following Chapters. CHAPTER 3. QUANTIFICATION OF MULTIPLE SPOT BEAMS FOR HTS . . .37 N u m b er o f B ea m s 0 50 100 150 200 250 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 107 95 84 72 60 214 190 167 143 119 User Downlink, DVB-S2X [4F1P] User Downlink, DVB-S2X [4F2P] (a) The number of beams in the user downlink for the 4-color schemes. N u m b er o f C ar ri er s 0 20000 40000 60000 80000 100000 Data Traffic Ratio [1:1] [3:2] [7:3] [4:1] [9:1] 9,309 18,620 27,972 37,296 46,680 18618 37240 55945 74646 93296 User Uplink, DVB-RCS2 [4F1P] User Uplink, DVB-RCS2 [4F2P] (b) The number of carriers in the user uplink for the 4-color schemes. Figure 3.9: The number of beams and carriers using both 4F1P and 4F2P schemes. 3.8 Contributions of the Research This chapter offers an initial study about the quantification of multiple beams and carriers for the HTS systems, therefore, the results have been published in IEEE Latin America Transactions journal and titled: • Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez, and Jose M. Matias. Analysis to Quantify and Optimize Spot Beams for a High Throughput Satellite in Ka and Q/V Bands. IEEE Lat. Am. Trans., 17(02):219–227, feb 2019 Chapter 4 Interference Evaluations in Frequency Reuse by Using Offset- Parabolic-Reflector Antennas 4.1 Introduction This chapter analyzes the features and parameters of an offset-fed parabolic reflector antenna for the HTS system. Indeed, some antenna parameters are important for satellite communication links, so that it is necessary to evaluate the effect of frequency-reuse configurations and spot-beam interferences by designing an offset-parabolic-reflector antenna for this satellite system. That is, the interferences such as cross-polarization (cross-polar) and co-polarization (co-polar) are vital for the system performance and its feasibility. To be precise, the main aim is to adjust and to reduce the interference levels to ensure satellite links for the HTS system, obtaining the maximum advantage for frequency reuse configurations, the number of beams, and the circular polarization. The evaluations of both Multiple Spot Beams and the Carrier-to-Interference employ well-known methods [9,18,59], but with slight modifications to this proposal. Finally, the designed antenna is theoretically and numerically assessed by both implemented methods. Consequently, it is possible to find a satellite reflector antenna suitable for the proposed HTS system. 4.2 Geometric Design of an Offset-Parabolic-Reflector Antenna Usually, the offset-parabolic-reflector antennas are a great option to reduce sidelobe levels. Motivated by this, moving the feed out of the aperture, some problems with axisymmetrical reflectors can reduce. Hence, diffraction-caused sidelobes, blockage losses, and cross-polarization can reduce or even disappear. For this reason, a proper antenna’s design for the proposed HTS system is necessary to accomplish the above-mentioned requirements. Thereby, some parameters were obtained from 38 CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .39 geometry and illumination laws by procedures from [19, 60]. In this section, the antenna geometry and its parameters are obtained by the following method. To begin with, the aperture plane diameter, also known as antenna diameter (Dant), depends on a coefficient obtained from the illumination law, whereby a coefficient with a typical value of 70 introduces some tapering at the edge of the reflector [19]. Consequently, the aperture plane diameter can be expressed by Dant = 70 ✓3dB , (4.1) where is the wavelength of the frequency band used in a specific satellite link, and the ✓3dB is the angle subtended by the half-power points of the main lobe [19]. This last parameter was used to characterize the beamwidth ✓BW (see Section 3.6), therefore, it was possible to assume that ✓BW = ✓3dB. Figure 4.1 shows the geometric parameters that are part of the parabolic-reflector-antenna [60, 61]. As the reflector antenna indicates, there is an offset distance that provides a blockage-free region for structures in the focal region [60]. The offset (h) is the distance from the axis of symmetry to the lower reflector edge. Generally, the offset distance is popular in VSAT applications. In this case, this h distance can be obtained from [60] and denoted by h = Dant 8 , h > 0 (4.2) The distance from the symmetry axis to the center of the reflector is known as the offset of the reflector center (H) which is described as H = Dant 2 + h (4.3) In this procedure, one choice of the antenna design is to keep the ratio of focal length (F ) to the antenna diameter (Dant) constant, i.e., the ratio is constant at 1 [62]. Therefore, F/Dant = 1. It is worth to mention that the F/Dant choice also impacts on cross-polarization performance [63]. The main contribution to this study was to modify Dant regarding different beamwidths (✓3dB) for both Ka and Q/V bands. Indeed, this is possible as the antenna diameter is a flexible parameter, in addition to exploring different cover areas with multiple spot beams. According to [61], the half of the angle subtended ( s) by the reflector as viewed from the focal point can be expressed as s = tan1 ✓ 8FDant 16F 2 + 4H2 D2 ant ◆ (4.4) Meanwhile, the angle which bisects the reflector subtended angle is defined by B = tan1 ✓ 16FH 16F 2 +D2 ant 4H2 ◆ (4.5) CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .40 xx s z y UU L C FA B P C L xf zf Figure 4.1: The geometry for the offset-parabolic-reflector antenna. The lower angle ( L) can be described as L = B s (4.6) Thus, the upper angle ( U) is determined by the sum of the subtended angle and the lower angle, which is expressed by U = 2 s + L (4.7) It is important to note that the feed is directed at an angle ( f ), i.e., the angle of the feed-antenna-pattern peak relative to reflector axis of symmetry, where the feed is directed toward the point P . The f is denoted by f = 2 tan1 ✓ H 2F ◆ (4.8) Furthermore, the angle C is similar to the angle f when the feed aims at the reflector point C, corresponding to the aperture center. The angle from the lower edge of the dish to feed pointing direction is defined by P = f L (4.9) For a parabolic reflector, the spherical wave nature of the feed radiation is referred to as spherical spreading loss (SSL), for both upper angle ( U) and lower angle ( L) edges [63], which is given by SSL( ) = 20 log  cos2 2 (4.10) CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .41 The feed-pointing angle gives a difference in edge illuminations (EI) [60], which is expressed by ∆EI = EIU EIL (4.11) The negative of the edge illumination (EI) is the sum of the feed taper (FT) and the spherical-spreading loss (SSL) [60] so that it can be denoted by FTL + SSLL = FTU + SSLU +∆EI (4.12) Finally, substituting Eq. (4.10) into Eq. (4.12) outputs the following design equation, ∆FT = FTL FTU = 40 log 8 > > > > < > > > > :  cos L 2  cos U 2 9 > > > > = > > > > ; +∆EI (4.13) Figure 4.1 illustrates the points of FTU , FTL, EIU , and EIL. For the case of balanced aperture illumination, then ∆EI = 0. To sum up, each parameter was rigorously evaluated and computed in order to obtain the best performance of the antenna in terms of reduced sidelobes with an acceptable antenna gain according to the focal-length-to- diameter ratio, F/Dant [63]. Therefore, this procedure is able to find a suitable offset-parabolic-reflector antenna for the HTS system. 4.3 Multiple Spot Beams Antenna for HTS Systems The multiple-aperture-antenna with a single element per beam was chosen to study in this thesis. This antenna is either 3 or 4 apertures, that is, it depends on the frequency-reuse schemes either 3 or 4 colors, respectively. Hereafter, this multiple-aperture-antenna is also known as the multiple beam antenna (MBA) or Type (c) MBA [9]. The MBAs have carried out important researches in this area [9, 13,59,62], which have provided some advantages such as: • The effective spectral bandwidth increases in several folds due to the frequency-reuse channels over numerous spot beams, • The beam has a smaller size so that the antenna has higher gain, resulting in enhanced effective isotropic radiated power (EIRP) for the downlink and improving the antenna gain-to-noise temperature (G/T ) for the uplink, • The MBAs allows the use of much smaller ground terminals such as GWs and VSATs. • The satellite reflector could be lower than 5.0 m diameter, which could lead to the best accommodation of multiple reflectors in the spacecraft. Naturally, the antenna diameter depends on its gain and the employed frequency. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .42 θ θ θ θ θ θ θ θ (a) 3-cell frequency-reuse θ θ θ θ θ θ θ θ (b) 4-cell frequency-reuse Figure 4.2: The hexagonal-grid layouts of both 3-cell and 4-cell for frequency reuse, illustrating the beam parameters. 4.3.1 Multiple Spot Beams: Design and Analysis Adjacent beams are generated from different apertures, which are formed in an interleaved multiple-spot-beam coverage on the GS. Therefore, the design of a multiple-spot-beam antenna is depended on the beam size, which is related to the minimum-coverage-area directivity requirement. Figure 4.2 depicts hexagonal grid layouts for both 3-reflector and 4-reflector antennas, where the minimum directivity occurs at the triple beam crossover of the three adjacent beams for MBAs with uniform-size beams. Furthermore, typical beam overlaps used for MBA designs are approximately 3 dB for two adjacent beams, and 4 dB for three adjacent beams [64]. The optimum overlap level depends on the minimum-coverage directivity, which requires the co-polar isolation among reuse beams and the frequency-reuse scheme (3-color scheme, 4-color scheme, etc.). Consequently, the spacing between adjacent-beam centers (✓s) determines the number of beams for the desired coverage. Figure 4.2a and Figure 4.2b illustrate the hexagonal-grid layout of the beams for 3-reflector and 4-reflector schemes, respectively. As a result, the ✓s can be expressed by ✓s = p 3 2 ✓0 = p 3rc, (4.14) where ✓0 is the beam diameter at the triple beam crossover and rc is the coverage radius of the spot beam. Thus, the minimum number of beams (Nbmin ), for the desired coverage area is CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .43 given approximately by Nbmin ⇡ Ac Ah , (4.15) where Ac is the coverage area and the Ah represents the area of the hexagonal cell associated with each spot beam. The area of the hexagon can be calculated by Ah = 3 p 3 2 r2c . It is important to note that the actual number of beams (Nb) is usually 20% larger than Nbmin for an efficient layout of the beams over the coverage area [59]. Moreover, the triple beam crossover levels for outer beams occur at the edge of the beam coverage. Further, the closest spacing between beam centers reusing the same frequency (✓c) for 3-reflector (using the 3-color frequency-reuse scheme) and 4-reflector (using the 4-color frequency-reuse scheme) antenna systems can be respectively denoted by ✓c,3 = p 3✓s = 3rc, (4.16) and, ✓c,4 = 2✓s = 2 p 3rc (4.17) Finally, the closest spacing between the reuse-beam edges (✓r), determines the achievable carrier-to-interference ratio (CIR), which is expressed by ✓r = ✓c ✓0. Therefore, the ✓r for both 3-reflector and 4-reflector hexagonal-grid layouts can be respectively expressed by ✓r,3 = ✓s 2 = rc, (4.18) and, ✓r,4 = ✓s( p 3 1) = 2( p 3 1)rc (4.19) 4.3.2 Spot Beam Pattern: Model Analysis The analysis of this model has been very similar to the previous research [18], but it has been more practical and simpler than from the aforecited method. Thus, the simplified analysis has been performed and adapted to this study successfully. As was previously mentioned in Section 4.2, the offset-parabolic-reflector antenna was a good option in order to reduce the sidelobe levels. For this purpose, it was necessary to taper the field distribution over the circular aperture. Thereby, an adequate alternative was to use a parabolic taper on an offset-distance value at the edge. In summary, the antenna performance can be determined analytically for integer taper roll-off values. For starting, the antenna beam is based on the Gaussian beam pattern obtained from [18], where the antenna pattern function is given by f(✓BW , n, h) = hf(✓BW , n = 0) + 1 h n+ 1 f(✓BW , n) h+ 1 h n+ 1 (4.20) CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .44 so that, f(✓BW , n) = 2n+1(n+ 1)! Jn+1(U) Un+1 (4.21) where, for simplicity, U = 2⇡ Dant sin ✓BW , (4.22) where h is the offset distance of the parabolic antenna, ✓BW is the beamwidth, n is an integer number ranging from 0–2, which represents the field taper roll-off factor. Moreover, Jn+1 is the Bessel function of the n + 1 kind, is the wavelength of the frequency band used, and Dant the diameter of the antenna aperture. Applied to this study, the relative gain of the antenna obtained from [18], Gr(✓), can be found by Gr(✓BW ) = 20 log10(|f(✓BW ), n, h|) (4.23) To sum up, the relative gain of the offset-parabolic-reflector antenna was an important parameter in order to evaluate the CIR of the downlinks for both Q band and Ka-band respectively. 4.4 Carrier-to-Interference: Evaluation Model In this Section, the methodology to evaluate the carrier-to-interference ratio (CIR) was only determined for both feeder uplinks and downlinks, and solely user downlinks. Thus, it is important to mention that the CIR, also known as ⇣, is independent of the propagation impairments, e.g., rain attenuation, as the useful and interfering signal follows the same path from the HTS to the considered ground point [18]. To begin with, a beam grid was defined by several points, where each of these points was scanned in order to compute the ⇣. This methodology has been obtained from [18], whose performances and results for the ⇣ evaluation have been successfully tested. Some assumptions were proposed regarding the downlink interferences, • Each beam transmitted identical signals • At the center of each beam, the forward uplink was the same • In the spectrum of interest, there was a unique carrier in each beam • Each GW was located at the beam center, therefore, its signal was emitted from there. With these considerations, the ⇣ can be computed by ⇣ = Gr(!) PLT n P i=1 Ii() PLi (4.24) CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .45 where Gr(!) is the antenna relative gain of the wanted beam at the point of interest by using the Eq. (4.23), ! is the angle that ranges from ! = 0 (beam center) to ! = ✓BW/2 (beam edge), PLT is the path loss from HTS to the user terminal (UT) at the point T , Ii() is a function that describes the nature of the interference, is the angle between the point T and the center of the i-th beam, and PLi is the path loss from the HTS to the center of the i-th beam [18,50]. The evaluation method was divided into 4 cases. Firstly, the method started when the i-th beam evaluated was the same color, (frequency), and the same polarization, then Ii would become the relative gain of the antenna at the point of interest. Secondly, when the i-th beam was of the same frequency but different polarization, then Ii would match to the beam relative gain of the cross-polar antenna at the point of interest. For the third case, if the i-th beam was in a different frequency but the same polarization, then Ii would be similar to the antenna relative gain of the beam at the point of interest but reduced by the Adjacent Carrier Isolation (ACI) factor. Lastly, if the i-th beam was neither in the same frequency-reuse nor the same polarization, then Ii would become the beam relative gain of the cross-polar antenna at the point of interest but reduced by the Cross-Polar Isolation (XPiso) factor. Figure 4.3 illustrates the complete interference geometry of the downlink used for the evaluation method. However, for the feeder downlink, the evaluation method only had 2 cases because the feeder link not only did it uses double polarization but it did not use frequency reuse. Hence, when the i-th beam evaluated was the same frequency and the same polarization, then Ii would be the relative gain of the antenna at the point of interest. Meanwhile, when the i-th beam was the same frequency but different polarization, then Ii would equal to the beam relative gain of the cross-polar antenna at the point of interest. The CIR evaluation mechanism used in this thesis was very similar to the method employed in cellular networks. For instance, the ⇣ of the cellular networks ranges from 13–15 dB [65]. By contrast, for satellite systems in Ka-band, the ⇣ ranging from 14.5–17.6 dB [66]. Meanwhile, the ⇣ for the downlink in the Q band must be above 20 dB, keeping an average of 29 dB [18]. This parameter was necessary to define in order to know whether the GW beams had good isolation between each other. For this reason, it was necessary to implement this method to find the minimum CIRs for the proposed HTS system. 4.5 Offset-Parabolic-Reflector Antennas: Numerical Results 4.5.1 Offset-Parabolic-Reflector Antenna: Geometric Parameters As was analyzed in Section 4.2, the Eqs. (4.1)–(4.9) were used to find each geometric parameter of the offset-parabolic-reflector antenna. For the downlink in Ka-band, the geometric parameters were calculated by 4 different beamwidths in order to explore CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .46 T HTS -th beami Figure 4.3: The interference geometry of the downlink. diverse antenna diameters, i.e., ✓BW = 0.26, ✓BW = 0.32, ✓BW = 0.40, and ✓BW = 0.48. Meanwhile, the geometric parameters in the Q band were calculated by only one beamwidth, ✓BW = 0.20. Table 4.1 shows the obtained geometric parameters of the antenna by using the previous equations. Furthermore, the antenna feed was modeled by a symmetric Gaussian radiation pattern, which was given by a value of 10.0 dB at the edges [60, 63]. Hence, 10.0 dB were defined for both lower (FTL) and upper (FTU) edge tapers. Table 4.2 indicates the values of spherical spread losses and edge illuminations obtained by using Eqs. (4.10)–(4.13). It is important to note that the EI values are not recommended because the difference between EIU and EIL must be zero. Thereby, it was necessary to point the antenna feed with an angle f in order to balance the aperture illumination. Table 4.3 indicates the balanced parameters of the offset-parabolic-reflector antenna when the feed is aiming to the point P with an angle f . The angle f was modified by little steps until a high performance of cross-polar isolation(XPiso) was achieved. With these results obtained, offset-parabolic-reflector antennas were simulated by a computer program. Thus, the computer program TICRA-GRASP was used to simulate the offset-parabolic-reflector antenna [67], which, among other things, was configured to operate in circular polarization, that is, LHCP and RHCP. Figure 4.4 depicts the radiation-pattern diagram of the offset-parabolic-reflector antenna for the feeder downlink, operating in the Q band. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .47 Table 4.1: Geometric Parameters of the Offset-Parabolic-Reflector Antenna Parameters Q band Ka-band Unit FreqsE 40.00 20.00 20.00 20.00 20.00 GHz ✓BW 0.20 0.48 0.40 0.32 0.26 deg Dant 2.63 2.19 2.63 3.28 4.10 m h 0.33 0.27 0.33 0.41 0.51 m H 1.64 1.37 1.64 2.05 2.56 m F/D 1.00 1.00 1.00 1.00 1.00 - B 32.93 32.93 32.93 32.93 32.93 deg s 25.78 25.78 25.78 25.78 25.78 deg L 7.15 7.15 7.15 7.15 7.15 deg U 58.72 58.72 58.72 58.72 58.72 deg f 34.71 34.71 34.71 34.71 34.71 deg P 27.56 27.56 27.56 27.56 27.56 deg Table 4.2: Spherical Spread Losses and Edges illuminations with a Symmetric Gaussian Radiation Pattern Parameters Q band Ka-band Unit FreqsE 40.00 20.00 20.00 20.00 20.00 GHz ✓BW 0.20 0.48 0.40 0.32 0.26 deg FTU 10.00 10.00 10.00 10.00 10.00 dB FTL 10.00 10.00 10.00 10.00 10.00 dB ∆FT 0.00 0.00 0.00 0.00 0.00 dB SSLU 2.39 2.39 2.39 2.39 2.39 dB SSLL 0.03 0.03 0.03 0.03 0.03 dB EIU 12.39 12.39 12.39 12.39 12.39 dB EIL 10.03 10.03 10.03 10.03 10.03 dB ∆EI 2.35 2.35 2.35 2.35 2.35 dB Table 4.3: Spherical Spread Losses and Edges illuminations, f = 34.71 Parameters Q band Ka-band Unit FreqsE 40.00 20.00 20.00 20.00 20.00 GHz ✓BW 0.20 0.48 0.40 0.32 0.26 deg FTU 10.00 10.00 10.00 10.00 10.00 dB FTL 12.35 12.35 12.35 12.35 12.35 dB ∆FT 2.35 2.35 2.35 2.35 2.35 dB SSLU 2.39 2.39 2.39 2.39 2.39 dB SSLL 0.03 0.03 0.03 0.03 0.03 dB EIU 12.39 12.39 12.39 12.39 12.39 dB EIL 12.39 12.39 12.39 12.39 12.39 dB ∆EI 0.00 0.00 0.00 0.00 0.00 dB Demonstrating the pointing of the antenna feed, this parameter is very sensitive so that it influences directly to the cross-polarization. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .48 Figure 4.4: Normalized pattern of the offset-parabolic-reflector antenna, 40 GHz. Table 4.4 shows the XPiso simulation results for both feeder and user downlinks. Table 4.4: Cross-polar isolation XPiso for both feeder and user downlinks. Parameters Q band Ka-band Unit FreqsE 40.00 20.00 20.00 20.00 20.00 GHz ✓BW 0.20 0.48 0.40 0.32 0.26 deg XPiso 27.78 27.39 27.33 27.25 27.16 dB The values of XPiso are very similar to each other because the antenna geometry is the same for all cases. Experiments have been carried out to find the most appropriate range of XPiso, which have been ranged from 20–40 dB [1,2,8,17,18,50,61]. Recommending a value of 25 dB, the results are totally convincing and viable for the final design of offset-parabolic-reflector antennas in this study. 4.5.2 Sizing of Spot Beams over the Coverage Area Initially, it is worth to notice that the Latin American region is the area of interest, where it was possible to find the approximate number of spot beams by using the Eq. (4.15). For this purpose, the Latin American region was divided into three coverage regions: Mexico, Central America & The Caribbean, and South America. Moreover, this evaluation was solely performed by both 3 and 4 frequency-reuse schemes, i.e., for user downlinks in Ka-band, as it is the service area. Table 4.5 displays the approximate number of beams for each coverage area regarding the beamwidths. It is important to note that the number of Nb is approximately 20% larger than the Nbmin because it is a more realistic scenario for an efficient layout of the spot beams over the coverage area [59]. Therefore, this is an excellent approximation for sizing the spot beams over the coverage area without considering the capacity of the HTS system. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .49 Table 4.5: The Number of Spot Beams (Nbmin /Nb) for the Latin American Regions. Beamwidths, ✓BW ✓ = 0.48 ✓ = 0.40 ✓ = 0.32 ✓ = 0.26 rc ⇡ 150 km rc ⇡ 125 km rc ⇡ 100 km rc ⇡ 80 km Region Ac Nbmin /Nb Mexico 1.973⇥ 106 km2 34/41 49/59 76/92 119/143 Central America & The Caribbean 7.328⇥ 105 km2 13/16 19/23 29/35 45/54 South America 1.801⇥ 107 km2 309/371 444/533 694/833 1084/1300 Total Beams 356/428 512/615 799/960 1248/1497 4.5.3 CIR Evaluation Results Primarily one of the advantages of the Q/V band was able to generate narrower beams than other frequency bands. Applying the method of Section 4.4, Table 4.6 shows the CIR results in the Q band for the feeder downlink. Also, it is important to note that this method evaluates and gives the co-channel interference (⇣co) as well as the adjacent-channel interference (⇣adj). Table 4.6: The CIR Evaluation for Feeder Downlink, 40 GHz. Parameters Results Denom. Values Denom. Values Denom. Values mFnP 1F2P Dant 2.63 m ⇣co 36.09 dB position 92.0 W EI 12.39 dB ⇣adj 38.17 dB FreqsE 40.00 GHz n 2 ⇣1/⇣co+1/⇣adj 33.99 dB ✓BW 0.20 ACI 30.00 dB rc ⇡ 65.50 km XPiso 27.78 dB The ACI is considered a constant value, which is obtained from [66]. As a result, the ⇣1/⇣co+1/⇣adj evaluation gives a value of 33.99 dB, which is higher than the average value of 29.00 dB [18]. Therefore, the offset-parabolic-reflector antenna design is robustness in terms of isolation between other feeder links, assuring an excellent performance for the proposed HTS system. Figure 4.5 depicts the spot beams of each feeder downlink projected over the Latin America area. Details of geographic locations for the spot beams are in Appendix A.1. This choice was based on the fact that those major cities could access multiple infrastructures of various types, guaranteeing the fast deployment of facilities for gateways stations. Furthermore, it was analyzed the reaching of the HTS system in the entire Latin American region, theoretically. Meanwhile, Table 4.7 indicates the CIR results for the 3-color scheme, evaluating both simple and double polarization. In this evaluation, the frequency band was of 20.00 GHz in the Ka-band, the HTS orbital position was 92.0 W, as was discussed in subsection 2.2.1, and the taper roll-off, n, was of zero for all cases. The co-polar evaluation was simplified by considering the closest six interferences [9,59,62]. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .50 Figure 4.5: Spot beams of feeder downlinks over the Latin America region. Furthermore, the crossover (triple-point) level was calculated by using the method from [64]. To sum up, the CIR results are very promising where each evaluation is higher than the range between 14.5–17.6 dB. Therefore, this scheme can be used as the main layout in order to cover the ground segment in Ka-band. Figure 4.6 illustrates the 3-color frequency-reuse schemes over the Mexico area. For the 4-color frequency-reuse scheme, the evaluation method was the same as the 3-color scheme, for this reason, the parameters were exactly the same. Table 4.8 shows the CIR results for the 4-color scheme, assessing both simple and double polarization. The 4-color frequency-reuse scheme is more aggressive than the 3-color scheme, therefore, the CIR results for the 4-color scheme are lower than CIR results for 3-color schemes. Although the CIR values are a few dBs lower than CIR values for 3-color schemes, it does not mean bad results. In fact, the CIR results for 4-color schemes are within the range value between 14.5–17.5 dB, where the scheme 4F1P overcomes slightly that range. Figure 4.7 illustrates the 4-color frequency-reuse scheme over the Mexico area. In conclusion, the antenna results are very encouraging, giving an excellent outlook on the design of the offset-parabolic-reflector antennas for HTS systems. The double polarization increases the capacity of the link without degrading the signal at the reception antenna. It is also important to mention that the larger beam spacing enables a proportionate increase in the feed horn size, which improves the antenna gain by reducing spillover loss, i.e., the reflector illuminates optimally increasing the CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .51 Table 4.7: The CIR Evaluation for the 3-color Frequency-reuse Scheme. Denom. Values ✓BW 0.48 0.40 0.32 0.26 rc ⇡ 150 km ⇡ 125 km ⇡ 100 km ⇡ 80 km Dant 2.19 m 2.63 m 3.28 m 4.10 m EI 12.39 dB 12.39 dB 12.39 dB 12.39 dB ACI 30.00 dB 30.00 dB 30.00 dB 30.00 dB XPiso 27.39 dB 27.33 dB 27.25 dB 27.16 dB Results Denom. 3F1P Scheme ⇣co 21.36 dB 21.29 dB 21.20 dB 21.03 dB ⇣adj 25.49 dB 25.45 dB 25.40 dB 25.34 dB ⇣1/⇣co+1/⇣adj 19.94 dB 19.88 dB 19.80 dB 19.66 dB Denom. 3F2P Scheme ⇣co 21.36 dB 21.29 dB 21.20 dB 21.03 dB ⇣adj 24.32 dB 24.19 dB 24.07 dB 23.99 dB ⇣1/⇣co+1/⇣adj 19.58 dB 19.49 dB 19.39 dB 19.25 dB Crossover level 2.88 dB 2.97 dB 3.05 dB 3.10 dB beam End-of-Coverage (EoC) gain and reducing sidelobe levels. Furthermore, these results demonstrate that both 3-color and 4-color frequency reuse schemes accomplish the interference requirements in order to generate spot beams from offset-parabolic-reflector antennas, standing out the 3-color frequency-reuse schemes so that it is possible to recommend these layouts for the HTS systems. Finally, the Latin America region requires a lot of spot beams in order to cover the entire area. For this purpose, an HTS fleet is necessary to supply the demand for spot beams in the region. 4.5.4 Link Margin According to [8], the aim of link margin evaluation is to determine the positive margin of operation between the feeder uplink and the user downlink by using the combined CNIR, i.e., this analysis is only for the forward link in clear-sky conditions. The average value of the CNR for feeder uplinks in the V band was about 32.36 dB, whereas the average value of the CNR for user downlinks in the Ka-band was about 24.61 dB, as was discussed in Chapter 3. Furthermore, the intermodulation interference (⇣im) is a constant value of 25.00 dB [8]. Table 4.9 shows the CNIR for both cases by using the interferences values obtained from simulations. For user downlinks, it was used the 3F1P scheme with a beamwidth (✓BW ) of 0.32. As a result, the combined CNIR for the forward link was 17.43 dB for the maximum co-channel CIR (⇣co) for both feeder uplink and user downlink, which meant a margin of 3.93 dB over the required value of 13.50 dB [8]. Figure 4.8 depicts the link margin as a function of co-channel CIR that ranges from 12.00 to 25.00 dB. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .52 (a) ✓BW = 0.26 (b) ✓BW = 0.32 (c) ✓BW = 0.40 (d) ✓BW = 0.48 Figure 4.6: The 3-color frequency-reuse schemes over the Mexico region with 4 different beamwidths. It is important to note that around 17.60 dB of co-channel CIR is required to obtain a positive margin. The co-channel CIR for the user downlink is much lower than the feeder uplink CIR, for this reason, it is a significant challenge and limiting factor so that it is necessary to further studies to improve the CIR antenna. In conclusion, these evaluations of offset-parabolic-antennas give excellent results but it is imperative to carry out real trials in order to obtain a more propitious scenario. All calculations in this thesis were performed on an Intel Core i5 2⇥ 2.70 GHz machine with 8 GB RAM. 4.6 Contributions of the Research The results of this Chapter were published for The International Journal Of Engineering and Science and Congreso Internacional de Computacion y Telecomunicaciones, COMTEL, as follows. However, It is important to mention that CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .53 Table 4.8: The CIR Evaluation for the 4-color Frequency-reuse Scheme. Denom. Values ✓BW 0.48 0.40 0.32 0.26 rc ⇡ 150 km ⇡ 125 km ⇡ 100 km ⇡ 80 km Dant 2.19 m 2.63 m 3.28 m 4.10 m EI 12.39 dB 12.39 dB 12.39 dB 12.39 dB ACI 30.00 dB 30.00 dB 30.00 dB 30.00 dB XPiso 27.39 dB 27.33 dB 27.25 dB 27.16 dB Results Denom. 4F1P Scheme ⇣co 18.95 dB 18.95 dB 18.95 dB 18.94 dB ⇣adj 25.49 dB 25.45 dB 25.40 dB 25.34 dB ⇣1/⇣co+1/⇣adj 18.07 dB 18.07 dB 18.06 dB 18.04 dB Denom. 4F2P Scheme ⇣co 18.95 dB 18.95 dB 18.95 dB 18.94 dB ⇣adj 23.14 dB 23.09 dB 23.03 dB 22.96 dB ⇣1/⇣co+1/⇣adj 17.54 dB 17.53 dB 17.51 dB 17.49 dB Crossover level 3.84 dB 3.96 dB 4.07 dB 4.13 dB Table 4.9: The CNIR Values for the Forward Link. Feeder Uplink User Downlink Parameters Values Parameters Values CNR 32.36 dB CNR 24.61 dB ⇣co 36.09 dB ⇣co 21.20 dB ⇣adj 38.17 dB ⇣adj 25.40 dB ⇣im 25.00 dB CNIRup 30.09 dB CNIRdn 17.67 dB the conference proceedings were published in "Revista de Tecnología e Información" by Universidad Inca Garcilaso de la Vega, Lima-Peru. • Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez-Rodriguez, and Jose M Matias. Interference Evaluations in Frequency Reuse by Using Offset- Parabolic-Reflector Antennas for a UHTS System. Int. J. Eng. Sci., 7(8):34–45, 2018. • Andres Cornejo, Salvador Landeros-Ayala, Ramon Martínez Rodríguez-Osorio, and Jose M Matias. A method for designing an offset-parabolic-reflector antenna for a ultra-high throughput satellite. In Rev. Tecnol. e Inf., volume 16, pages 84–87, Lima, Peru, 2018. Universidad Inca Garcilaso de la Vega. CHAPTER 4. INTERFERENCE EVALUATIONS IN FREQUENCY REUSE . . .54 (a) ✓BW = 0.26 (b) ✓BW = 0.32 (c) ✓BW = 0.40 (d) ✓BW = 0.48 Figure 4.7: The 4-color frequency-reuse schemes over the Mexico region with 4 different beamwidths. L in k M ar g in [ d B ] -5.00 -3.75 -2.50 -1.25 0.00 1.25 2.50 3.75 5.00 Co-channel CIR [dB] 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Figure 4.8: Forward link margin vs. co-channel CIR. Chapter 5 Method of Rain Attenuation Prediction Based On Long-Short Term Memory Network 5.1 Introduction Satellite communication links operate at different frequency bands such as L band, C band, and higher. Despite the higher frequency bands have more available spectrum, the satellite links are more susceptible to weather impairments, especially the rain attenuation. For this reason, a lot of research has been carried out in order to find accurate models of rain attenuation, whose methods have been developed by stochastic processes [37,68,69]. The Maseng-Bakken model is currently employed for the International Telecommunication Union (ITU) and its Recommendation ITU-R P.1853 [38]. Other researchers have been performed experimental models, such as the Prévision d’Ensemble ARPEGE (PEARP) system by Météo-France [15] and fade mitigation experiments for the ALPHASAT Satellite [70]. However, the main problem is the lack of historical rain database for each location and very few experimental models so that the stochastic models are the only theoretical methods in order to determine the main implications of the rain attenuation over satellite links. Nowadays, Machine Learning techniques are employed by several real-world applications as well as theoretical problems, especially in clustering, classification, and regression problems. To be specific, Machine learning is the study of computer algorithms that improve automatically through experience. It is related to a subfield of computer sciences and is considered a subset of artificial intelligence. In this context, a novel method is proposed in this thesis by a machine learning method, to be precise, a deep learning technique. Thereby, the Long-short Term Memory (LSTM) network is a deep learning technique and predicts, accurately, events of rain-attenuation without relying on either mathematical or stochastic models. The main objective is to train and validate the proposed models based on LSTM networks by using artificial rain attenuation time-series at the input. That is, the model learns from experience where the deep learning algorithms employ advanced 55 CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 56 computational methods in order to learn directly from input data without appealing to predetermined models or equations. Moreover, the rain-attenuation outcomes are useful to determine the status-in-advance of the satellite link and to anticipate a sudden link outage due to heavy rain. Indeed, it is important to obtain reliable results with the aim of guaranteeing the availability of satellite links and improving mechanisms such as the satellite link switching [71–73], site diversity on the ground segment [14, 22, 26], and uplink power control (ULPC) on satellite links [74–76], especially in extremely high-frequency bands (EHF). Finally, a comparison with other methods/models is employed to determine the best model in terms of performance, generalization, and accuracy. 5.2 Implementation of the Proposed Deep Learning Method Based on LSTM Network 5.2.1 Deep Learning Network: Model Architecture LSTM is based on a recurrent architecture network, which is designed to overcome error back-flow problems. An LSTM layer is able to support sequence data and time series in a network. Despite the input sequence data can be either noisy or incompressible, the LSTM network can learn to join time intervals in excess of 1000 steps without losing short-time-capabilities [77]. This is possible by an efficient gradient-based algorithm. In this thesis, there is a need to predict the values of future time steps of the input time-series. Therefore, the input time-series are trained by the proposed LSTM network with sequence-to-sequence mode, where the output data are sequences with values shifted by a one time step. In other words, the LSTM network learns to predict the value of the next time step, t + 1, for each time step, t, of the input time-series sequence. A. The Architecture of a Single LSTM Cell Consider a dataset x = (x(1),x(2), . . . ,x(m)), where each element is a vector (sequence) x(m) 2 R K , and m is the number of examples of each dataset. For simplicity and readability, this general approach only considers m = 1 examples in dataset x. Figure 5.1 depicts the architecture of a single LSTM cell, providing two recurrent features (LSTM cell outputs). The outputs are also known as the hidden (ht) and cell (ct) states. For this purpose, let U = [0, 1] indicate the unit interval, whereas let ±U = [1, 1]. Denoted by L, the LSTM cell is a mathematical function that enables three inputs and generates two outputs. The LSTM cell function can be expressed as (ht, ct) = L(ht1, ct1,xt), (5.1) where ht, ht1, ct, ct1 2 ±U and the input vector xt 2 R K [77, 78]. In order to compute the first output and updated cell state, the initial state of the cell and the CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 57 Forget Update Output ht−1 ∈ ±U AAACAXicbVBNS8NAEN34WetX1IvgZbEIXixJFfRY9OKxgmkLTQib7aZdursJuxuhhHrxr3jxoIhX/4U3/42bNgdtfTDweG+GmXlRyqjSjvNtLS2vrK6tVzaqm1vbO7v23n5bJZnExMMJS2Q3QoowKoinqWakm0qCeMRIJxrdFH7ngUhFE3GvxykJOBoIGlOMtJFC+3AY5vrMnfhUQD/lPkd6GEW5NwntmlN3poCLxC1JDZRohfaX309wxonQmCGleq6T6iBHUlPMyKTqZ4qkCI/QgPQMFYgTFeTTDybwxCh9GCfSlNBwqv6eyBFXaswj01lcqOa9QvzP62U6vgpyKtJME4Fni+KMQZ3AIg7Yp5JgzcaGICypuRXiIZIIaxNa1YTgzr+8SNqNunteb9xd1JrXZRwVcASOwSlwwSVoglvQAh7A4BE8g1fwZj1ZL9a79TFrXbLKmQPwB9bnD1d3ltM= ct−1 ∈ ±U AAACAXicbVBNS8NAEN34WetX1IvgZbEIXixJFfRY9OKxgmkLTQib7bZdursJuxuhhHjxr3jxoIhX/4U3/42bNgdtfTDweG+GmXlRwqjSjvNtLS2vrK6tVzaqm1vbO7v23n5bxanExMMxi2U3QoowKoinqWakm0iCeMRIJxrfFH7ngUhFY3GvJwkJOBoKOqAYaSOF9iEOM33m5j4V0E+4z5EeRVHm5aFdc+rOFHCRuCWpgRKt0P7y+zFOOREaM6RUz3USHWRIaooZyat+qkiC8BgNSc9QgThRQTb9IIcnRunDQSxNCQ2n6u+JDHGlJjwyncWFat4rxP+8XqoHV0FGRZJqIvBs0SBlUMewiAP2qSRYs4khCEtqboV4hCTC2oRWNSG48y8vknaj7p7XG3cXteZ1GUcFHIFjcApccAma4Ba0gAcweATP4BW8WU/Wi/Vufcxal6xy5gD8gfX5A09wls4= × AAAB7XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Ae0oWy2m3btZhN2J0IJ/Q9ePCji1f/jzX/jts1BWx8MPN6bYWZekEhh0HW/ncLa+sbmVnG7tLO7t39QPjxqmTjVjDdZLGPdCajhUijeRIGSdxLNaRRI3g7GtzO//cS1EbF6wEnC/YgOlQgFo2ilVg9FxE2/XHGr7hxklXg5qUCORr/81RvELI24QiapMV3PTdDPqEbBJJ+WeqnhCWVjOuRdSxW1S/xsfu2UnFllQMJY21JI5urviYxGxkyiwHZGFEdm2ZuJ/3ndFMNrPxMqSZErtlgUppJgTGavk4HQnKGcWEKZFvZWwkZUU4Y2oJINwVt+eZW0alXvolq7v6zUb/I4inACp3AOHlxBHe6gAU1g8AjP8ApvTuy8OO/Ox6K14OQzx/AHzucPt3mPOA== ct ∈ ±U AAAB/nicbVBPS8MwHE39O+e/qnjyEhyCp9FOQY9DLx4n2G2wlpJm6RaWpCVJhVEKfhUvHhTx6ufw5rcx3XrQzQeBx3u/H7+XF6WMKu0439bK6tr6xmZtq769s7u3bx8cdlWSSUw8nLBE9iOkCKOCeJpqRvqpJIhHjPSiyW3p9x6JVDQRD3qakoCjkaAxxUgbKbSPcZjrwqfCT7nPkR5HUe4Vod1wms4McJm4FWmACp3Q/vKHCc44ERozpNTAdVId5Ehqihkp6n6mSIrwBI3IwFCBOFFBPotfwDOjDGGcSPOEhjP190aOuFJTHpnJMqFa9ErxP2+Q6fg6yKlIM00Enh+KMwZ1Assu4JBKgjWbGoKwpCYrxGMkEdamsbopwV388jLptpruRbN1f9lo31R11MAJOAXnwAVXoA3uQAd4AIMcPINX8GY9WS/Wu/UxH12xqp0j8AfW5w8RtpYy ht ∈ ±U AAAB/nicbVBPS8MwHE39O+e/qnjyEhyCp9FOQY9DLx4n2G2wlpJm6RaWpCVJhVEKfhUvHhTx6ufw5rcx3XrQzQeBx3u/H7+XF6WMKu0439bK6tr6xmZtq769s7u3bx8cdlWSSUw8nLBE9iOkCKOCeJpqRvqpJIhHjPSiyW3p9x6JVDQRD3qakoCjkaAxxUgbKbSPx2GuC58KP+U+R3ocRblXhHbDaTozwGXiVqQBKnRC+8sfJjjjRGjMkFID10l1kCOpKWakqPuZIinCEzQiA0MF4kQF+Sx+Ac+MMoRxIs0TGs7U3xs54kpNeWQmy4Rq0SvF/7xBpuPrIKcizTQReH4ozhjUCSy7gEMqCdZsagjCkpqsEI+RRFibxuqmBHfxy8uk22q6F83W/WWjfVPVUQMn4BScAxdcgTa4Ax3gAQxy8AxewZv1ZL1Y79bHfHTFqnaOwB9Ynz8ZrpY3 + AAAB6HicbVDLSgNBEOyNrxhfUY9eBoMgCGE3CnoMevGYgHlAsoTZSW8yZnZ2mZkVQsgXePGgiFc/yZt/4yTZgyYWNBRV3XR3BYng2rjut5NbW9/Y3MpvF3Z29/YPiodHTR2nimGDxSJW7YBqFFxiw3AjsJ0opFEgsBWM7mZ+6wmV5rF8MOME/YgOJA85o8ZK9YteseSW3TnIKvEyUoIMtV7xq9uPWRqhNExQrTuemxh/QpXhTOC00E01JpSN6AA7lkoaofYn80On5MwqfRLGypY0ZK7+npjQSOtxFNjOiJqhXvZm4n9eJzXhjT/hMkkNSrZYFKaCmJjMviZ9rpAZMbaEMsXtrYQNqaLM2GwKNgRv+eVV0qyUvctypX5Vqt5mceThBE7hHDy4hircQw0awADhGV7hzXl0Xpx352PRmnOymWP4A+fzB3LTjLM= × AAAB7XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Ae0oWy2m3btZhN2J0IJ/Q9ePCji1f/jzX/jts1BWx8MPN6bYWZekEhh0HW/ncLa+sbmVnG7tLO7t39QPjxqmTjVjDdZLGPdCajhUijeRIGSdxLNaRRI3g7GtzO//cS1EbF6wEnC/YgOlQgFo2ilVg9FxE2/XHGr7hxklXg5qUCORr/81RvELI24QiapMV3PTdDPqEbBJJ+WeqnhCWVjOuRdSxW1S/xsfu2UnFllQMJY21JI5urviYxGxkyiwHZGFEdm2ZuJ/3ndFMNrPxMqSZErtlgUppJgTGavk4HQnKGcWEKZFvZWwkZUU4Y2oJINwVt+eZW0alXvolq7v6zUb/I4inACp3AOHlxBHe6gAU1g8AjP8ApvTuy8OO/Ox6K14OQzx/AHzucPt3mPOA== xt ∈ R K AAACBXicbVC7TsMwFHXKq5RXgBEGiwqJqUoKEowVLEgsBdGH1ITIcZ3WquNEtoOooiws/AoLAwix8g9s/A1OmwFajmTp+Jx7de89fsyoVJb1bZQWFpeWV8qrlbX1jc0tc3unLaNEYNLCEYtE10eSMMpJS1HFSDcWBIU+Ix1/dJH7nXsiJI34rRrHxA3RgNOAYqS05Jn7TojU0A/Sh8xTDuVw+vfTm+zuyjOrVs2aAM4TuyBVUKDpmV9OP8JJSLjCDEnZs61YuSkSimJGsoqTSBIjPEID0tOUo5BIN51ckcFDrfRhEAn9uIIT9XdHikIpx6GvK/Md5ayXi/95vUQFZ25KeZwowvF0UJAwqCKYRwL7VBCs2FgThAXVu0I8RAJhpYOr6BDs2ZPnSbtes49r9euTauO8iKMM9sABOAI2OAUNcAmaoAUweATP4BW8GU/Gi/FufExLS0bRswv+wPj8AQnkmOg= × AAAB7XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Ae0oWy2m3btZhN2J0IJ/Q9ePCji1f/jzX/jts1BWx8MPN6bYWZekEhh0HW/ncLa+sbmVnG7tLO7t39QPjxqmTjVjDdZLGPdCajhUijeRIGSdxLNaRRI3g7GtzO//cS1EbF6wEnC/YgOlQgFo2ilVg9FxE2/XHGr7hxklXg5qUCORr/81RvELI24QiapMV3PTdDPqEbBJJ+WeqnhCWVjOuRdSxW1S/xsfu2UnFllQMJY21JI5urviYxGxkyiwHZGFEdm2ZuJ/3ndFMNrPxMqSZErtlgUppJgTGavk4HQnKGcWEKZFvZWwkZUU4Y2oJINwVt+eZW0alXvolq7v6zUb/I4inACp3AOHlxBHe6gAU1g8AjP8ApvTuy8OO/Ox6K14OQzx/AHzucPt3mPOA== tanh AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGCaQttKJvtpl262YTdiVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXplIYdN1vZ219Y3Nru7RT3t3bPzisHB23TJJpxn2WyER3Qmq4FIr7KFDyTqo5jUPJ2+H4bua3n7g2IlGPOEl5ENOhEpFgFK3k95CqUb9SdWvuHGSVeAWpQoFmv/LVGyQsi7lCJqkxXc9NMcipRsEkn5Z7meEpZWM65F1LFY25CfL5sVNybpUBiRJtSyGZq78nchobM4lD2xlTHJllbyb+53UzjG6CXKg0Q67YYlGUSYIJmX1OBkJzhnJiCWVa2FsJG1FNGdp8yjYEb/nlVdKq17zLWv3hqtq4LeIowSmcwQV4cA0NuIcm+MBAwDO8wpujnBfn3flYtK45xcwJ/IHz+QPcCI63 fgt AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGC/YA2hM120y7dbMLuRCihP8KLB0W8+nu8+W/ctjlo64OBx3szzMwLUykMuu63s7a+sbm1Xdop7+7tHxxWjo7bJsk04y2WyER3Q2q4FIq3UKDk3VRzGoeSd8Lx3czvPHFtRKIecZJyP6ZDJSLBKFqpEwX5MMBpUKm6NXcOskq8glShQDOofPUHCctirpBJakzPc1P0c6pRMMmn5X5meErZmA55z1JFY278fH7ulJxbZUCiRNtSSObq74mcxsZM4tB2xhRHZtmbif95vQyjGz8XKs2QK7ZYFGWSYEJmv5OB0JyhnFhCmRb2VsJGVFOGNqGyDcFbfnmVtOs177JWf7iqNm6LOEpwCmdwAR5cQwPuoQktYDCGZ3iFNyd1Xpx352PRuuYUMyfwB87nD5ZWj7s= igt AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGC/YA2hM120y7dbMLuRCihP8KLB0W8+nu8+W/ctjlo64OBx3szzMwLUykMuu63s7a+sbm1Xdop7+7tHxxWjo7bJsk04y2WyER3Q2q4FIq3UKDk3VRzGoeSd8Lx3czvPHFtRKIecZJyP6ZDJSLBKFqpI4J8GOA0qFTdmjsHWSVeQapQoBlUvvqDhGUxV8gkNabnuSn6OdUomOTTcj8zPKVsTIe8Z6miMTd+Pj93Ss6tMiBRom0pJHP190ROY2MmcWg7Y4ojs+zNxP+8XobRjZ8LlWbIFVssijJJMCGz38lAaM5QTiyhTAt7K2EjqilDm1DZhuAtv7xK2vWad1mrP1xVG7dFHCU4hTO4AA+uoQH30IQWMBjDM7zCm5M6L86787FoXXOKmRP4A+fzB5r0j74= cut AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGC/YA2hM120y7dbMLuRCihP8KLB0W8+nu8+W/ctjlo64OBx3szzMwLUykMuu63s7a+sbm1Xdop7+7tHxxWjo7bJsk04y2WyER3Q2q4FIq3UKDk3VRzGoeSd8Lx3czvPHFtRKIecZJyP6ZDJSLBKFqpw4I8C3AaVKpuzZ2DrBKvIFUo0AwqX/1BwrKYK2SSGtPz3BT9nGoUTPJpuZ8ZnlI2pkPes1TRmBs/n587JedWGZAo0bYUkrn6eyKnsTGTOLSdMcWRWfZm4n9eL8Poxs+FSjPkii0WRZkkmJDZ72QgNGcoJ5ZQpoW9lbAR1ZShTahsQ/CWX14l7XrNu6zVH66qjdsijhKcwhlcgAfX0IB7aEILGIzhGV7hzUmdF+fd+Vi0rjnFzAn8gfP5A6caj8Y= ogt AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGC/YA2hM120y7dbMLuRCihP8KLB0W8+nu8+W/ctjlo64OBx3szzMwLUykMuu63s7a+sbm1Xdop7+7tHxxWjo7bJsk04y2WyER3Q2q4FIq3UKDk3VRzGoeSd8Lx3czvPHFtRKIecZJyP6ZDJSLBKFqpkwT5MMBpUKm6NXcOskq8glShQDOofPUHCctirpBJakzPc1P0c6pRMMmn5X5meErZmA55z1JFY278fH7ulJxbZUCiRNtSSObq74mcxsZM4tB2xhRHZtmbif95vQyjGz8XKs2QK7ZYFGWSYEJmv5OB0JyhnFhCmRb2VsJGVFOGNqGyDcFbfnmVtOs177JWf7iqNm6LOEpwCmdwAR5cQwPuoQktYDCGZ3iFNyd1Xpx352PRuuYUMyfwB87nD6Qwj8Q= L AAAB8nicbVDLSgMxFL1TX7W+qi7dBIvgqsxUQZdFNy5cVLAPmA4lk2ba0EwyJBmhDP0MNy4UcevXuPNvzLSz0NYDgcM595JzT5hwpo3rfjultfWNza3ydmVnd2//oHp41NEyVYS2ieRS9UKsKWeCtg0znPYSRXEcctoNJ7e5332iSjMpHs00oUGMR4JFjGBjJb8fYzMmmGf3s0G15tbdOdAq8QpSgwKtQfWrP5QkjakwhGOtfc9NTJBhZRjhdFbpp5ommEzwiPqWChxTHWTzyDN0ZpUhiqSyTxg0V39vZDjWehqHdjKPqJe9XPzP81MTXQcZE0lqqCCLj6KUIyNRfj8aMkWJ4VNLMFHMZkVkjBUmxrZUsSV4yyevkk6j7l3UGw+XteZNUUcZTuAUzsGDK2jCHbSgDQQkPMMrvDnGeXHenY/FaMkpdo7hD5zPH4JTkWY= Figure 5.1: A single LSTM cell diagram [78]. first time step of the sequence are used by the LSTM cell. That is, the current state of the cell, at time step t, is employed by the LSTM cell (ht1, ct1,), whereas the next time step of the sequence is used to compute the output state ht, in addition to updating the cell state ct. Therefore, the hidden and cell states are part of the state of the cell. At time step t, ht and ct states are left at the output so that the same cell can be fed back by these states at time step t + 1. It is important to mention that an element of the input sequence x ∈ R K is also fed into the cell any time step t [78]. Meanwhile, the learned information from previous time steps is contained in the cell state. In summary, the cell appends information to or deletes information from the cell state at each time step, in other words, the cell is able to control these updates employing gates. For this purpose, the flow of data plays an important role in the LSTM cell, where the hidden state, ht1 ∈ ±U, and the input vector, xt ∈ R K , feed three gates (functions), as can be seen in Figure 5.1. At the time t, the three gates (forget, input, and output functions) are respectively given by fgt(xt, ht1) = g(wx T f xt + whf ht1 + bf ) ∈ U, (5.2) igt(xt, ht1) = g(wx T i xt + whi ht1 + bi) ∈ U, (5.3) ogt(xt, ht1) = g(wx T o xt + who ht1 + bo) ∈ U, (5.4) where g is the gate activation function, wxf ,wxi,wxo ∈ R K are the weight vectors, and whf , whi , who , bf , bi, bo ∈ R are the recurrent weights and biases, respectively. During the training process of the cell, the weights are capable of learning. By default, g is based on the sigmoid function to compute the gate activation function. For this reason, the gates of a single LSTM cell produce scalar values. Figure 5.1 stands out how the gates forget, update, and output the cell and hidden states. These three CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 58 gates can be interpreted as switches, that is, if their outputs are near 1, then they are on. Otherwise, when the outputs are close to 0, then they are off. Furthermore, the cell update function is built from a single neuron, which, at time step t, is expressed as cut (xt, ht1) = tanh(wx Txt + whht1 + b) 2 ±U, (5.5) where tanh is the state activation function, wx 2 R K is the weight vector, and wh, b 2 R are the recurrent weights and bias, respectively. Also, these weight parameters are learned in the training process. The state activation function is based on the hyperbolic tangent function, which is also set by default. Specifically, the tanh and sigmoid activation functions are discussed in Section 5.2.2. Finally, the forget gate, fg, controls the level of the cell state reset (forget), whereas the input gate, ig, controls the level of the cell state update, cu, that adds it to the cell state. Moreover, the output gate, og, controls the modified cell state to become the next hidden state [77, 78]. As a result, the new cell and hidden states, at time step t, can be expressed as ct = fgt · ct1 + igt · cut 2 ±U, (5.6) ht = ogt · tanh(ct) 2 ±U, (5.7) where both values are scalars. For readability, it is important to note that all of these functions and parameters are encapsulated in the function L, as can be seen in Eq. (5.1). B. The Architecture of a Layer of LSTM Cells Figure 5.2 illustrates a layer composed of several LSTM cells U , also known as the number of hidden units, and features C. For this purpose, the LSTM layer, denoted by LU , is the concatenation of LSTM cells, L1,L2, . . . ,LU , creating an LSTM Block. At time step t, both hidden, ht, and cell, ct, states indicate the LSTM Block output. Each cell has a different set of weight parameters, thus, the mathematical expression of the LSTM layer is given by (h1t , c1t) = L1(h1(t−1) , c1(t−1) ,xt), (h2t , c2t) = L2(h2(t−1) , c2(t−1) ,xt), ... (hUt , cUt ) = LU(hU(t−1) , cU(t−1) ,xt), therefore, the expression can be also rewritten as (ht, ct) = LU(ht1, ct1,xt), (5.8) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 59 Number of Hidden Units Number of Features Number of Time Steps LU AAAB9HicbVBNS8NAFHypX7V+RT16WSyCp5JUQY9FLx48VDBtoQ1ls920SzebuLsplNDf4cWDIl79Md78N27aHLR1YGGYeY83O0HCmdKO822V1tY3NrfK25Wd3b39A/vwqKXiVBLqkZjHshNgRTkT1NNMc9pJJMVRwGk7GN/mfntCpWKxeNTThPoRHgoWMoK1kfxehPWIYJ7dz/pe3646NWcOtErcglShQLNvf/UGMUkjKjThWKmu6yTaz7DUjHA6q/RSRRNMxnhIu4YKHFHlZ/PQM3RmlAEKY2me0Giu/t7IcKTUNArMZB5SLXu5+J/XTXV47WdMJKmmgiwOhSlHOkZ5A2jAJCWaTw3BRDKTFZERlpho01PFlOAuf3mVtOo196JWf7isNm6KOspwAqdwDi5cQQPuoAkeEHiCZ3iFN2tivVjv1sditGQVO8fwB9bnD+Z3ki4= c t−1 h t−1 c t h t LU AAAB9HicbVBNS8NAFHypX7V+RT16WSyCp5JUQY9FLx48VDBtoQ1ls920SzebuLsplNDf4cWDIl79Md78N27aHLR1YGGYeY83O0HCmdKO822V1tY3NrfK25Wd3b39A/vwqKXiVBLqkZjHshNgRTkT1NNMc9pJJMVRwGk7GN/mfntCpWKxeNTThPoRHgoWMoK1kfxehPWIYJ7dz/pe3646NWcOtErcglShQLNvf/UGMUkjKjThWKmu6yTaz7DUjHA6q/RSRRNMxnhIu4YKHFHlZ/PQM3RmlAEKY2me0Giu/t7IcKTUNArMZB5SLXu5+J/XTXV47WdMJKmmgiwOhSlHOkZ5A2jAJCWaTw3BRDKTFZERlpho01PFlOAuf3mVtOo196JWf7isNm6KOspwAqdwDi5cQQPuoAkeEHiCZ3iFN2tivVjv1sditGQVO8fwB9bnD+Z3ki4= LU AAAB9HicbVBNS8NAFHypX7V+RT16WSyCp5JUQY9FLx48VDBtoQ1ls920SzebuLsplNDf4cWDIl79Md78N27aHLR1YGGYeY83O0HCmdKO822V1tY3NrfK25Wd3b39A/vwqKXiVBLqkZjHshNgRTkT1NNMc9pJJMVRwGk7GN/mfntCpWKxeNTThPoRHgoWMoK1kfxehPWIYJ7dz/pe3646NWcOtErcglShQLNvf/UGMUkjKjThWKmu6yTaz7DUjHA6q/RSRRNMxnhIu4YKHFHlZ/PQM3RmlAEKY2me0Giu/t7IcKTUNArMZB5SLXu5+J/XTXV47WdMJKmmgiwOhSlHOkZ5A2jAJCWaTw3BRDKTFZERlpho01PFlOAuf3mVtOo196JWf7isNm6KOspwAqdwDi5cQQPuoAkeEHiCZ3iFN2tivVjv1sditGQVO8fwB9bnD+Z3ki4= Initial State Final State LSTM Block LU AAAB9HicbVBNS8NAFHypX7V+RT16WSyCp5JUQY9FLx48VDBtoQ1ls920SzebuLsplNDf4cWDIl79Md78N27aHLR1YGGYeY83O0HCmdKO822V1tY3NrfK25Wd3b39A/vwqKXiVBLqkZjHshNgRTkT1NNMc9pJJMVRwGk7GN/mfntCpWKxeNTThPoRHgoWMoK1kfxehPWIYJ7dz/pe3646NWcOtErcglShQLNvf/UGMUkjKjThWKmu6yTaz7DUjHA6q/RSRRNMxnhIu4YKHFHlZ/PQM3RmlAEKY2me0Giu/t7IcKTUNArMZB5SLXu5+J/XTXV47WdMJKmmgiwOhSlHOkZ5A2jAJCWaTw3BRDKTFZERlpho01PFlOAuf3mVtOo196JWf7isNm6KOspwAqdwDi5cQQPuoAkeEHiCZ3iFN2tivVjv1sditGQVO8fwB9bnD+Z3ki4= LSTM Block LSTM Block LSTM Layer ……LSTM Block x11 x21 ... xC1 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AAACOXicbZDLSsNAFIYnXmu8VV26CRbBVUmqoEvRjcsKtgpNCJPJSTs4mYSZk2IJfS03voU7wY0LRdz6Ak7bLLwdGPj4z23OH+WCa3TdJ2tufmFxabm2Yq+urW9s1re2uzorFIMOy0SmbiKqQXAJHeQo4CZXQNNIwHV0ez7JXw9BaZ7JKxzlEKS0L3nCGUUjhfW2LyDBnu1H0OeypErR0bhkY/suLL2wNfb9CbVm5A/jDPVMOjeS7YOMqx7bV7w/wCCsN9ymOw3nL3gVNEgV7bD+6McZK1KQyATVuue5OQZmKnImwMwtNOSU3dI+9AxKmoIOyunlY2ffKLGTZMo8ic5U/d5R0lTrURqZypTiQP/OTcT/cr0Ck5Og5DIvECSbLUoK4WDmTGx0Yq6AoRgZoExx81eHDaiiDI3ZtjHB+33yX+i2mt5hs3V51Dg9q+yokV2yRw6IR47JKbkgbdIhjNyTZ/JK3qwH68V6tz5mpXNW1bNDfoT1+QVkgK1F x1t x2t . . . xCt 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 x1K x2K . . . xCK 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 h11 h21 . . . hU1 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 h12 h22 . . . hU2 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 h1t h2t . . . hUt 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 h1K h2K . . . hUK 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 Figure 5.2: The architecture of an LSTM layer [77]. where ht,ht1, ct, ct1 2 ±U U , and xt 2 R K . As a result, the cell and hidden states, at time step t, can be respectively given by ct = fgt ct1 + igt cut 2 ±U U , (5.9) ht = ogt tanh(ct) 2 ±U U , (5.10) where is the Hadamard product, that is the element-wise multiplication of vectors. Moreover, the dot products become matrix-vector products. Here, the individual weight vectors and biases from each LSTM cells can be stored in matrices. Therefore, the three gates and the cell update function contain weight matrices, Wxf ,Wxi,Wxo,Wx 2 R U⇥K , respectively. Meanwhile, the stacked hidden state is a U -dimensional vector, therefore, the gates contain recurrent weight matrices, Whf ,Whi,Who,Wh 2 R U⇥U , and bias vectors bf ,bi,bo,b 2 R U [78]. As a shorthand, all parameters of the LSTM network are usually concatenated and expressed as a whole by parameter ΘL [79]. For notational convenience, the parameter ΘL can be written as ΘL ⌘ 8 > > < > > : Wxf , Whf , bf Wxi, Whi, bi Wxo, Who, bo Wx, Wh, b 9 > > = > > ; (5.11) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 60 C. The Architecture of an LSTM Multi-Layer Network In this case, multiple layers could improve the output accuracy, increasing the LSTM network complexity. At time step t, the function LU has two outputs ht, ct 2 U U , thereby, the next LSTM layer can be sequentially fed by the hidden state from the previous LSTM layer. Figure 5.3 depicts how the states pass through an LSTM multi-layer network. 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AAACAHicbVBNS8NAEJ34WetX1IMHL8Ei1IMlaQU9Fr14rGDaQhvCZrtpl242YXcjlJCLf8WLB0W8+jO8+W/ctD1o64OBx3szzMwLEkalsu1vY2V1bX1js7RV3t7Z3ds3Dw7bMk4FJi6OWSy6AZKEUU5cRRUj3UQQFAWMdILxbeF3HomQNOYPapIQL0JDTkOKkdKSbx73I6RGQZjh3M/chp9V1YVznue+WbFr9hTWMnHmpAJztHzzqz+IcRoRrjBDUvYcO1FehoSimJG83E8lSRAeoyHpacpRRKSXTR/IrTOtDKwwFrq4sqbq74kMRVJOokB3FufKRa8Q//N6qQqvvYzyJFWE49miMGWWiq0iDWtABcGKTTRBWFB9q4VHSCCsdGZlHYKz+PIyaddrTqNWv7+sNG/mcZTgBE6hCg5cQRPuoAUuYMjhGV7hzXgyXox342PWumLMZ47gD4zPHyBtlhc= ... AAAB7XicbVBNS8NAEJ3Ur1q/qh69BIvgqSRV0GPRi8cKthbaUDabTbt2sxt2J4VS+h+8eFDEq//Hm//GbZuDtj4YeLw3w8y8MBXcoOd9O4W19Y3NreJ2aWd3b/+gfHjUMirTlDWpEkq3Q2KY4JI1kaNg7VQzkoSCPYbD25n/OGLacCUfcJyyICF9yWNOCVqp1R1FCk2vXPGq3hzuKvFzUoEcjV75qxspmiVMIhXEmI7vpRhMiEZOBZuWuplhKaFD0mcdSyVJmAkm82un7plVIjdW2pZEd67+npiQxJhxEtrOhODALHsz8T+vk2F8HUy4TDNkki4WxZlwUbmz192Ia0ZRjC0hVHN7q0sHRBOKNqCSDcFffnmVtGpV/6Jau7+s1G/yOIpwAqdwDj5cQR3uoAFNoPAEz/AKb45yXpx352PRWnDymWP4A+fzB8y9j0Y= Figure 5.3: The architecture of an LSTM multi-layer [80]. For simplicity, an LSTM multi-layer network can be encapsulated by a function S, where ... (hU3t , cU3t) = LU3(hU3(t−1) , cU3(t−1) ,hU2t), (hU2t , cU2t) = LU2(hU2(t−1) , cU2(t−1) ,hU1t), (hU1t , cU1t) = LU1(hU1(t−1) , cU1(t−1) ,xt), can be given by (Ht,Ct) = S(Ht1,Ct1,xt). (5.12) It is important to mention that each layer can have a different number of LSTM units U1, U2, U3 . . . , so that the dimensions of the hidden and cell states can be uneven for each LSTM layer. At time step t, the variables Ht and Ct represent the collection of all hidden and cell states, respectively [78]. As can be seen, the LSTM multi-layer network is a larger model, containing a lot of stacked LSTM cells. For this CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 61 reason, the single and multiple layer LSTM networks can be employed in time-series forecasting [77,78,80], which is the aim of this thesis. D. The Architecture of the Proposed Deep Learning Network Figure 5.4 describes in detail the proposed LSTM layer where each input dataset obtained from ITU-R P.1853 [38], A0 i = (A0(1) t,i ,A 0(2) t,i , . . . ,A 0(m) t,i ) for i = 1, 2, . . . , N , and t = 1, 2, . . . , K, is made up of m examples, A0(m) t,i 2 R K , where K is the number of samples in each time-series, and N is the number of GW-sites on the ground segment. Here, each rain-attenuation time-series must be normalized to improve the convergence of the gradient descendent, for this reason, the input dataset of rain attenuation is denoted by A 0 i. Indeed, the normalization method is discussed in more detail in Section 5.2.2. In this thesis, each time series is a univariate sequence, that is, it is a single series of observations. Furthermore, each time series has a single feature, C = 1, and each dataset has 40 examples, i.e., m = {1, 2, . . . , 40}. Therefore, it is a many-to-one sequence problem with a single feature. Motivated by this, an LSTM network model is built in order to learn from the time series of past observations to predict the next value in the sequence. Number of Hidden Units c t−1 h t−1 c t h t Initial State Final State LSTM Layer ……LU AAAB9HicbVBNS8NAFHypX7V+RT16WSyCp5JUQY9FLx48VDBtoQ1ls920SzebuLsplNDf4cWDIl79Md78N27aHLR1YGGYeY83O0HCmdKO822V1tY3NrfK25Wd3b39A/vwqKXiVBLqkZjHshNgRTkT1NNMc9pJJMVRwGk7GN/mfntCpWKxeNTThPoRHgoWMoK1kfxehPWIYJ7dz/pe3646NWcOtErcglShQLNvf/UGMUkjKjThWKmu6yTaz7DUjHA6q/RSRRNMxnhIu4YKHFHlZ/PQM3RmlAEKY2me0Giu/t7IcKTUNArMZB5SLXu5+J/XTXV47WdMJKmmgiwOhSlHOkZ5A2jAJCWaTw3BRDKTFZERlpho01PFlOAuf3mVtOo196JWf7isNm6KOspwAqdwDi5cQQPuoAkeEHiCZ3iFN2tivVjv1sditGQVO8fwB9bnD+Z3ki4= LU 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The LSTM network can be made up of a single layer, LU , i.e, S = {LU} with hidden units, U , or multi-layer, S = {LU1,LU2,LU3, . . .} with different number of hidden units, U1, U2, U3, . . ., in each layer. For a single LSTM layer, the hidden and CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 62 cell states, with m examples and LSTM units U , are given by (ht, ct) = LU(ht1, ct1,A 0(m) t,i ), for 8 > < > : i = 1, 2, . . . , N t = 1, 2, . . . , K m = 1, 2, . . . , 40 (5.13) Meanwhile, the output function of the LSTM multi-layer network, S, is denoted by (Ht,Ct) = S(Ht1,Ct1,A 0(m) t,i ), for 8 > < > : i = 1, 2, . . . , N t = 1, 2, . . . , K m = 1, 2, . . . , 40 (5.14) As a result, the LSTM network presents K hidden states at the output, h1,h2, . . . ,ht, . . . ,hK 2 ±U U , increasing the network complexity by stacking several hidden outputs. However, it is important to find a single sequence at the output. For this purpose, dense layers can reduce from multiple inputs to a single output by an activation function either linear or non-linear. Figure 5.5 illustrates the proposed deep learning network, which connects the proposed LSTM network to the dense layer. To be precise, the obtained output is the predicted rain attenuation time-series, at the time step t+ 1, Â0 t+1,i 2 R K . 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AAACCXicbVBNS8NAEN3Ur1q/oh69LBbBU0mqoMeiF48VTFtoYthsN+3S3U3Y3Qgl9OrFv+LFgyJe/Qfe/Ddu2hy09cHA470ZZuZFKaNKO863VVlZXVvfqG7WtrZ3dvfs/YOOSjKJiYcTlshehBRhVBBPU81IL5UE8YiRbjS+LvzuA5GKJuJOT1IScDQUNKYYaSOFNvQ50qMozkfTsOlT4ad8rkS5N703Fdp1p+HMAJeJW5I6KNEO7S9/kOCME6ExQ0r1XSfVQY6kppiRac3PFEkRHqMh6RsqECcqyGefTOGJUQYwTqQpoeFM/T2RI67UhEems7hSLXqF+J/Xz3R8GeRUpJkmAs8XxRmDOoFFLHBAJcGaTQxBWFJzK8QjJBHWJryaCcFdfHmZdJoN96zRvD2vt67KOKrgCByDU+CCC9ACN6ANPIDBI3gGr+DNerJerHfrY95ascqZQ/AH1ucPha2a3A== ht ∈ ±U U AAACCXicbVBNS8NAEN3Ur1q/oh69LBbBU0mqoMeiF48VTFtoYthsN+3S3U3Y3Qgl9OrFv+LFgyJe/Qfe/Ddu2hy09cHA470ZZuZFKaNKO863VVlZXVvfqG7WtrZ3dvfs/YOOSjKJiYcTlshehBRhVBBPU81IL5UE8YiRbjS+LvzuA5GKJuJOT1IScDQUNKYYaSOFNvQ50qMozkfTUPtU+CmfK1HuTe9NhXbdaTgzwGXilqQOSrRD+8sfJDjjRGjMkFJ910l1kCOpKWZkWvMzRVKEx2hI+oYKxIkK8tknU3hilAGME2lKaDhTf0/kiCs14ZHpLK5Ui14h/uf1Mx1fBjkVaaaJwPNFccagTmARCxxQSbBmE0MQltTcCvEISYS1Ca9mQnAXX14mnWbDPWs0b8/rrasyjio4AsfgFLjgArTADWgDD2DwCJ7BK3iznqwX6936mLdWrHLmEPyB9fkD7t2bHg== hK ∈ ±U U AAACCXicbVBNS8NAEN34WetX1KOXxSJ4KkkV9Fj0InipYNpCE8Nmu2mX7m7C7kYooVcv/hUvHhTx6j/w5r9x0+agrQ8GHu/NMDMvShlV2nG+raXlldW19cpGdXNre2fX3ttvqySTmHg4YYnsRkgRRgXxNNWMdFNJEI8Y6USjq8LvPBCpaCLu9DglAUcDQWOKkTZSaEOfIz2M4nw4CW98KvyUz5Qo9yb3pkK75tSdKeAicUtSAyVaof3l9xOccSI0ZkipnuukOsiR1BQzMqn6mSIpwiM0ID1DBeJEBfn0kwk8Nkofxok0JTScqr8ncsSVGvPIdBZXqnmvEP/zepmOL4KcijTTRODZojhjUCewiAX2qSRYs7EhCEtqboV4iCTC2oRXNSG48y8vknaj7p7WG7dnteZlGUcFHIIjcAJccA6a4Bq0gAcweATP4BW8WU/Wi/Vufcxal6xy5gD8gfX5A62FmvU= A (m) t,i ∈ R K , for          i = 1, 2, . . . , N t = 1, 2, . . . ,K C = 1 m = 1, 2 . . . , 40 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  t+1,i ∈ R K 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 Figure 5.5: The architecture of the proposed deep learning network. For readability and simplicity, the proposed LSTM network is analyzed as a single LSTM layer, LU , where each output, also known as the hidden state at time step t, is a U -dimensional vector, ht 2 ±U U . The LSTM outputs become the inputs of the dense layer. In this context, the dense layer is a deeply connected neural network, where each connection can be typically considered as a multiple-input neuron [81,82]. Usually, the neuron’s output can be denoted by y = f(W · p + b), where W is the weight matrix, b is the bias, f is the activation function, and p is the input CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 63 vector [81–83]. In this thesis, the dense layer can be mathematically expressed as Â0 2,i = selu(wd T 1 · h1 + bd1) 2 R Â0 3,i = selu(wd T 2 · h2 + bd2) 2 R ... Â0 t+1,i = selu(wd T t · ht + bdt) 2 R ... Â0 K+1,i = selu(wd T K · hK + bdK ) 2 R where each value, Â0 t+1,i, is stored in the output vector. Therefore, the output of the dense layer is encapsulated and rewritten as Â0 t+1,i = D(ht) 2 R K , for ( i = 1, 2, . . . , N, t = 1, 2 . . . , K, (5.15) where D is the dense layer function and ht 2 ±U U for t = 1, 2, . . . , K, are the input vectors of the dense layer. The scaled-exponential-linear-unit (SELU) activation function is employed in this layer, which is discussed in more detail in Section 5.2.2. Moreover, Wd 2 R U⇥K is the weight matrix that contains each weight vector wdt 2 R U and bd 2 R K is the bias vector that includes each bias element bdt 2 R. Similarly to the LSTM network, the weight parameters of the dense layer are also learned during the training process. Furthermore, the weight parameters of the dense layer can be combined under one symbol ΘD [79], which is given by ΘD ⌘ {Wd,bd}. (5.16) Finally, the output vectors obtained from the proposed deep learning network can be stacked in the matrix, Â0 2 R K⇥N , whose predicted values of rain attenuation for each GW’s feeder uplink are contained within the matrix. To be specific, these values allow the Network Control Center (NCC) to know the feeder uplink status in advance, managing resources, e.g. gateway redundancy, to avoid link outages due to the heavy rain. 5.2.2 Deep Learning Network: Model Description A. Activation Functions The activation function is used to determine the nature of the output of a neural network, in addition to limiting the amplitude of the output of a neuron. That is, it can map the outcome values between 0 to 1, -1 to 1, yes or no, etc., depending upon the type of activation function. For this reason, the activation function can be divided into two types, linear and non-linear activation functions. Generally, the most frequent activation functions are non-linear functions because they can facilitate the generalization and adaptation of the model with a lot of varied data. The activation functions are also known as transfer functions and/or squashing functions [83, 84]. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 64 Usually, the most employed activation functions are in the following. • Sigmoid Activation Function: the sigmoid function, also known as logistic activation function, is especially used for models that are able to predict the probability at the output. For this purpose, the sigmoid function always returns a value between 0–1, therefore, it is ideal for probabilistic outputs [85]. The sigmoid activation function, (z), is given by (z) = 1 1 + exp(z) (5.17) Figure 5.6 depicts the sigmoid function, where, for small values (z < 5), the results of the sigmoid function get close to zero, and for large values (z > 5) the sigmoid function returns values close to 1. σ (z ) 0.00 0.25 0.50 0.75 1.00 z -5 -4 -3 -2 -1 0 1 2 3 4 5 Figure 5.6: Sigmoid activation function. The sigmoid function is differentiable, therefore, the slope of the sigmoid curve can be found at any two points. However, it is important to mention that the sigmoid function could provoke a jam at the training process [83]. Also, it is possible to assume that the sigmoid function is similar to a 2-element Softmax, where the second element is zero. Indeed, the softmax activation function for multiclass classification problems is based on the sigmoid function but with n-elements [85]. • Hyperbolic Tangent Activation Function: the hyperbolic tangent activation function (tanh) is similar to sigmoid function but with a wider range, which varies from -1 to 1. In this case, the negative inputs are directly mapped in the negative range whereas the zero inputs are mapped close to zero in the tanh function. Naturally, this is the main advantage of the tanh activation function. The tanh function is expressed as tanh(z) = sinh(z) cosh(z) = 1 1 + exp(2z) 1 (5.18) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 65 Figure 5.7 illustrates the tanh function, where it is possible to distinguish the range between -1 to 1. ta n h (z ) -1.00 -0.50 0.00 0.50 1.00 z -5 -4 -3 -2 -1 0 1 2 3 4 5 Figure 5.7: Hyperbolic tangent activation function. It is important to mention that the tanh function is differentiable, in addition to being mainly used in classification problems, especially, between two classes. Both sigmoid and tanh activation functions are used in feed-forward neural networks [83,85]. • Rectifier-Linear-Unit Activation Function: it is also known as ReLU, which is one of the most popular activation functions to use in machine learning algorithms. This activation function is especially employed in deep learning and convolutional neural networks [83]. The ReLU activation function expression is given by R(z) = max(0, z) = ( 0 for z < 0 z for z 0 (5.19) Figure 5.8 shows the ReLU activation function, which ranges from 0 to 1. In other words, the ReLU is half rectified, i.e., R(z) = 0 when z is less than zero (z < 0) and R(z) = z when z is above or equal to zero (z 0) [85]. However, this activation function can become a problem if there are negative input values, which turn into zero values. In a sense, this issue can affect the ability of the model to train or fit from the data. For this reason, the input data must be previously analyzed to apply the proper activation function. • Scaled-Exponential-Linear-Unit Activation Function: it is also known as SELU activation function, which is defined as selu(z) = selu · ( z for z 0 ↵selu[exp(z) 1] for z < 0 , (5.20) where selu and ↵selu are pre-defined constants (selu = 1.05070098 and ↵selu = 1.67326324) [85]. For the sake of simplicity, the SELU activation function CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 66 R (z ) 0.00 1.00 2.00 3.00 4.00 5.00 z -5 -4 -3 -2 -1 0 1 2 3 4 5 Figure 5.8: Rectifier-Linear-Unit activation function. multiplies scale (↵selu > 1) with the exponential and the linear functions to assure a slope larger than 1 for positive inputs. Figure 5.9 depicts the SELU activation function. The values of selu and ↵selu are chosen so that the mean and variance of the inputs are preserved between two consecutive layers as long as the weights are initialized correctly, in addition to the number of input units is large enough [85,86]. se lu (z ) -2.00 0.00 2.00 4.00 6.00 z -5 -4 -3 -2 -1 0 1 2 3 4 5 Figure 5.9: Scaled-Exponential-Linear-Unit activation function. Self-normalizing neural networks (SNN) use the SELU activation function, which is able to enable high-level abstract representations. SELU activation functions induce self-normalizing properties, improving the convergence and accuracy, in addition to being widely used in machine learning and deep learning models. [86]. To sum up, the choice of the best activation function depends on the type and nature of input data, which translates into better convergence, accuracy, and generalization of the neural network model. Therefore, each activation function must be rigorously tested to find a strong and functional model. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 67 B. Feature Scaling To begin with, the rain attenuation time-series for each i-th GW, A (m) t,i 2 R K , is pre-processed by using feature scaling, also known as normalization, which is expressed by A0(m) t,i = A (m) t,i min1tK A (m) t,i max1tK A (m) t,i min1tK A (m) t,i , for 8 > < > : i = 1, 2, . . . , N t = 1, 2, . . . , K m = 1, 2, . . . , 40 , (5.21) where A0(m) t,i 2 R K and each component A0(m) t,i corresponds to a time step, t. This process is carried out for each example sequence (m) from dataset Ai. The main advantage of feature scaling is that the gradient descent converges much faster with normalization than without it. Normalization is often employed in neural networks when the distribution of data is not a Gaussian distribution. In this case, the nature of rain attenuation data follows a log-normal distribution [28,38]. In summary, the normalized rain-attenuation time-series are ready to be employed at the input layer of the LSTM network. C. Initialization of Biases and Weights The values of weights are usually initialized by random values, whereas the default value for the bias is 1. However, the initialization could manually be changed. The weights can be represented by concatenated matrices (Θ), where their dimensions depend on how deep is the neural network and the number of features of the hypothesis function. D. The Loss Function The loss functions are a measure in order to understand how well a model is able to predict the expected outcome [84]. It is important to mention that there is not a unique loss function, therefore, the choice depends on multiple factors such as the type of machine learning algorithm, presence of outliers, differentiable loss functions, the efficiency of optimization algorithms, and accurate predictions. Depending on the machine learning problem, loss functions must be for either regression or classification [80]. In order to predict the rain attenuation time-series, the chosen machine-learning-algorithm must be based on a regression problem, therefore, the loss functions for regression are considered in this thesis. To begin with, a model is built from the proposed deep learning network (Section 5.2.1), whose performance is evaluated by a loss function. In this context, the loss function evaluates the differences between predicted and observed values, reaching the minimum when the prediction is exactly equal to the observed (true) value. For this purpose, the mean absolute error (MAE) is a loss function used for regression, which is more robust to outliers [84]. That is, rain-attenuation datasets contain outliers due to the nature of the rain, therefore, the MAE loss function is useful in these cases. In CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 68 general terms, the MAE loss function is given by L(Θ)i = 1 m m X j=1 |A0(j) t,i Â0 t,i|, 8 > < > : i = 1, 2, . . . , N j = 1, 2, . . . ,m t = 1, 2, . . . , K (5.22) where the parameter Θ is implicit in the predicted values Â0 t,i. During the training process, the learning of the parameter Θ is continuous so that the output can have a better fit and the model can be more accurate. Furthermore, it is important to note that the parameter Θ is comprised of ΘL and ΘD, where each parameter is updated in its respective training process. The loss function can be applied to both the training and validation process. Thus, the model can be evaluated by the training loss function, L(Θ)train, and the validation loss function L(Θ)val. E. Optimization Algorithms Machine Learning algorithms depend on maximizing or minimizing a function. In this case, the loss function is minimized by optimization algorithms in order to find the best performance and the minimum of the function. The main optimization algorithms are presented in the following items. • Stochastic Gradient Descent Algorithm: this algorithm updates the parameter Θ to minimize the loss function in the direction of its negative gradient by taking small steps [82–84]. The update algorithm of the parameter Θ is denoted by Θ`+1 := Θ` ↵rΘL(Θ`), (5.23) where ` is the iteration number and ↵ is the step size or learning rate. The learning rate setting could be quite tricky. For instance, if the learning rate is constant, ↵ > 0, but its value is too small, convergence can be very slow, but if the value is too large, the method can fail to converge at all [84]. In general, this algorithm evaluates the function gradient and updates the parameter Θ by using a subset derived from the training set. Usually, the subset is also known as mini-batch [84], whose gradient evaluation using the mini-batch is performed by each iteration `. During each iteration, the algorithm is one step closer to minimizing the loss function. Finally, the full-pass when the training algorithm ends up its process in all mini-batches is an epoch. • Root Mean Square Propagation (RMSProp): this algorithm tries to improve network training by using different learning rates, ↵. That is, the RMSProp algorithm can automatically adapt to the loss function, optimizing the training process in addition to updating the parameter Θ efficiently [87]. A moving average of the element-wise squares of the parameter gradients is kept by this algorithm, which is given by v` = 2v`1 + (1 2)[rΘL(Θ`)] 2, (5.24) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 69 where 2 is the decay factor rate, whose value usually can be 0.9, 0.99, or 0.999. This moving average is used by the RMSProp algorithm to normalize the updates of the parameter Θ, individually. Parameter Θ is normalized and updated by the following expression Θ`+1 := Θ` ↵rΘL(Θ`)p v` + ✏ , (5.25) where ✏ is a small constant in order to avoid division by zero. By using RMSProp algorithms, the learning rate decreases with larger gradients and increases with small gradients [87]. • Adaptive Moment Estimation Optimizer (ADAM): the adaptive moment estimation algorithm is a stochastic gradient-descent algorithm with momentum which keeps an element-wise moving average of both parameter gradients and their squared values [87]. These average values can be expressed by m` = 1m`1 + (1 1)rΘL(Θ`), (5.26) v` = 2v`1 + (1 2)[rΘL(Θ`)] 2, (5.27) where gradient decay factors, 1 and 2, are linear and quadratic respectively. Also,rΘL(Θ`) is the gradient of the loss function, and ` is the iteration number. ADAM optimizer uses these averages to update the parameter Θ, using the following expression Θ`+1 := Θ` ↵ m`p v` + ✏ , (5.28) where ↵ > 0 is the learning rate, and ✏ is a small constant added in order to avoid division by zero. In this algorithm, the moving average of the gradient enables the parameter Θ updates, picking up the momentum in a definite direction as long as gradients throughout many iterations are similar. Also, the moving average and parameter Θ can become smaller whether the gradients are noisy. In general, there is not a specific learning rate, therefore, different learning rates are tried out to find the optimal values. It can be stipulated a different learning rate for each layer. Finally, the ADAM optimizer is more efficient than RMSProp and stochastic gradient descent algorithms, especially due to the fast convergence and adaptability [87]. F. L2 Regularization The overfitting can be reduced by adding a regularization term for the weights of the loss function L(Θ) [87]. Therefore, the loss function with the regularization term is defined as L(Θ)R = L(Θ) + RΩ(Θ), (5.29) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 70 where R is the regularization coefficient, and Ω(Θ) is the regularization function. Thus, the regularization function is given by vector notation, which is represented by Ω(Θ) = 1 2 Θ | Θ (5.30) It is important to mention that the biases are not regularized. The R coefficient can manually be modified, also, it is possible to specify different regularization coefficients for different layers. G. Dropout Regularization Dropout is a regularization method that is capable of dropping out inputs to a layer by probabilistically removing. To be specific, dropout simulates a large number of networks but with different structures. Thus, nodes in the network are more robust to the inputs. For this purpose, the probability of establishing each input to zero is determined in the layer which is also known as the dropout rate. For instance, if a dropout rate sets at 0.8, it means that 20% of inputs are to zero. Therefore, dropout is a computationally-low-cost method to regularize a deep learning network, to reduce the overfitting, and to improve the generalization error at the LSTM network. H. Training Process By setting the network hyperparameters, the model, let F , is trained by the proposed deep learning network to forecast rain attenuation time-series in K-time steps into the future. In this case, the used method is many-to-one, where the input dataset, A 0 i, is comprised of multiple time-series, A0(1) t,i = [A0(1) 1,i , A 0(1) 2,i , . . . , A 0(1) t,i , . . . , A 0(1) K,i] 2 R K A0(2) t,i = [A0(2) 1,i , A 0(2) 2,i , . . . , A 0(2) t,i , . . . , A 0(2) K,i] 2 R K ... A0(m) t,i = [A0(m) 1,i , A 0(m) 2,i , . . . , A 0(m) t,i , . . . , A0(m) K,i ] 2 R K , for 8 > < > : i = 1, 2, . . . , N t = 1, 2, . . . , K m = 1, 2, . . . , 40 , and the single time-series obtained from the deep learning network at the output is given by Â0 t+1,i = [Â0 2,i, Â0 3,i, . . . , Â0 t+1,i, . . . , Â0 K+1,i] 2 R K , for ( i = 1, 2, . . . , N t = 1, 2, . . . , K Here, the feature scaling must be undone according to the feature range parameters calculated earlier (sub-section 5.2.2-Feature Scaling) [88]. As a result, each rain-attenuation time-series is denoted by Ât+1,i 2 R K . CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 71 I. Metrics The proposed regression model is based on supervised learning, which must be estimated and evaluated in its performance and fit. Usually, three metrics are used for this purpose, such as the root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (R-Squared or R2). • Root Mean Squared Error: this metric is the most commonly used in regression problems, which indicates how well the model fits the data. That is, how near the observed values are from the predicted values, providing an absolute measure of fit. The RMSE is given by RMSEi = v u u t 1 K K X j=1 (Aj,i Âj,i)2, for i = 1, 2, . . . , N (5.31) To be precise, the RMSE represents the square root of the differences between observed and predicted values. In other words, it is the quadratic mean of these differences [82–84]. For calculations over the data sample, these deviations are known as residuals, whereas they are called errors for out-of-sample calculations. In general, a lower RMSE value indicates a better fit and accuracy of the model to predict, which is the most important criterion in prediction models. However, it is important to mention that RMSE is sensitive to outliers [89]. • Mean Absolute Error: it is the arithmetic average of the absolute errors, i.e., between observed and predicted values. This statistical metric is often used as a measure of forecast error in the time-series analysis [89]. The MAE is calculated as MAEi = 1 K K X j=1 |Aj,i Âj,i|, for i = 1, 2, . . . , N (5.32) Both RMSE and MAE metrics express the average prediction error for LSTM models. Furthermore, both metrics are indifferent to the direction errors, i.e., RMSE and MAE are negatively-oriented scores, which means lower values are much better. Finally, it is important to mention that MAE is a linear score in addition to being more robust to outliers [84]. • Coefficient of Determination: it is also known as R-Squared, R2, which is used in the context of statistical models. Indeed, the main purpose is either the prediction of future results or the testing of hypotheses, on the basis of other related information. That is, it is implemented as a measure of how well the observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model [90]. The R-Squared is computed as R2 i = 1 PK j=1(Aj,i Âj,i) 2 PK j=1(Aj,i Āj,i)2 , for i = 1, 2, . . . , N (5.33) CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 72 In other words, the coefficient of determination is employed to indicate the goodness of fit of the LSTM model. In this context, R2 could be employed as an accuracy metric where a value of about 1 indicates that the data predictions perfectly fitted the proposed model, whereas an R2 = 0 indicates that the proposed model did not improve the predictions [90]. J. CNIR Time-series Calculation Predicted by the deep learning network, the rain attenuation time-series are trained and denoted by Â0 t+1,i = F(A0(m) t,i ) for each GW location, i = 1, 2, . . . , N . As previously stated, the normalization must be undone so the time-series can be expressed on the original scale. Thus, rain attenuation time-series can be given by Ât+1,i 2 R K . By using Eq. (2.3), the predicted sequence of CNR time-series for each feeder uplink can be expressed by Γ̂t+1,i = 10 log10(csi) Ât+1,i, for ( i = 1, 2, . . . , N t = 1, 2, . . . , K (5.34) where Γ̂t+1,i 2 R K and each element, Γ̂t+1,i, is given in decibels, dB. Finally, substituted the predicted CNR into Eq. (2.6), the predicted sequence of CNIR time-series is calculated for each feeder uplink and rewritten as Ξ̂t+1,i = Γ̂t+1,i · ⇣T Γ̂t+1,i + ⇣T , for ( i = 1, 2, . . . , N t = 1, 2, . . . , K (5.35) where Ξ̂t+1,i 2 R K is the CNIR prediction for the next time step, t + 1. Figure 5.10 depicts a block diagram of the proposed method where each GW processes its both rain-attenuation and CNIR predictions to send them to the Network Control Center (NCC), At NCC, each predicted time-series component of both rain attenuation and CNIR can be stored into matrices, Â, Ξ̂ 2 R K⇥N , respectively. Thus, the NCC analyzes each feeder-uplink status in order to determine which of them are threatened in advance by rain impairments. 5.3 Experimentation In order to prove the deep learning network performance, two experiments were executed by employing a high-level programming language. For this purpose, 24 locations were chosen as possible GW sites, therefore, there were obtained 24 rain attenuation datasets with 40 sequences for each one of them. In this context, the possible GW-sites are dispersed in Mexico, Central America, and The Caribbean, as these cities can access easier to high-quality services and infrastructures so the implementation and deployment can be faster and more efficient than in minor cities. Furthermore, the number of examples, m, emulates a historical database of 40 years. Table A.2 (Appendix A.2) shows in detail the main features of each GW site, in CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 73 NCC Matrices: Â, Ξ̂ 2 R K⇥N Data processing in situ, GW1 Feature Scaling Deep Learning Network F CNIR Calculation A (m) t,1 time step, t A0(m) t,1 time step, t Â0 t+1,1 time step, t+ 1 Ξ̂t+1,1 time step, t+ 1 Data processing in situ, GW2 Feature Scaling Deep Learning Network F CNIR Calculation A (m) t,2 time step, t A0(m) t,2 time step, t Â0 t+1,2 time step, t+ 1 Ξ̂t+1,2 time step, t+ 1 ... Data processing in situ, GWN Feature Scaling Deep Learning Network F CNIR Calculation A (m) t,N time step, t A0(m) t,N time step, t Â0 t+1,N time step, t+ 1 Ξ̂t+1,N time step, t+ 1 Figure 5.10: Block diagram of the proposed method based on the deep learning network. addition to its calculated carrier-to-noise ratio under clear-sky conditions according to the discussed method in Chapters 2 and 3, csi , for i = 1, 2, . . . , N [dB]. In this context, a lot of time was invested by computer coding to carry out the experiments successfully. Provided in the following sub-sections, each experiment details the employed settings and procedure. 5.3.1 Experiment 1: Training and validation subsets partitioning, 70/30 To begin with, the rain attenuation datasets for the set [N ] = {1, 2, . . . , 24} were calculated by using the model presented in sub-section 2.4. This model employed CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 74 geographic coordinates (latitude, longitude, and height) of each GW site, satellite orbital position at 92 West, the frequency band of the feeder uplink at 50 GHz, and Ts = 1 min. It is important to highlight that the rain attenuation time-series were sampled every Ts = 1 min at 1 year period, therefore, the number of samples of each rain-attenuation time-series is 525600, that is, each sequence has a dimensionality of K = 525600. Each time-series was partitioned into training and validation subsets, where the training subset was 70% and the validation subset was 30%. Hereinafter, each rain attenuation time-series was normalized by feature scaling to be trained and validated in the deep learning network. Table 5.1 shows the hyperparameters that are incorporated into the deep learning network configuration. To be precise, the hyperparameters adjustment is an important role in the learning process. For this purpose, different values were assigned to each hyperparameter such as the number of hidden layers, dropout rate, number of LSTM units, learning rate, etc. In this case, the deep learning network employed a single LSTM layer, S = {LU}. After several trials, where about 400 models were tried out with different hyperparameter combinations, the best model was found according to the best hyperparameters. In summary, this deep learning network configuration was able to train and validate 960 rain attenuation time-series regarding 24 GW sites with 40 examples by the site-specific. Table 5.1: Hyperparameters for Experiment 1 Parameter Arg./Value Parameter Arg./Value LSTM units, U 100 Dense Layer: (D) output 1 Activation Function (LU ) tanh Activation Function (D) selu L2 R 1⇥ 104 1 0.9 Dropout 0.2 2 0.999 Loss Function MAE ✏ 1⇥ 108 Optimizer ADAM Metrics RMSE, MAE, R2 Learning rate 5⇥ 103 Validation Yes Epochs 250 Batch Size 1024 Early Stopping Yes Patient 5 5.3.2 Experiment 2: Training and validation subsets partitioning, 90/10 This procedure was similar to Experiment 1, but the rain attenuation time-series were divided into 90% for the training subsets and 10% for the validation subsets. Unlike in Experiment 1, the number of hidden units increased in the LSTM layer. Also, the LSTM network was modified by adding more layers. Therefore, the LSTM multi-layer network contributed to the proposed model to be deeper than Experiment 1. Thus, the deeper network might need fewer epochs to train the model, but the computational cost might be higher. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 75 Table 5.2 indicates the obtained hyperparameters for Experiment 2. Similarly, the hyperparameters tuning was performed according to the Experiment 1 process. However, it was necessary to test about 600 models to find the best hyperparameters that are part of the model settings for Experiment 2. It is important to mention that the deep learning network is comprised of 5 LSTM layers, where each layer of the LSTM multi-layer network, S = {LU1,LU2,LU3,LU4,LU5}, such that U1 = 200, U2 = 75, U3 = 50, U4 = 25, U5 = 5 has its own LSTM hidden units, respectively. Table 5.2: Hyperparameters for Experiment 2 Parameter Arg./Value Parameter Arg./Value LSTM units, U1 200 LSTM units, U2 75 Activation Function (LU1) tanh Activation Function (LU2) tanh LSTM units, U3 50 LSTM units, U4 25 Activation Function (LU3) tanh Activation Function (LU4) tanh LSTM units, U5 5 Dense Layer: (D) output 1 Activation Function (LU5) tanh Activation Function (D) selu L2 R 1⇥ 106 1 0.9 Dropout 0.2 2 0.999 Loss Function MAE ✏ 1⇥ 108 Optimizer ADAM Metrics RMSE, MAE, R2 Learning rate 1⇥ 103 Validation Yes Epochs 250 Batch 1024 Early Stopping Yes Patient 5 5.4 Results Both experiments were performed by computer resources to train and validate the proposed models, where Python programming language was employed, in addition to using tensor processor units (TPU) and graphics processor units (GPU) to accelerate the training and validation processes, reducing the computing time and improving the general performance. In order to evaluate both experiments, three statistical metrics were used for this purpose: root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2). Figure 5.11 and Figure 5.12 depict RMSE scores for both training and validation subsets, respectively. In both cases, the best results were obtained by Experiment 2. However, some RMSE scores for training subsets that were evaluated in each site by Experiment 1 such as San Jose, Tegucigalpa, Guadalajara, La Habana, and Belmopan were lower than RMSE scores from Experiment 2, without having a remarkable difference for all reported cases. Furthermore, for validation experiments, some RMSE scores from Experiment 1 such as Tijuana, Torreon, La Paz B.C., Tuxtla Gtz., San Pedro Sula, Belmopan, Kingston, and Oaxaca were also lower than RMSE scores from Experiment 2. Anyway, the average RMSE score obtained from Experiment 2 was lower than Experiment 1. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 76 Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average RMSE scores 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1.2497 0.5645 2.1529 1.6796 1.4175 1.6505 1.4767 0.4130 0.9962 0.5574 1.4978 1.4395 0.5575 0.3757 2.2306 1.9227 1.5236 1.4686 0.4728 0.8090 0.9335 0.8344 1.0816 1.3889 2.5494 1.4128 0.6186 2.2341 1.8961 1.4263 1.6471 1.5923 0.8004 1.0823 0.6657 1.9313 1.8645 0.6558 0.3986 2.2711 2.2610 1.8496 1.4448 0.5073 0.7815 1.8806 1.0982 0.9481 1.0899 2.9620 Experiment 1 Experiment 2 Figure 5.11: RMSE scores for training subsets. Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average RMSE scores 0.00 0.50 1.00 1.50 2.00 2.50 3.00 1.1161 0.5084 1.5361 0.6879 1.7276 1.4397 1.4027 0.2835 1.3592 0.4522 1.2996 1.1320 0.4628 0.4678 2.0507 1.6287 1.8867 1.4921 0.4668 0.7949 0.5452 0.6607 1.1814 1.6696 1.6492 1.2780 0.4671 1.7611 0.8933 1.4451 1.3434 1.3723 0.7270 1.1784 0.6492 1.6838 1.6038 0.4368 0.4123 2.2320 1.9099 2.1635 1.7415 0.3821 0.9179 1.9136 0.7154 1.2707 1.7785 1.6739 Experiment 1 Experiment 2 Figure 5.12: RMSE scores for validation subsets. Figure 5.13 and Figure 5.14 show MAE scores for training and validation subsets, respectively. For both training and validation subsets, the MAE scores were closely similar to each other. Here, the average MAE score from Experiment 2 was lower than Experiment 1 for both training and validation evaluations. Nevertheless, some MAE scores from Experiment 1 were lower than Experiment 2, but these scores did not influence strongly in the final average score. In many cases, RMSE scores are larger than MAE scores, but if the errors have the same magnitude, then RMSE=MAE. Figure 5.15 and Figure 5.16 illustrate the training and validation rain attenuation subsets of each site, respectively. In order to visualize properly, 50 samples were picked out by each training and validation figure. That is, each range was randomly chosen by illustrating rain attenuation samples. Furthermore, each figure, either training or validation subset, depicted both Experiments and the Observed data. In this sense, results from Experiment 2 were adequately fitted better than Experiment 1. For instance, although Tijuana training and validation subsets, Figure 5.15g and Figure 5.16g respectively, were practically the same for both experiments, other evaluations CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 77 Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average MAE scores 0.00 0.40 0.80 1.20 1.60 2.00 0.2737 0.0742 0.4900 0.2450 0.5665 0.5031 0.2653 0.0242 0.1728 0.0740 0.6175 0.2043 0.0429 0.0945 0.8975 0.2852 0.4857 0.1622 0.0924 0.2127 0.1111 0.1141 0.1396 0.4334 0.2615 0.5384 0.1768 0.7351 0.1654 0.3561 0.2078 0.7701 0.6915 0.4645 0.2688 1.4042 0.9200 0.1918 0.0330 0.2894 0.4480 1.3543 0.7583 0.0827 0.2096 1.6538 0.4870 0.1823 0.2891 0.7828 Experiment 1 Experiment 2 Figure 5.13: MAE scores for training subsets. Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average MAE scores 0.00 0.40 0.80 1.20 1.60 2.00 0.2777 0.0777 0.4528 0.1977 0.5786 0.5131 0.2702 0.0189 0.2155 0.0639 0.6010 0.2026 0.0424 0.1047 0.8935 0.3230 0.5557 0.1875 0.0943 0.2100 0.0753 0.1320 0.1737 0.4506 0.2295 0.5355 0.1639 0.7318 0.1255 0.3462 0.1876 0.7517 0.6835 0.4798 0.2744 1.3750 0.9172 0.1825 0.0362 0.2831 0.4503 1.4161 0.7709 0.0752 0.2149 1.6585 0.4774 0.2058 0.3196 0.7259 Experiment 1 Experiment 2 Figure 5.14: MAE scores for validation subsets. such as Monterrey (Figure 5.15e and Figure 5.16e) or Torreon (Figure 5.15l and Figure 5.16l) had shown a remarkable difference. Unfortunately, some training subsets experienced troubles during the training process, therefore, the hyperparameters such as dropout or LSTM units were modified in some evaluations such as: Torreon, La Paz, B.C., Queretaro, Cd. Juarez, and Pto. Cabezas. This was necessary to avoid under-fitting and over-fitting on predicted subsets. Figure 5.17 and Figure 5.18 indicate the R2 values of both training and validation subsets respectively, where Experiment 2 predicted the outcomes slightly better than Experiment 1. R2 indicated how well the regression predictions approximated the real data points. According to results from Experiment 2, Figure 5.19 shows the validation metrics for each evaluated rain-attenuation. Experiment 2 was chosen because the overall model performance obtained from it was better than Experiment 1. It was possible to note that in some cases because of the many outliers, the predicted values did not fit well on the regression line. For instance, in a few cases such as La Paz, B.C. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 78 (a) Panama, range: k = 19110, . . . , 19160 (b) San Jose, range: k = 25540, . . . , 25590 (c) Tegucigalpa, range: k = 14075, . . . , 14125 (d) Mexico City, range: k = 10520, . . . , 10570 (e) Monterrey, range: k = 26090, . . . , 26140 (f) Guadalajara, range: k = 13100, . . . , 13150 (g) Tijuana, range: k = 259980, . . . , 260030 (h) La Habana, range: k = 26170, . . . , 26220 (i) Sto. Domingo, range: k = 50465, . . . , 50515 (j) San Salvador, range: k = 32255, . . . , 32305 (k) San Juan, range: k = 18050, . . . , 18100 (l) Torreon, range: k = 41965, . . . , 42015, dropout=0.5 Figure 5.15: The training rain-attenuation subsets obtained from deep learning models. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 79 (m) La Paz, B.C., range: k = 52215, . . . , 52265, dropout= 0.5 (n) Veracruz, range: k = 14183, . . . , 14233 (o) Cancun, range: k = 37100, . . . , 37150, dropout= 0.5 (p) Queretaro, range: k = 15215, . . . , 15265, dropout= 0.5 (q) Tuxtla, Gtz., range: k = 38320, . . . , 38370 (r) Cd. Juarez, range: k = 74145, . . . , 74195, LU1 = 400, dropout=0.5 (s) San Pedro Sula, range: k = 10000, . . . , 10050 (t) Belmopan, range: k = 12165, . . . , 12215 (u) Kingston, range: k = 17350, . . . , 17400 (v) Merida, range: k = 27598, . . . , 27648, dropout= 0.3 (w) Pto. Cabezas, range: k = 19180, . . . , 19230, dropout= 0.5 (x) Oaxaca, range: k = 11680, . . . , 11730 Figure 5.15: The training rain-attenuation subsets obtained from deep learning models (cont.). CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 80 (a) Panama, range: k = 475460, . . . , 475510 (b) San Jose, range: k = 477390, . . . , 477440 (c) Tegucigalpa, range: k = 482140, . . . , 482190 (d) Mexico City, range: k = 477490, . . . , 477540 (e) Monterrey, range: k = 474550, . . . , 474600 (f) Guadalajara, range: k = 479480, . . . , 479530 (g) Tijuana, range: k = 510090, . . . , 510140 (h) La Habana, range: k = 505318, . . . , 505368 (i) Sto. Domingo, range: k = 504330, . . . , 504380 (j) San Salvador, range: k = 503138, . . . , 503188 (k) San Juan, range: k = 519440, . . . , 519490 (l) Torreon, range: k = 496275, . . . , 496325, dropout=0.5 Figure 5.16: The validation rain-attenuation subsets obtained from deep learning models. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 81 (m) La Paz, B.C., range: k = 518740, . . . , 518790, dropout= 0.5 (n) Veracruz, range: k = 493940, . . . , 493990 (o) Cancun, range: k = 495150, . . . , 495200, dropout= 0.5 (p) Queretaro, range: k = 501165, . . . , 501215, dropout= 0.5 (q) Tuxtla, Gtz., range: k = 483430, . . . , 483480 (r) Cd. Juarez, range: k = 475245, . . . , 475295, LU1 = 400, dropout=0.5 (s) San Pedro Sula, range: k = 483840, . . . , 483890 (t) Belmopan, range: k = 488025, . . . , 488075 (u) Kingston, range: k = 486550, . . . , 486600 (v) Merida, range: k = 499855, . . . , 499905, dropout= 0.3 (w) Pto. Cabezas, range: k = 476680, . . . , 476730, dropout= 0.5 (x) Oaxaca, range: k = 505970, . . . , 506020 Figure 5.16: The validation rain-attenuation subsets obtained from deep learning models (cont.). CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 82 Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average R-Squared 0.00 0.22 0.44 0.66 0.88 1.10 0.9020 0.9013 0.9216 0.9414 0.8828 0.9090 0.8947 0.8851 0.9032 0.9047 0.8856 0.9186 0.8588 0.8242 0.9156 0.9168 0.9045 0.8998 0.9088 0.9062 0.9101 0.9251 0.9054 0.9036 0.9214 0.8626 0.8935 0.9238 0.9389 0.8896 0.9166 0.8873 0.6403 0.8920 0.8602 0.8331 0.8711 0.8396 0.8187 0.9128 0.8923 0.8316 0.8748 0.9088 0.8942 0.5694 0.8948 0.8952 0.9116 0.9117 Experiment 1 Experiment 2 Figure 5.17: R2 for training subsets. Panama San Jose Tegucigalpa Mexico City Monterrey Guadalajara Tijuana La Habana Sto. Domingo San Salvador San Juan Torreon La Paz, B.C. Veracruz Cancun Queretaro Tuxtla, Gtz. Cd. Juarez San Pedro Sula Belmopan Kingston Merida Pto. Cabezas Oaxaca Average R-Squared 0.00 0.22 0.44 0.66 0.88 1.10 0.8783 0.8810 0.8892 0.8435 0.9068 0.8979 0.8988 0.7265 0.9224 0.8653 0.8877 0.8959 0.8045 0.8156 0.9027 0.9033 0.9160 0.8900 0.8867 0.9180 0.8080 0.8864 0.9038 0.9223 0.9076 0.8399 0.8922 0.9021 0.9023 0.8908 0.9128 0.8833 0.3332 0.8963 0.8543 0.7579 0.8534 0.7324 0.7762 0.9062 0.8846 0.8819 0.9064 0.8969 0.9160 0.6495 0.7884 0.9264 0.9221 0.8909 Experiment 1 Experiment 2 Figure 5.18: R2 for validation subsets. (Figure 5.19m), or Cd. Juarez (Figure 5.19r), the squared residuals with respect to the linear regression were higher than the best models such as Tuxtla, Gtz. (Figure 5.19q), or San Jose (Figure 5.19b). By using Eq. (5.34) and Eq. (5.35), it was possible to predict the CNIR for the next time step, t + 1. For this purpose, the co-channel interference value, ⇣co = 36.09 dB, and the adjacent interference value, ⇣adj = 38.17 dB, were obtained from subsection 4.5.3. Figure 5.20 depicts the model with higher R-Squared, R2 = 0.9224, which demonstrates that the rain attenuation, Figure 5.20a, directly influences on the CNIR, Figure 5.20b, and spectral efficiency, Figure 5.20c. On the other hand, Figure 5.21 indicates the model with lower R-Squared, R2 = 0.7265. In both cases, only 50 samples were employed to visualize properly the effects of rain attenuation. Also, the spectral efficiency was determined from CNIR values by the DVB-S2X table [6]. These two approaches can be also analyzed from a climatological perspective to compare with the obtained prediction models. For instance, Tuxtla, Gtz. is located in the rainforest area of Mexico regarding the Köppen-Geiger climate type map [91]. On the other hand, Cd. Juarez is located in the cold desert zone of Mexico according to the Köppen-Geiger climate type map of North America [91]. This makes sense, as the mean annual precipitation at Tuxtla, Gtz. is about 1900 mm, whereas at Cd. Juarez is less than 200 mm [92]. For this reason, the Tuxtla prediction model was not difficult to train because there were more precipitation data than at Cd. Juarez. That CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 83 (a) Panama (b) San Jose (c) Tegucigalpa (d) Mexico City (e) Monterrey (f) Guadalajara (g) Tijuana (h) La Habana (i) St. Domingo (j) San Salvador (k) San Juan (l) Torreon, dropout=0.5 Figure 5.19: Model performance results: measured vs. predicted rain-attenuation values for validation. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 84 (m) La Paz, dropout= 0.5 (n) Veracruz (o) Cancun, dropout= 0.5 (p) Queretaro, dropout= 0.5 (q) Tuxtla, Gtz. (r) Cd. Juarez, LU1 = 400, dropout=0.5 (s) San Pedro Sula (t) Belmopan (u) Kingston (v) Merida, dropout= 0.3 (w) Pto. Cabezas, dropout= 0.5 (x) Oaxaca Figure 5.19: Model performance results: measured vs. predicted rain-attenuation values for validation (cont.). CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 85 (a) Rain attenuation window (b) CNIR window (c) Spectral efficiency window Figure 5.20: The higher R-Squared, R2 = 0.9224 at Tuxtla, Gtz. (a) Rain attenuation window (b) CNIR window (c) Spectral efficiency window Figure 5.21: The lower R-Squared, R2 = 0.7265 at Cd. Juarez. is, the lack of data is a big problem because it can be difficult to train and validate the model, obtaining low accuracy, in addition to not finding reasonable results. Finally, Figure 5.22 indicates the performance of the deep learning network configuration by showing both training and validation loss functions for each rain-attenuation time series. Both loss function graphics were the results of Experiment 2. 5.5 Discussions The outcomes of Experiment 2 were better than Experiment 1, improving scores of metrics such as RMSE and MSE. Therefore, the trained and validated model obtained from Experiment 2 was the basis for understanding and forecasting accurately the rain-attenuation and their strong influence on feeder links. However, the most important metric was the coefficient of determination or R2, which was decisive in order to pick out the best Experiment in this study. R2 is a number between 0 and 1 that estimates the changes in the dependent variable by changes in the independent CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 86 (a) Panama (b) San Jose (c) Tegucigalpa (d) Mexico City (e) Monterrey (f) Guadalajara (g) Tijuana (h) La Habana (i) St. Domingo (j) San Salvador (k) San Juan (l) Torreon, dropout=0.5 Figure 5.22: Training and validation loss functions for each rain-attenuation time series. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 87 (m) La Paz, dropout= 0.5 (n) Veracruz (o) Cancun, dropout= 0.5 (p) Queretaro, dropout= 0.5 (q) Tuxtla, Gtz. (r) Cd. Juarez, LU1 = 400, dropout=0.5 (s) San Pedro Sula (t) Belmopan (u) Kingston (v) Merida, dropout= 0.3 (w) Pto. Cabezas, dropout= 0.5 (x) Oaxaca Figure 5.22: Training and validation loss functions for each rain-attenuation time series (cont.). CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 88 variable. In fact, a high R2, close to 1, is necessary for precise predictions, therefore, the found R2 from validation subsets were between 0.7265 and 0.9224. Potentially, these values demonstrate a high accuracy of deep learning networks obtained from Experiment 2 unlike deep learning networks from Experiment 1, as seen in Figure 5.18. In order to understand graphically R2, data points of deep learning networks with high R2 are lying near to the regression line, whereas data points of deep learning networks with low R2 are dispersed, as demonstrated in Figure 5.19. After all, determining an adequate R2 is a matter of judgment. Hence, the found R2s accomplish the requirements for all rain-attenuation models. In this sense, the predictive model of rain attenuation with high R2, Figure 5.20, is compared with the predictive model with low R2, Figure 5.21. For instance, the first model predicted an aggressive rain-attenuation in the range from k = 483430–483480. In this case, CNIR predictions varied from -50.0–30.0 dB, approximately, impacting strongly on the spectral efficiency. On the contrary, a non-aggressive rain-attenuation was predicted by the second model in the range from k = 475245–475295. In this case, CNIR predictions are more stable due to the lower attenuation of the rain, therefore, the spectral efficiency is almost constant in that range, as seen in Figure 5.21c. It is important to mention that the upper limit of the DVB-S2X standard, in power terms, is 19.57 dB, which corresponds to the best modulation and codification, 256 APSK 3/4, and spectral efficiency of 5.9009 b/s/Hz [6]. That is, the CNIR has a margin of about 10.00 dB until the signal is degraded by rain attenuation. In other words, the spectral efficiency varies according to the CNIR level, as shown in Figure 5.20b and Figure 5.20c. In this case, the rain attenuation greater than 10.00 dB affects strongly the CNIR level, degrading the spectral efficiency until there is no signal, i.e., if the CNIR < 2.85 dB, then spectral efficiency = 0.00 b/s/Hz. Furthermore, it was figured out that the validation loss, L(Θ)val, is lower than training loss, L(Θ)train, during the training and validation processes of the proposed models, as shown in Figure 5.22. Nonetheless, this is not fundamentally an uncertain phenomenon in essence. Indeed, the structure of both training and validation subsets can have a smaller validation loss than the training loss. This usually happens for five main reasons, • When the training data is harder to train or learn patterns on it, whereas it is possible to have an easier validation subset. • Dropout is not enabled during the validation process, therefore, this can lead to greater outcomes on the validation subset. • By default, regularization is solely applied during the training process but not during the validation or testing process. Nevertheless, when the regularization is present during the validation process, then both loss functions can be more similar. • On average, the training loss is performed during each epoch whereas the validation loss is performed after each epoch. That is, the training loss can be out of phase a half epoch regarding the validation loss. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 89 Accuracy Model [%] 0% 25% 50% 75% 100% Random Forest, XGBoost 77.00% Statistical Method 77.55% Statistical Method 81.15% LSTM 87.99% LSTM 87.83% LSTM 72.65% LSTM 92.24% Proposed method (High R-Squared) Proposed method (Low R-Squared) Proposed method (Average 24 sites) Poornima - Pushpalatha method ARIMA method Holt-Winters method Aguasca-Colomo et. al method Figure 5.23: Comparison between predictive models. • It is possible that in the early phase of the training process the validation loss is smaller than the training loss. In this thesis, dropout and regularization methods were added to the LSTM networks, there were even some different configurations to train hard LSTM networks, for instance, Torreon (dropout = 0.5), La Paz, B.C. (dropout= 0.5), Cancun (dropout = 0.5), Queretaro (dropout = 0.5), Cd. Juarez (LU1 = 400 units and dropout = 0.5), Merida (dropout = 0.3), and Pto. Cabezas (dropout = 0.5). Thus, the first reason is essentially the main factor to diminish the validation loss in contrast to the training loss. Hence, data are prepared carefully, as the outcomes depend significantly on the quality of data, i.e, pre-processing data, cleaning data, and partitioning training/validation subsets. Finally, Figure 5.23 illustrates the comparison between predictive models/methods according to the accuracy metric. For instance, the best model found in this thesis, Experiment 2: 90/10, has better accuracy than the Poornima-Pushpalatha method [93], i.e., 92.24% vs. 87.99%. However, on average, the proposed method is slightly lower than the Poornima-Pushpalatha method, 87.83% vs. 87.99%. It is important to mention that the proposed method in this thesis evaluated 24 locations whereas the Poornima-Pushpalatha method evaluated a single location at Hyderabad, India. Other proposals employed statistical methodologies, such as the autoregressive integrated moving average (ARIMA) method, 81.15% of accuracy, [94], and Holt-Winters method, 77.55% of accuracy, [95], but they could not overcome the accuracy of the proposed LSTM method. At last but not least, the Aguasca-Colomo et. al method proposed a random forest model based on classification with an accuracy of 77.00% [96]. As a result, Machine Learning methods based on regression techniques have better performance and accuracy than statistical methods in order to predict rain events. To sum up, this proposal guarantees an accurate rain-attenuation prediction at the evaluated sites, generalizing efficiently the models. Therefore, this method can efficiently contribute to managing the resources of both the space segment and the ground segment of a high throughput satellite system. CHAPTER 5. METHOD OF RAIN ATTENUATION PREDICTION . . . 90 5.6 Contributions of the Research The proposed method and found results in this chapter were submitted to Neural Processing Letters journal to be reviewed and published later. Also, in this context, an initial study based on neural networks was presented in a specialized conference: "XXXIII Simposium Nacional de la Unión Científica Internacional de Radio, URSI 2018," at Granada, Spain. • Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez Rodriguez-Osorio, and Jose Maria Matias. Optimization of the Ground Segment for an UHTS System through Neural Networks. In XXXIII Simp. Nac. la Unión Científica Int. Radio (URSI 2018), pages 1–5, Granada, Spain, 2018 Chapter 6 Ground Segment Optimization by Using Smart Strategies of Switching Between Gateway Stations 6.1 Introduction The ground segment (GS) is an important part of satellite communications, which contains the gateways stations (GW) and user terminals (UT-VSAT) necessary to communicate to/from the high throughput satellite HTS. When a user requires the satellite service, then the operator adds a VSAT to the network, as long as there is availability. Meanwhile, the number of nominal gateways NGWs depends on the satellite capacity, i.e., each NGW manages a portion of the total capacity, as can be seen in Section 3.4. In this context, it is simple to determine the number of GWs, but it does not consider when the rain affects the feeder links. That is, if the rain impairs one or more GWs, the satellite capacity diminishes, impacting directly on the quality of service (QoS) and leaving several VSATs out-of-service. In a sense, by using the Adaptive Coding and Modulation (ACM) from the DVB-S2X standard, the system availability might not drop dramatically [6]. Also, the Uplink Power Control (ULPC) can manage a few dBs to compensate for channel degradation [74–76]. Despite the fact that both techniques can mitigate channel degradation, they can not combat the aggressive effects of the heavy rain over feeder links. For this reason, some researchers recommend that the NGWs must be separated by a distance D to avoid the correlated rain to each other, i.e. so that the rain affects only one NGW at a time. Each NGW has an extra resource to support when an affected feeder link is in an outage due to the heavy rain. This technique is known as Smart Gateway Diversity (SGD), where the affected NGW is capable of re-routing traffic to an alternate NGW with extra resources for temporary allocation, improving the availability considerably [26,28]. Other researchers have proposed to add redundant gateway stations as a backup (PGWs), i.e., when the rain attenuation impacts on NGW’s feeder link, an available 91 CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 92 PGW gets into the network rather than the affected NGW. Temporarily, the PGW manages all traffic of the affected NGW and establishes a link between the satellite and PGW, waiting for the NGW is available again. This configuration is also known as the N̄ + P̄ scheme, whose NGWs are denoted by N̄ , and PGWs are described by P̄ [22, 23,26,97]. However, this scheme could be an inelegant solution and very little efficient without evaluating the adequate number of PGWs necessary for keeping up the system availability. Here, some researchers have simplified the analysis by proposing a 1 + 1 scheme and using stationary distributions or Markov Chains to calculate the number of PGWs properly [21, 25, 98, 99]. Naturally, this leads to a better switching strategy between NGWs and PGWs but without achieving an adequate optimization of the ground segment. Other authors have developed interesting methods in order to optimize the ground segment in a particular way [100,101]. Despite the smart gateway diversity is focused on increasing the system availability and improving the switching strategies, it is not based on reducing the number of PGWs optimally. For this purpose, a predictive method, as proposed in Chapter 5, provides predictions of rain attenuation by time intervals, identifying how many times the NGWs could be with a link outage due to the rain and which PGWs could temporarily replace to each one of them. Compared with other methods, this predictive method aids to a large degree to optimize the number of PGWs. This contribution must guarantee an availability higher than 99.9%, foreseeing accurately when a feeder link is going to be affected by the rain. Also, this method contributes to the switching strategy to be of lower complexity than previous methods. 6.2 Proposed Model To begin with, the ITU-R 1815 recommended that the distance between two GWs must be 80 km to avoid the correlated rain, dropping the spatial correlation coefficient ⇢a to < 0.1, as can be seen in Section2.3. By using the coordinates of Appendix A.2, it was possible to determine the distance matrix, D, between the GW locations. Furthermore, GW locations were the same as those employed by analysis of Chapter 5. Appendix A.3 presents the distance matrix between pairs of locations. In all cases, the distances were greater than 80 km between each other, ensuring the uncorrelated rain for all locations. 6.2.1 Sizing of Nominal Gateways, NGWs In the high throughput satellite (HTS) systems, the total capacity is strongly related to the number of nominal gateways (NGW) on the ground segment (GS). Initially, the data traffic is symmetrically assumed between forward and return links. That is, 50% of the inbound’s throughput and 50% in the outbound, [1 : 1]. In this context, the upload speed is not strained by the symmetrical connection, whose data is flowed in a proper way [18]. Each NGW manages its feeder link where the feeder uplink is the focus of this CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 93 study. For this case, the feeder uplink does not use the frequency reuse, although it uses double polarization. Based on Eq. (3.1) and Eq. (3.2), the capacity, in b/s, of each feeder uplink is expressed as Cpi = Np · Savail Nsb Seffi , for i = 1, 2, . . . , N̄ , (6.1) where Np is the number of polarizations, Nsb is the number of frequency sub-bands, Savail is the available spectrum, and Seff is the spectral efficiency from the DVB-S2X standard by each feeder uplink [6,18], as was discussed in Chapter 3. At this point, the inbound uplink beams are received and demodulated by the satellite communication subsystem. Naturally, each NGW transmits its corresponding feeder uplink beam. Thus, the total capacity is directly related to the number of NGWs on the GS, which is denoted by CpT = N̄ X i=1 Cpi (6.2) In this study, the inbound CpT is computed by four configurations of NGWs, where N̄ = 4, 8, 12, and 16. 6.2.2 Smart Method for Forecasting Rain Attenuation and CNIR at each GW This novel method is based on Machine Learning algorithms by the implementation of LSTM networks. To begin with, the rain attenuation time-series for each possible GW location was obtained by ITU Recommendation, ITU-R 1853 [38]. Thus, each rain attenuation time-series was trained and validated by LSTM networks, as can be seen in Chapter 5 in detail. As a result, each predicted rain attenuation time-series, at time step t + 1, can be denoted by Ât+1,i = F(A (m) t,i ) for i = 1, 2, . . . , N , where F is the deep learning model, m is the number of examples of the rain attenuation time-series by each GW-site. Figure 5.10 illustrates the block diagram of the smart method employed to predict rain attenuation time-series in this proposal. Finally, each prediction of rain attenuation time-series can be stored in matrix  2 R K⇥N . Using Eq. (5.34) and Eq. (5.35), it was possible to compute the predicted CNIR, Ξ̂ 2 R K⇥N , at time step t + 1. Both matrices can be processed and employed by NCC to supervise and monitor the status of each feeder uplink in advance. 6.2.3 Method to Decide the Best NGWs In order to evaluate the status of each feeder uplink, a CNIR threshold, ⇠th, leads to understanding how well the feeder uplink signal works between the NGW and satellite, i.e., when the CNIR above the threshold, in addition to knowing if the rain affects each feeder uplink, i.e., when the CNIR below the threshold. However, an adequate CNIR threshold could result in a challenge in this study. For this purpose, CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 94 the predicted CNIR matrix, Ξ̂, is evaluated by the CNIR threshold. By each GW-site, it is important to mention that each CNIR prediction is implicit in each column i of the matrix. Therefore, if Ξ̂t+1,i ⇠th for i = 1, 2, . . . , N , and t = 1, 2, . . . , K, then the feeder uplink is active at that time step, otherwise, the feeder uplink is inactive. Based on the previous statement, it is possible to find the availability of each feeder uplink, which is denoted by ⌫i = 1 K K X k=1 ⇥ (Ξ̂k,i ⇠th ! x = 1) ^ (Ξ̂k,i < ⇠th ! x = 0) ⇤ , for i = 1, 2, . . . , N, (6.3) where x is a temporary variable. As a result, GWs can be sorted from the highest to the lowest according to individual availability, ⌫i. Thus, each i column of the matrix Ξ̂ 2 R K⇥N is also sorted by individual availability, ⌫i. This method allows us to define the best candidates in order to set up the ground network system with NGWs. Therefore, it is essential to find system availability regarding its network configuration. In this context, the system availability, [102], is given by ⌫ = ⌫1 · ⌫2·, . . . , ·⌫N̄ = N̄ Y i=1 ⌫i, (6.4) where N̄ corresponds to the number of NGWs, comprising the ground network configuration. However, it is highly probable that the system availability is lower than 99.9%, dropping even more when increasing the number of NGWs. Indeed, the ITU Recommendation, ITU-R S.1557, indicates that for gateway stations at geographically dispersed hubs must require the end-to-end system availability of at least 99.9% [16]. For this reason, it is necessary to add redundancy to the ground network, increasing the system availability equal to or greater than 99.9%. 6.2.4 A Strategy to Allocate the Best PGWs It is necessary to mention that the sorted matrix Ξ̂ contains the possible NGWs and PGWs for this study. The first N̄ columns correspond to the number of NGWs of the ground network, whereas the next columns correspond to the number of possible PGWs to be added to the ground network by this strategy. Therefore, in general terms, the columns for redundant gateways are denoted by Ξ̂t+1,N̄+j, for j = 1, 2, . . . , P̄ , where P̄ is the number of PGWs. To be precise, this procedure consists of adding a redundant gateway, PGW, when an NGW feeder uplink is an outage due to the rain. For this purpose, a switching strategy is implemented between NGW and PGW by a straightforward mechanism. That is, when an NGW is going to experience an outage in its feeder uplink at time step t + 1, i.e., Ξ̂t+1,i < ⇠th, for i = 1, 2, . . . , N̄ , then the affected NGW will commute all its data traffic to an available PGW. Also, this mechanism is able to verify if the assigned PGW feeder uplink is active, i.e., Ξ̂t+1,N̄+1 ⇠th. Otherwise, the mechanism goes to the next candidate, as long as Ξ̂t+1,N̄+2 ⇠th, and so on CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 95 until reaching the condition. However, the picked PGW could still be working with another affected NGW. Therefore, the mechanism is also capable of looking for the next PGW candidate. When the initial NGW is active again, then the mechanism commutes all data traffic from the current PGW towards the initial NGW. To sum up, this switching mechanism can be called the 1 + P̄ configuration, where each NGW is backed up by redundant gateways P̄ to increase the feeder uplink availability. Figure 6.1 depicts the flowchart of the 1+ P̄ switching strategy for each NGW that explains the described process in this proposal in detail. In other words, the multiple 1 + P̄ mechanism, running N̄ times, provides a scheme N̄ + P̄ as a result. The number of feeder uplink outages can be individually accounted for by the expression (1 ⌫i) ·K, for i = 1, 2, . . . , N̄ , where K is the total number of samples at a time period. Based on the above formulation, the total number of feeder uplink outages in the system is given by outages = K · N̄ X i=1 (1 ⌫i) (6.5) In order to decrease the network complexity, the system unavailability only with NGWs must be equal or lower than 5% in a year, i.e. (1⌫) ·100  5%, reducing the number of switchings between NGWs and PGWs. As a result, the value of the CNIR threshold, ⇠th, is set up based on the system’s unavailability percentage. Finally, used the 1 + P̄ strategy, the feeder-uplink availability expression can be denoted by ⌫Bi = 1 K K X k=1 n (Ξ̂k,i ⇠th ! x = 1)^ ^ ⇥ (Ξ̂k,N̄+1 ⇠th ! x = 1) ^ (Ξ̂k,N̄+2 ⇠th ! x = 1) ^ . . . ^(Ξ̂k,N̄+P̄ ⇠th ! x = 1) ^ (Ξ̂k,N̄+P̄ < ⇠th ! x = 0) ⇤ o , for i = 1, 2, . . . , N̄ (6.6) Indeed, this expression determines how many redundant PGW gateways, denoted by P̄ , can provide instant support to an affected NGW at an annual period, improving the feeder uplink availability as much as possible. Finally, the total system availability is computed by the Eq. (6.4), so that ⌫B = ⌫B1 · ⌫B2 · . . . · ⌫BN̄ . Naturally, this leads to determine the necessary number of P̄ to aid in the ground network to maintain it above 99.9%, finding an optimized N̄ + P̄ scheme. 6.3 The 1 + P̄ Scheme Analyzed by a Markov Chain The 1+P̄ scheme was also analyzed using a stationary distribution by a Markov Chain. Therefore, it was necessary to find the probability of rain for each GW location. For this purpose, the ITU Recommendation ITU-R P. 837 models the characteristics of precipitation for propagation, whose aim is to calculate the rainfall rate exceeded for the desired average annual probability of exceedance and a given location of the Earth [29]. CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 96 Start (k, i = 1) Collect all CNIRs Ξ̂ 2 R K⇥N Sort Ξ̂ according to ⌫ ⌫1 ⌫2 . . . ⌫N NGW scheme N̄ = 4, 8, 12 or 16 Ξ̂k,i ⇠th j = 1 Ξ̂k,N̄+j < ⇠th _ Pj is busy j = j+1 N̄ + j > N Switching Unreachable i = i+1 i > N̄ k = k + 1 i = 1 k > K Stop Switching between N̄i and P̄j No Yes Yes Yes No Yes No No Yes No Figure 6.1: Flowchart of the multiple 1 + P̄ switching strategy. 6.3.1 Method to Calculate the Probability of Rain, P0 To begin with, the ITU Recommendation ITU-R P.837 includes digital maps with information about the monthly mean total rainfall data, MTii, and the annual rainfall rate data exceeded for 0.01% of an average year, R0.01. In both cases, these maps are georeferenced by grids of geographical coordinates. For the MTii map, each coordinate of latitude and longitude is separated by steps with a resolution of 0.25, whereas a resolution of 0.125 for the R0.01 map. CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 97 In this context, the ITU-R P.837 method enables three input parameters, which are the desired annual probability of exceedance, pd [%], the latitude of the desired location Lati [degrees], and the longitude of the desired location Loni [degrees]. Table A.2 shows the latitude, Lati, and longitude, Loni, for each i = 1, 2, . . . , N . Also, the method generates two output parameters, which are the rainfall rate exceeded for the desired probability of exceedance, Rp [mm/h], and the annual probability of rain, P0i [%]. The ITU-R P.837 method [29] is discussed and developed in the following. • Step 1: Table 6.1 indicates the representations of months to employ in this method. Let ii the month number and let Nii the number of days in each month. Table 6.1: Month Numbers and Number of Days Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ii 01 02 03 04 05 06 07 08 09 10 11 12 Nii 31 28.25 31 30 31 30 31 31 30 31 30 31 • Step 2: Determine the monthly mean surfaces temperatures, Tii [K], at the i-th GW location (Lati, Loni), where ii = {01, 02, 03, . . . , 12} and i = 1, 2, . . . , N . In this case, the monthly mean surface temperatures are obtained from the digital maps included in ITU Recommendation ITU-R P.1510 [34]. • Step 3: Likewise, determine the monthly mean total rainfall, MTii, at the i-th GW location (Lati, Loni), from the digital maps included in this ITU Recommendation. However, to determine the MTii at the specific site (Lati, Loni), it is necessary to use bilinear interpolation, which gives by the ITU Recommendation ITU-R P.1144 in more detail [33]. • Step 4: Convert the temperature Tii[K] to tii[ C], for each month number, ii. • Step 5: Calculate rii [mm/h] for each month number as follows rii = 0.5874 · exp (0.0833 · tii) for tii 0C rii = 0.5874 for tii < 0C (6.7) • Step 6a: Calculate the monthly probability of rain [%] for each month number, ii, as follows P0ii = 100 · MTii 24 ·Nii · rii (6.8) • Step 6b: if P0ii > 70, then set P0ii = 70 and rii = 100 70 · MTii 24 ·Nii • Step 7: For each i-th GW location, calculate the annual probability of rain, P0i = P (R > 0) [%] as follows P0i = P12 ii=1 Nii · P0ii 365.25 , for i = 1, 2, . . . , N (6.9) CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 98 • Step 8: In this case, it is not necessary to find Rp for this study. For further details, consult the ITU-R P.837 [29]. It is important to note that the probabilities of rain P0i and P rain i are the same but using different notations. The first one is well-known by the ITU-R P.837, whereas the ITU-R P.618 uses the second one often [28,29]. 6.3.2 The Switching Strategy, 1 + P̄ , from the perspective of a Markov Chain Calculated the annual probability of rain, P0i(Lati, Loni, pd), for each i-th GW-site by Table A.2 coordinates, the GWs can be sorted from the best to the worst regarding no-rain probabilities by each site, so that 1P01 1P02 . . . 1P0N . Likewise, the best first N̄ sites are assigned to be part of the NGWs scheme, whereas the rest of the sites are becoming part of the PGWs as those are added to the ground network later. Although this analysis is using the Markov Chain, the switching mechanism is similar to the scheme 1 + P̄ , as was discussed in subsection 6.2.4 in more detail. Thus, each GW has three states, the active state, non-active state, and the switching state. The active state is related to the no-rain probability at each GW-site, whereas the non-active state occurs as one of the NGWs of the ground network experiences an outage due to the rain, i.e., there is a total outage probability of the system, Pout. At this point, the switching state works as a link between the affected NGW and the picked PGW. It is important to note that there is always a strong emphasis on the first PGW. Nonetheless, if the mentioned PGW is busy or in a feeder-uplink outage, the transition probability goes to the next switching state towards an available PGW, and so on. As a result, the first three states correspond to the analyzed NGW, whereas the next states, in threes, are for each PGW. Figure 6.2 shows the transition probabilities from one state to another by a Markov chain graph. Also, as the Markov chain is a discrete-time process, it can be represented by a state transition matrix P, for i = 1, 2, . . . , N̄ and j = 1, 2, . . . , P̄ , as can be seen in Eq. (6.10). In general terms, the stationary distribution is the fraction of time that the system spends in each state as the number of samples tends to the infinity. As a result, if there are 3(1+P̄ ) states, then the stationary distribution is a vector of length 3(1+P̄ ). Indeed, the stationary distribution is usually referred to as π and is given by π = s0 ·P n, n!1 (6.11) where n is the number of iterations and s0 is the initial state vector s0 = [1, 0, 0, . . . , 0] 2 [0, 1]3(1+P̄ ). In this context, a Markov chain is stationary with stationary distribution π if π · P = π, and P3(1+P̄ ) i=1 πi = 1, where π = [⇡1, ⇡2, . . . , ⇡3(1+P̄ )]. Therefore, the switching probability is calculated as Psw = ⇡3 + ⇡6 + . . .+ ⇡3(1+j), for j = 0, 1, 2 . . . , P̄ (6.12) CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 99 Figure 6.2: The 1 + P̄ strategy represented by a Markov Chain graph. Finally, the switching rate is calculated by Rsw = Psw/Tsw, where Tsw is the interval between switching instants [21,98]. This switching rate is important to determine the effectiveness of the switching strategy in addition to finding the optimal number of PGWs necessary to maintain the availability of the ground network above 99.9%. 6.4 Results To begin with, the smart method to predict both rain attenuation time-series and CNIR time-series at each GW was trained and validated in Chapter 5 by Experiment 2. This method found a model with an average accuracy of 87.83%, generating high-reliability results in comparison with other models. Each ground network configuration has a different capacity, depending on the number of NGWs. By using Eq. (6.1), it was possible to find the feeder uplink capacity at each GW location. For this purpose, the V band provided 4 GHz of CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 100 P =                          s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 · · · s 3 j + 1 s 3 j + 2 s 3 j + 3 s 1 1 P 0 i P o u t P 0 i P o u t 0 0 0 0 0 0 · · · 0 0 0 s 2 1 P 0 i P o u t P 0 i P o u t 0 0 0 0 0 0 · · · 0 0 0 s 3 0 0 0 1 P 0 N̄ + 1 P o u t P 0 N̄ + 1 P o u t 0 0 0 · · · 0 0 0 s 4 0 0 0 1 P 0 N̄ + 1 P o u t P 0 N̄ + 1 P o u t 0 0 0 · · · 0 0 0 s 5 0 0 0 1 P 0 N̄ + 1 P o u t P 0 N̄ + 1 P o u t 0 0 0 · · · 0 0 0 s 6 1 P 0 i P o u t 0 0 0 0 P 0 i P o u t 0 0 · · · 0 0 0 s 7 0 0 0 0 0 0 1 P 0 N̄ + 2 P o u t P 0 N̄ + 2 P o u t · · · 0 0 0 s 8 0 0 0 0 0 0 1 P 0 N̄ + 2 P o u t P 0 N̄ + 2 P o u t · · · 0 0 0 s 9 1 P 0 i P o u t 0 0 0 0 0 0 0 · · · P 0 i P o u t 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s 3 j + 1 0 0 0 0 0 0 0 0 0 · · · 1 P 0 N̄ + j P o u t P 0 N̄ + j P o u t s 3 j + 2 0 0 0 0 0 0 0 0 0 · · · 1 P 0 N̄ + j P o u t P 0 N̄ + j P o u t s 3 j + 3 1 P 0 i P o u t P 0 i P o u t 0 0 0 0 0 0 · · · 0 0 0                          (6 .1 0) CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 101 available spectrum, Savail. Furthermore, the feeder uplink models employed the 1F2P scheme so that they did not use frequency reuse, Nsb = 1, however, they employed double polarization, Np = 2. In order to determine the maximum capacity, each feeder uplink was defined to work under clear sky conditions. Therefore, the best MODCOD, 256 APSK 3/4, based on DVB-S2X, has a spectral efficiency of 5.6199 b/s/Hz with a roll-off of 5%, as can be seen in Chapter 3. As a result, all feeder uplinks obtained an individual capacity of 44.96 Gb/s. Consequently, the inbound capacity was calculated by Eq. (6.2) and using schemes N̄ = 4, 8, 12, and 16. To be precise, Table 6.2 indicates the inbound capacity of an HTS system for each N̄ scheme with a traffic ratio of [1 : 1]. Table 6.2: The Inbound and Total Capacity of the Ground Network Segment. Scheme N̄ Inbound Capacity [Gb/s] Total Capacity [Gb/s] 4 179.84 ⇡ 360.00 8 359.68 ⇡ 720.00 12 539.52 ⇡ 1000.00 16 719.36 ⇡ 1400.00 The matrix Ξ̂ 2 R K⇥N contains the predicted CNIR time-series of each GW obtained from the deep learning model. To be specific, 24 GW locations (Table A.2) were trained and validated by the machine learning model, as can be seen in Chapter 5. Thus, the availability, ⌫i, of each feeder uplink was calculated by Eq. (6.3). For this purpose, the CNIR threshold varied from 0–29 dB to verify the feeder uplink behavior at each step, in addition to sorting the obtained availability from the best to the worst for each N̄ configuration scheme. The best N̄s, according to availability, were part of each ground network configuration, finding the system availability, ⌫, for each N̄ configuration scheme by using Eq. (6.4). Figure 6.3 depicts the unavailability percentage, 1⌫ [%], vs. the CNIR threshold range, ⇠th, for all configuration schemes, N̄ = 4, 8, 12, 16. In this case, ⇠th = 14 dB was a good measure as for all N̄ schemes, the system unavailability percentage was lower than 5% per year. For 1 ⌫ > 5%, the system unavailability increased considerably, so that the number of outages of the system could be tough to manage. The capacity of the feeder uplink is also affected by the rain. For this reason, the CNIR threshold must be capable of balancing as the system available as the capacity of the feeder uplink. Figure 6.4 shows how the threshold ⇠th = 14 dB indicates the limit of the system availability, ⌫, not to be lower than 0.95, and the capacity of feeder uplinks, on average, must not be lower than 44.70 Gb/s. Here the desired availability, ⌫i of each feeder uplink for the GW set, [N ] = {1, 2, . . . , 24}, was calculated using the threshold ⇠th = 14 dB by Eq. (6.3). Then, the GW locations were sorted from the highest to the lowest according to the availability. Table 6.3 shows the sorted availabilities where the best N̄ GWs correspond to the number of GWs according to the ground network configuration, N̄ = 4, 8, 12, 16. As a result, none of the four configuration schemes reached the minimum system CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 102 Figure 6.3: Unavailability percentage per year, for all N̄ configuration schemes. Figure 6.4: System availability vs. the feeder uplink capacity, on average, by ranging the CNIR threshold, ⇠th. CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 103 availability, established in 99.90%. Therefore, all schemes must add redundancy to outperform the required minimum availability. Table 6.3: Gateway Availabilities. Locations [N ] = {1, 2, . . . , 24} Availability ⌫i N̄ = 4 N̄ = 8 N̄ = 12 N̄ = 16 Torreon 0.9994 N̄1 N̄1 N̄1 N̄1 Cd. Juarez 0.9992 N̄2 N̄2 N̄2 N̄2 La Paz, B.C. 0.9992 N̄3 N̄3 N̄3 N̄3 Tijuana 0.9990 N̄4 N̄4 N̄4 N̄4 Oaxaca 0.9986 P̄N̄+1 N̄5 N̄5 N̄5 Queretaro 0.9985 P̄N̄+2 N̄6 N̄6 N̄6 Mexico City 0.9982 P̄N̄+3 N̄7 N̄7 N̄7 Guadalajara 0.9977 P̄N̄+4 N̄8 N̄8 N̄8 Monterrey 0.9968 P̄N̄+5 P̄N̄+1 N̄9 N̄9 Tegucigalpa 0.9963 P̄N̄+6 P̄N̄+2 N̄10 N̄10 Merida 0.9961 P̄N̄+7 P̄N̄+3 N̄11 N̄11 Tuxtla, Gtz. 0.9953 P̄N̄+8 P̄N̄+4 N̄12 N̄12 La Habana 0.9949 P̄N̄+9 P̄N̄+5 P̄N̄+1 N̄13 Kingston 0.9942 P̄N̄+10 P̄N̄+6 P̄N̄+2 N̄14 San Jose 0.9941 P̄N̄+11 P̄N̄+7 P̄N̄+3 N̄15 Cancun 0.9938 P̄N̄+12 P̄N̄+8 P̄N̄+4 N̄16 Veracruz 0.9934 P̄N̄+13 P̄N̄+9 P̄N̄+5 P̄N̄+1 San Pedro Sula 0.9932 P̄N̄+14 P̄N̄+10 P̄N̄+6 P̄N̄+2 Belmopan 0.9925 P̄N̄+15 P̄N̄+11 P̄N̄+7 P̄N̄+3 San Salvador 0.9917 P̄N̄+16 P̄N̄+12 P̄N̄+8 P̄N̄+4 St. Domingo 0.9911 P̄N̄+17 P̄N̄+13 P̄N̄+9 P̄N̄+5 San Juan 0.9902 P̄N̄+18 P̄N̄+14 P̄N̄+10 P̄N̄+6 Panama 0.9898 P̄N̄+19 P̄N̄+15 P̄N̄+11 P̄N̄+7 Pto. Cabezas 0.9889 P̄N̄+20 P̄N̄+16 P̄N̄+12 P̄N̄+8 System Availability, ⌫ [%] 99.68% 98.98% 97.46% 95.23% In this context, the proposed strategy was carried out in this analysis by the switching mechanism, 1+P̄ . Table 6.4 indicates the number of feeder uplink outages of each NGW, backing up by one PGW, at a year-round. Table 6.5 shows the combined availability between NGW and PGW, proving the increase of availability of each feeder uplink. As a result, only one redundant GW was necessary to overcome the required system availability, picking out Oaxaca as the backup GW. Therefore, the optimized scheme was 4 + 1. For the scheme 8+ P̄ , two PGWs (Monterrey and Tegucigalpa) were necessary to back up the ground network about 100%. Table 6.6 displays the number of outages of each NGW, where P̄1 (Monterrey) backs up 99% of feeder uplink outages from all NGWs. Table 6.7 shows the system availability with and without redundancy. In this case, only one PGW (Monterrey) was needful to overcome the required system availability (99.9%), obtaining a 99.99%. Therefore, the 8+ 1 scheme met the aim of improving the required system availability. CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 104 Table 6.4: The Number of Outages of Each NGW for the 4 + P̄ Scheme. Locations [N̄ ] = {1, 2, 3, 4} Oaxaca P̄1 Torreon 293 Cd. Juarez 412 La Paz, B.C. 444 Tijuana 549 Total Outages 1698 Table 6.5: The System Availability for the 4 + P̄ Scheme. Locations [N̄ ] = {1, 2, 3, 4} 4 + 0 4 + 1 Torreon 0.9994 1.0000 Cd. Juarez 0.9992 1.0000 La Paz, B.C. 0.9992 1.0000 Tijuana 0.9990 1.0000 ⌫B [%] 99.68% 100.0% Table 6.6: The Number of Outages of Each NGW for the 8 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 8} Monterrey P̄1 Tegucigalpa P̄2 Torreon 292 1 Cd. Juarez 412 0 La Paz, B.C. 444 0 Tijuana 549 0 Oaxaca 730 0 Queretaro 793 20 Mexico City 907 24 Guadalajara 1190 6 Total Outages 5317 51 Table 6.7: The System Availability for the 8 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 8} 8 + 0 8 + 1 8 + 2 Torreon 0.9994 0.9999 1.0000 Cd. Juarez 0.9992 1.0000 1.0000 La Paz, B.C. 0.9992 1.0000 1.0000 Tijuana 0.9990 1.0000 1.000 Oaxaca 0.9986 1.0000 1.0000 Queretaro 0.9985 0.9999 1.0000 Mexico City 0.9982 0.9999 1.0000 Guadalajara 0.9977 0.9999 1.0000 ⌫B [%] 98.98% 99.99% 100.0% CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 105 Likewise, Table 6.8 indicates the feeder uplink outages for the scheme 12 + P̄ , where two PGWs (La Habana and Kingston) support all outages. Naturally, the P̄1 (La Habana) backed up 98.9%of the feeder uplink outages for all NGWs. Table 6.9 exhibits the system availability for 12 + P̄ schemes. The switching strategy gave two PGWs as a result, but only one PGW (La Habana) was useful to improve the system availability of the ground network. For this reason, the 12 + 1 scheme overcame the required system availability, providing a 99.97%. Table 6.8: The Number of Outages of Each NGW for the 12 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 12} La Habana P̄1 Kingston P̄2 Torreon 292 1 Cd. Juarez 412 0 La Paz, B.C. 444 0 Tijuana 547 2 Oaxaca 730 0 Queretaro 810 3 Mexico City 898 33 Guadalajara 1189 7 Monterrey 1668 30 Tegucigalpa 1892 30 Merida 2052 7 Tuxtla, Gtz. 2419 40 Total Outages 13353 153 Table 6.9: The System Availability for the 12 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 12} 12 + 0 12 + 1 12 + 2 Torreon 0.9994 0.9999 1.0000 Cd. Juarez 0.9992 1.0000 1.0000 La Paz, B.C. 0.9992 1.0000 1.0000 Tijuana 0.9990 0.9999 1.0000 Oaxaca 0.9986 1.0000 1.0000 Queretaro 0.9985 0.9999 1.0000 Mexico City 0.9982 0.9999 1.0000 Guadalajara 0.9977 0.9999 1.0000 Monterrey 0.9968 0.9999 1.0000 Tegucigalpa 0.9963 0.9999 1.0000 Merida 0.9961 0.9999 1.0000 Tuxtla, Gtz. 0.9953 0.9999 1.0000 ⌫B [%] 97.46% 99.97% 100.0% In the last case, the results of the evaluated 16 + P̄ scheme were published by Tables 6.10 and 6.11. In the same context, Table 6.10 shows the number of CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 106 feeder uplink outages in each NGW, whereas three PGWs (Veracruz, San Pedro Sula, and Belmopan) give support to them. The first P̄1 (Veracruz) provided support to the ground network in 97.72% of the time. Table 6.11 indicates the system availability of each 16+P̄ configuration scheme. To be precise, the scheme needed two PGWs (Veracruz and San Pedro Sula) to outperform the required system availability. Consequently, the optimal scheme resulted in 16 + 2, providing a system availability of 99.99%. Table 6.10: The Number of Outages of Each NGW for the 16 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 16} Veracruz P̄1 San Pedro Sula P̄2 Belmopan P̄3 Torreon 293 0 0 Cd. Juarez 412 0 0 La Paz, B.C. 444 0 0 Tijuana 548 1 0 Oaxaca 705 25 0 Queretaro 808 5 0 Mexico City 905 23 3 Guadalajara 1173 23 0 Monterrey 1664 34 0 Tegucigalpa 1882 40 0 Merida 2044 15 0 Tuxtla, Gtz. 2409 50 0 La Habana 2653 39 1 Kingston 2973 95 0 San Jose 3025 82 1 Cancun 3124 148 0 Total Outages 25062 580 5 Finally, for better visualization, these results can be presented in an unavailability graph. Figure 6.5 depicts the different N̄ + P̄ schemes, where the minimum reference is 1⇥ 103 (99.9%). Hence, it is possible to perceive the best schemes that overcome the reference 1⇥ 103, which are: 4 + 1, 8 + 1, 12 + 1, and 16 + 2. However, it is impossible to have an ideal system availability, that is, an availability of 100.0%. Although it is theoretically possible to obtain 100.0% of availability, a more realistic scenario could be as the best unavailability reaches a value of 1⇥ 107. For the Markov Chain method, it was necessary to obtain the probability of rain of each GW-site, P0i , by the ITU Recommendation ITU-R P.837, as can be seen in the subsection 6.3.1. Then, the operation (no-rain) probabilities were sorted from the result of the expression 1P0i , i.e., from the highest to the lowest. Table 6.12 shows the sorted operation probability of each GW-site. Here, the best N̄ GWs became part of the ground network according to the N̄ schemes, 4, 8, 12, and 16. By applying the switching strategy of Section 6.3, the stationary distribution, π, of each 1+P̄ scheme was obtained from the state transition matrix, Eq. 6.10. For this purpose, the system outage probability, Pout, was set in 1⇥ 104. Table 6.13 presents CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 107 Table 6.11: The System Availability for the 16 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 16} 16 + 0 16 + 1 16 + 2 16 + 3 Torreon 0.9994 1.0000 1.0000 1.0000 Cd. Juarez 0.9992 1.0000 1.0000 1.0000 La Paz, B.C. 0.9992 1.0000 1.0000 1.0000 Tijuana 0.9990 0.9999 1.0000 1.0000 Oaxaca 0.9986 0.9999 1.0000 1.0000 Queretaro 0.9985 0.9999 1.0000 1.0000 Mexico City 0.9982 0.9998 0.9999 1.0000 Guadalajara 0.9977 0.9999 1.0000 1.0000 Monterrey 0.9968 0.9999 1.0000 1.0000 Tegucigalpa 0.9963 0.9999 1.0000 1.0000 Merida 0.9961 0.9999 1.0000 1.0000 Tuxtla, Gtz. 0.9953 0.9999 1.0000 1.0000 La Habana 0.9949 0.9998 0.9999 1.0000 Kingston 0.9942 0.9999 1.0000 1.0000 San Jose 0.9941 0.9998 0.9999 1.0000 Cancun 0.9938 0.9999 1.0000 1.0000 ⌫B [%] 95.23% 99.89% 99.99% 100.0% Figure 6.5: Performance of the N̄ + P̄ schemes, as a function of system unavailability and the number of P̄ . CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 108 Table 6.12: The Operation Probability of Gateways. Locations [N ] = {1, 2, . . . , 24} Operation Probability 1 P0i N̄ = 4 N̄ = 8 N̄ = 12 N̄ = 16 La Paz, B.C. 0.9962 N̄1 N̄1 N̄1 N̄1 Torreon 0.9945 N̄2 N̄2 N̄2 N̄2 Cd. Juarez 0.9920 N̄3 N̄3 N̄3 N̄3 Merida 0.9840 N̄4 N̄4 N̄4 N̄4 Monterrey 0.9835 P̄N̄+1 N̄5 N̄5 N̄5 Tijuana 0.9826 P̄N̄+2 N̄6 N̄6 N̄6 Queretaro 0.9797 P̄N̄+3 N̄7 N̄7 N̄7 Cancun 0.9752 P̄N̄+4 N̄8 N̄8 N̄8 Oaxaca 0.9738 P̄N̄+5 P̄N̄+1 N̄9 N̄9 La Habana 0.9729 P̄N̄+6 P̄N̄+2 N̄10 N̄10 Tegucigalpa 0.9728 P̄N̄+7 P̄N̄+3 N̄11 N̄11 Tuxtla, Gtz. 0.9727 P̄N̄+8 P̄N̄+4 N̄12 N̄12 Guadalajara 0.9723 P̄N̄+9 P̄N̄+5 P̄N̄+1 N̄13 Kingston 0.9714 P̄N̄+10 P̄N̄+6 P̄N̄+2 N̄14 Veracruz 0.9709 P̄N̄+11 P̄N̄+7 P̄N̄+3 N̄15 St. Domingo 0.9671 P̄N̄+12 P̄N̄+8 P̄N̄+4 N̄16 San Juan 0.9671 P̄N̄+13 P̄N̄+9 P̄N̄+5 P̄N̄+1 Mexico City 0.9645 P̄N̄+14 P̄N̄+10 P̄N̄+6 P̄N̄+2 San Salvador 0.9638 P̄N̄+15 P̄N̄+11 P̄N̄+7 P̄N̄+3 San Pedro Sula 0.9614 P̄N̄+16 P̄N̄+12 P̄N̄+8 P̄N̄+4 Panama 0.9592 P̄N̄+17 P̄N̄+13 P̄N̄+9 P̄N̄+5 Belmopan 0.9568 P̄N̄+18 P̄N̄+14 P̄N̄+10 P̄N̄+6 Pto. Cabezas 0.9473 P̄N̄+19 P̄N̄+15 P̄N̄+11 P̄N̄+7 San Jose 0.9356 P̄N̄+20 P̄N̄+16 P̄N̄+12 P̄N̄+8 System Operation Probability, [%] 96.70% 89.28% 80.03% 70.97% the stationary distribution of each NGW for the 4+P̄ scheme. Although each π has 63 states, only the first 12 states were necessary for this analysis as the next probabilities were practically negligible. Table 6.14 displays the system operation probabilities for each 4 + P̄ scheme. In this case, the scheme 4 + 2 overcame the required system availability of 99.9% in terms of probability. The two picked redundant GWs were Monterrey and Tijuana. It is important to note that the inactive states were not considered to determine the operation probability. Table 6.15 and Table 6.16 indicate the stationary distribution and the system operation probabilities for the 8+P̄ Scheme, respectively. In this case, each stationary distribution had 51 states, but only the first 12 states were useful to determine the number of PGWs to be added to the ground network. As a result, the scheme 8 + 3 was the most suitable scheme (99.92%) to work above the reference (99.9%), in terms of probability. The three picked redundant GWs were Oaxaca, La Habana, and Tegucigalpa. CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 109 Table 6.13: The Stationary Distribution of Each NGW for the 4 + P̄ Scheme. States N̄1 N̄2 N̄3 N̄4 s1 0.8114 0.7473 0.6705 0.4996 s2 8.1449⇥ 105 7.5146⇥ 105 6.7586⇥ 105 5.0776⇥ 105 s3 0.0030 0.0041 0.0053 0.0080 s4 0.1818 0.2432 0.3164 0.4768 s5 1.8485⇥ 105 2.4726⇥ 105 3.2171⇥ 105 4.8480⇥ 105 s6 0.0030 0.0041 0.0053 0.0080 s7 6.5697⇥ 104 1.2762⇥ 103 2.4081⇥ 103 7.3383⇥ 103 s8 6.5704⇥ 108 1.2764⇥ 107 2.4084⇥ 107 7.3390⇥ 107 s9 1.1356⇥ 105 2.2061⇥ 105 4.1626⇥ 105 1.2685⇥ 104 s10 2.1016⇥ 106 5.9290⇥ 106 1.6224⇥ 105 9.9978⇥ 105 s11 2.1018⇥ 1010 5.9296⇥ 1010 1.6226⇥ 109 9.9988⇥ 109 s12 4.2484⇥ 108 1.1986⇥ 107 3.2797⇥ 107 2.0211⇥ 106 Table 6.14: The System Operation Probabilities for the 4 + P̄ Scheme. Locations [N̄ ] = {1, 2, 3, 4} 4 + 0 4 + 1 4 + 2 4 + 3 La Paz, B.C. 0.9962 0.9992 0.9999 0.9999 Torreon 0.9945 0.9986 0.9999 0.9999 Cd. Juarez 0.9920 0.9974 0.9999 0.9999 Merida 0.9840 0.9923 0.9998 0.9999 Operation Probability, [%] 96.70% 98.76% 99.95% 99.96% Table 6.17 and Table 6.18 provide the results of the stationary distribution and the system operation probabilities for the 12 + P̄ Scheme, respectively. The total number of states of each stationary distribution was 39. However, the first 15 states of each distribution were required to evaluate the operation probability of the system. Consequently, the scheme 12 + 3 obtained an operation probability of 99.90%, achieving the minimum requirement in terms of probability. The three picked redundant GWs were Guadalajara, Kingston, and Veracruz. Finally, Table 6.19 and Table 6.20 give the outcomes obtained from the stationary distribution and the system operation probabilities for the 16+P̄ Scheme, respectively. Each stationary distribution vector had a length of 27 elements or states, where the only first 15 states were necessary to obtain the operation probability of the system. To sum up, the scheme 16 + 4 provided an operation probability of 99.91%, which outperformed the reference of 99.9%, in terms of probability. The four picked redundant GWs were San Juan, Mexico City, San Salvador, and San Pedro Sula. It is important to note that all evaluated state-transition-matrices were ergodic and irreducibles. In other words, a Markov chain is ergodic if it is both irreducible and aperiodic. This condition is equivalent to the state transition matrix being a primitive non-negative matrix. In this context, ergodicity means the long-term proportion of time spent by the chain in state si, corresponding to the steady-state probability. C H A P T E R 6 . G R O U N D S E G M E N T O P T IM IZ A T IO N B Y U S IN G ... 110 Table 6.15: The Stationary Distribution of Each NGW for the 8 + P̄ Scheme. States N̄1 N̄2 N̄3 N̄4 N̄5 N̄6 N̄7 N̄8 s1 0.8714 0.8234 0.7623 0.6114 0.6041 0.5916 0.5526 0.5020 s2 8.7480⇥ 105 8.2793⇥ 105 7.6842⇥ 105 6.2140⇥ 105 6.1426⇥ 105 6.0208⇥ 105 5.6407⇥ 105 5.1473⇥ 105 s3 0.0033 0.0045 0.0060 0.0097 0.0099 0.0102 0.0112 0.0124 s4 0.1215 0.1667 0.2238 0.3630 0.3696 0.3810 0.4162 0.4613 s5 1.2474⇥ 105 1.7116⇥ 105 2.2982⇥ 105 3.7277⇥ 105 3.7961⇥ 105 3.9127⇥ 105 4.2740⇥ 105 4.7369⇥ 105 s6 0.0033 0.0045 0.0060 0.0097 0.0099 0.0102 0.0112 0.0124 s7 0.0005 0.0009 0.0018 0.0057 0.0060 0.0065 0.0084 0.0113 s8 4.5125⇥ 108 8.9921⇥ 108 1.7509⇥ 107 5.7431⇥ 107 6.0280⇥ 107 6.5392⇥ 107 8.3537⇥ 107 1.1296⇥ 106 s9 1.2197⇥ 105 2.4306⇥ 105 4.7327⇥ 105 1.5524⇥ 104 1.6294⇥ 104 1.7675⇥ 104 2.2580⇥ 104 3.0532⇥ 104 s10 1.6812⇥ 106 4.8653⇥ 106 1.3739⇥ 105 9.1128⇥ 105 9.8584⇥ 105 1.1256⇥ 104 1.6816⇥ 104 2.7742⇥ 104 s11 1.6813⇥ 1010 4.8658⇥ 1010 1.3740⇥ 109 9.1137⇥ 109 9.8594⇥ 109 1.1257⇥ 108 1.6818⇥ 108 2.7744⇥ 108 s12 4.5630⇥ 108 1.3205⇥ 107 3.7289⇥ 107 2.4734⇥ 106 2.6757⇥ 106 3.0550⇥ 106 4.5641⇥ 106 7.5296⇥ 106 Table 6.16: The System Operation Probabilities for the 8 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 8} 8 + 0 8 + 1 8 + 2 8 + 3 La Paz, B.C. 0.9962 0.9994 0.9999 0.9999 Torreon 0.9945 0.9990 0.9999 0.9999 Cd. Juarez 0.9920 0.9981 0.9999 0.9999 Merida 0.9840 0.9939 0.9998 0.9999 Monterrey 0.9835 0.9936 0.9998 0.9999 Tijuana 0.9826 0.9931 0.9998 0.9999 Queretaro 0.9797 0.9911 0.9997 0.9999 Cancun 0.9752 0.9880 0.9996 0.9999 Operation Probability, [%] 89.28% 95.70% 99.84% 99.92% C H A P T E R 6 . G R O U N D S E G M E N T O P T IM IZ A T IO N B Y U S IN G ... 111 Table 6.17: The Stationary Distribution of Each NGW for the 12 + P̄ Scheme. States N̄1 N̄2 N̄3 N̄4 N̄5 N̄6 N̄7 N̄8 N̄9 N̄10 N̄11 N̄12 s1 0.8773 0.8310 0.7718 0.6240 0.6168 0.6044 0.5657 0.5153 0.5004 0.4918 0.4907 0.4902 s2 8.8067⇥ 105 8.3559⇥ 105 7.7801⇥ 105 6.3418⇥ 105 6.2714⇥ 105 6.1511⇥ 105 5.7747⇥ 105 5.2838⇥ 105 5.1388⇥ 105 5.0550⇥ 105 5.0449⇥ 105 5.0396⇥ 105 s3 0.0033 0.0045 0.0061 0.0099 0.0101 0.0104 0.0114 0.0127 0.0131 0.0133 0.0133 0.0133 s4 0.1156 0.1590 0.2142 0.3502 0.3568 0.3680 0.4028 0.4476 0.4607 0.4682 0.4691 0.4696 s5 1.1889⇥ 105 1.6355⇥ 105 2.2029⇥ 105 3.6018⇥ 105 3.6693⇥ 105 3.7845⇥ 105 4.1426⇥ 105 4.6035⇥ 105 4.7380⇥ 105 4.8155⇥ 105 4.8248⇥ 105 4.8297⇥ 105 s6 0.0033 0.0045 0.0061 0.0099 0.0101 0.0104 0.0114 0.0127 0.0131 0.0133 0.0133 0.0133 s7 0.0004 0.0009 0.0017 0.0056 0.0058 0.0063 0.0081 0.0110 0.0120 0.0126 0.0127 0.0127 s8 4.3083⇥ 108 8.6069⇥ 108 1.6813⇥ 107 5.5587⇥ 107 5.8367⇥ 107 6.3359⇥ 107 8.1107⇥ 107 1.0997⇥ 106 1.1995⇥ 106 1.2608⇥ 106 1.2683⇥ 106 1.2723⇥ 106 s9 1.2279⇥ 105 2.4530⇥ 105 4.7917⇥ 105 1.5843⇥ 104 1.6635⇥ 104 1.8058⇥ 104 2.3116⇥ 104 3.1342⇥ 104 3.4188⇥ 104 3.5934⇥ 104 3.6149⇥ 104 3.6263⇥ 104 s10 1.5841⇥ 106 4.5960⇥ 106 1.3020⇥ 105 8.7049⇥ 105 9.4207⇥ 105 1.0763⇥ 104 1.6113⇥ 104 2.6654⇥ 104 3.0815⇥ 104 3.3496⇥ 104 3.3831⇥ 104 3.4011⇥ 104 s11 1.5843⇥ 1010 4.5964⇥ 1010 1.3021⇥ 109 8.7057⇥ 109 9.4217⇥ 109 1.0764⇥ 108 1.6115⇥ 108 2.6657⇥ 108 3.0818⇥ 108 3.3499⇥ 108 3.3835⇥ 108 3.4014⇥ 108 s12 4.5936⇥ 108 1.3327⇥ 107 3.7754⇥ 107 2.5242⇥ 106 2.7318⇥ 106 3.1211⇥ 106 4.6725⇥ 106 7.7292⇥ 106 8.9357⇥ 106 9.7130⇥ 106 9.8104⇥ 106 9.8624⇥ 106 s13 5.2411⇥ 109 2.2083⇥ 108 9.0723⇥ 108 1.2266⇥ 106 1.3682⇥ 106 1.6453⇥ 106 2.8805⇥ 106 5.8133⇥ 106 7.1231⇥ 106 8.0072⇥ 106 8.1201⇥ 106 8.1806⇥ 106 s14 5.2416⇥ 1013 2.2086⇥ 1012 9.0732⇥ 1012 1.2267⇥ 1010 1.3684⇥ 1010 1.6454⇥ 1010 2.8808⇥ 1010 5.8139⇥ 1010 7.1238⇥ 1010 8.0080⇥ 1010 8.1209⇥ 1010 8.1814⇥ 1010 s15 1.7185⇥ 1010 7.2408⇥ 1010 2.9746⇥ 109 4.0218⇥ 108 4.4862⇥ 108 5.3946⇥ 108 9.4446⇥ 108 1.9061⇥ 107 2.3355⇥ 107 2.6254⇥ 107 2.6624⇥ 107 2.6823⇥ 107 Table 6.18: The System Operation Probabilities for the 12 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 12} 12 + 0 12 + 1 12 + 2 12 + 3 12 + 4 La Paz, B.C. 0.9962 0.9995 0.9999 0.9999 0.9999 Torreon 0.9945 0.9990 0.9999 0.9999 0.9999 Cd. Juarez 0.9920 0.9982 0.9999 0.9999 0.9999 Merida 0.9840 0.9941 0.9998 0.9999 0.9999 Monterrey 0.9835 0.9938 0.9998 0.9999 0.9999 Tijuana 0.9826 0.9933 0.9998 0.9999 0.9999 Queretaro 0.9797 0.9914 0.9997 0.9999 0.9999 Cancun 0.9752 0.9883 0.9996 0.9999 0.9999 Oaxaca 0.9738 0.9872 0.9996 0.9999 0.9999 La Habana 0.9729 0.9866 0.9995 0.9999 0.9999 Tegucigalpa 0.9728 0.9865 0.9995 0.9999 0.9999 Tuxtla, Gtz. 0.9727 0.9865 0.9995 0.9999 0.9999 Operation Probability, [%] 80.03% 90.82% 99.66% 99.90% 99.91% C H A P T E R 6 . G R O U N D S E G M E N T O P T IM IZ A T IO N B Y U S IN G ... 112 Table 6.19: The Stationary Distribution of Each NGW for the 16 + P̄ Scheme. States N̄1 N̄2 N̄3 N̄4 N̄5 N̄6 N̄7 N̄8 N̄9 N̄10 N̄11 N̄12 N̄13 N̄14 N̄15 N̄16 s1 0.8942 0.8532 0.7999 0.6624 0.6555 0.6437 0.6064 0.5570 0.5423 0.5337 0.5327 0.5322 0.5283 0.5202 0.5158 0.4842 s2 8.9761⇥ 105 8.5790⇥ 105 8.0635⇥ 105 6.7323⇥ 105 6.6656⇥ 105 6.5511⇥ 105 6.1898⇥ 105 5.7118⇥ 105 5.5691⇥ 105 5.4863⇥ 105 5.4763⇥ 105 5.4710⇥ 105 5.4340⇥ 105 5.3550⇥ 105 5.3123⇥ 105 5.0063⇥ 105 s3 0.0033 0.0046 0.0063 0.0106 0.0108 0.0111 0.0123 0.0137 0.0142 0.0144 0.0145 0.0145 0.0146 0.0148 0.0150 0.0159 s4 0.0987 0.1367 0.1859 0.3114 0.3176 0.3282 0.3616 0.4052 0.4181 0.4256 0.4265 0.4269 0.4303 0.4373 0.4412 0.4683 s5 1.0203⇥ 105 1.4138⇥ 105 1.9224⇥ 105 3.2194⇥ 105 3.2837⇥ 105 3.3937⇥ 105 3.7387⇥ 105 4.1901⇥ 105 4.3234⇥ 105 4.4005⇥ 105 4.4098⇥ 105 4.4147⇥ 105 4.4490⇥ 105 4.5222⇥ 105 4.5616⇥ 105 4.8417⇥ 105 s6 0.0033 0.0046 0.0063 0.0106 0.0108 0.0111 0.0123 0.0137 0.0142 0.0144 0.0145 0.0145 0.0146 0.0148 0.0150 0.0159 s7 0.0004 0.0007 0.0014 0.0048 0.0050 0.0054 0.0070 0.0096 0.0105 0.0110 0.0111 0.0111 0.0114 0.0119 0.0123 0.0147 s8 3.5367⇥ 108 7.1172⇥ 108 1.4034⇥ 107 4.7527⇥ 107 4.9964⇥ 107 5.4348⇥ 107 7.0021⇥ 107 9.5743⇥ 107 1.0470⇥ 106 1.1021⇥ 106 1.1089⇥ 106 1.1125⇥ 106 1.1380⇥ 106 1.1942⇥ 106 1.2255⇥ 106 1.4708⇥ 106 s9 1.2515⇥ 105 2.5186⇥ 105 4.9662⇥ 105 1.6818⇥ 104 1.7681⇥ 104 1.9232⇥ 104 2.4778⇥ 104 3.3880⇥ 104 3.7051⇥ 104 3.9000⇥ 104 3.9240⇥ 104 3.9367⇥ 104 4.0272⇥ 104 4.2259⇥ 104 4.3366⇥ 104 5.2046⇥ 104 s10 1.2968⇥ 106 3.7901⇥ 106 1.0838⇥ 105 7.4224⇥ 105 8.0424⇥ 105 9.2073⇥ 105 1.3873⇥ 104 2.3143⇥ 104 2.6823⇥ 104 2.9199⇥ 104 2.9497⇥ 104 2.9656⇥ 104 3.0795⇥ 104 3.3361⇥ 104 3.4829⇥ 104 4.7264⇥ 104 s11 1.2970⇥ 1010 3.7905⇥ 1010 1.0839⇥ 109 7.4231⇥ 109 8.0432⇥ 109 9.2082⇥ 109 1.3874⇥ 108 2.3145⇥ 108 2.6826⇥ 108 2.9202⇥ 108 2.9500⇥ 108 2.9659⇥ 108 3.0798⇥ 108 3.3365⇥ 108 3.4832⇥ 108 4.7268⇥ 108 s12 4.6819⇥ 108 1.3683⇥ 107 3.9129⇥ 107 2.6797⇥ 106 2.9035⇥ 106 3.3241⇥ 106 5.0084⇥ 106 8.3553⇥ 106 9.6840⇥ 106 1.0542⇥ 105 1.0649⇥ 105 1.0707⇥ 105 1.1118⇥ 105 1.2044⇥ 105 1.2574⇥ 105 1.7063⇥ 105 s13 4.5534⇥ 109 1.9327⇥ 108 8.0148⇥ 108 1.1100⇥ 106 1.2396⇥ 106 1.4936⇥ 106 2.6318⇥ 106 5.3567⇥ 106 6.5801⇥ 106 7.4077⇥ 106 7.5134⇥ 106 7.5701⇥ 106 7.9793⇥ 106 8.9241⇥ 106 9.4781⇥ 106 1.4543⇥ 105 s14 4.5539⇥ 1013 1.9329⇥ 1012 8.0157⇥ 1012 1.1101⇥ 1010 1.2397⇥ 1010 1.4938⇥ 1010 2.6321⇥ 1010 5.3572⇥ 1010 6.5808⇥ 1010 7.4085⇥ 1010 7.5142⇥ 1010 7.5709⇥ 1010 7.9801⇥ 1010 8.9250⇥ 1010 9.4791⇥ 1010 1.4545⇥ 109 s15 1.7515⇥ 1010 7.4341⇥ 1010 3.0830⇥ 109 4.2695⇥ 108 4.7682⇥ 108 5.7453⇥ 108 1.0124⇥ 107 2.0605⇥ 107 2.5311⇥ 107 2.8494⇥ 107 2.8901⇥ 107 2.9119⇥ 107 3.0693⇥ 107 3.4327⇥ 107 3.6458⇥ 107 5.5942⇥ 107 Table 6.20: The System Operation Probabilities for the 16 + P̄ Scheme. Locations [N̄ ] = {1, 2, . . . , 16} 16 + 0 16 + 1 16 + 2 16 + 3 16 + 4 La Paz, B.C. 0.9962 0.9995 0.9999 0.9999 0.9999 Torreon 0.9945 0.9992 0.9999 0.9999 0.9999 Cd. Juarez 0.9920 0.9984 0.9999 0.9999 0.9999 Merida 0.9840 0.9949 0.9998 0.9999 0.9999 Monterrey 0.9835 0.9946 0.9998 0.9999 0.9999 Tijuana 0.9826 0.9942 0.9998 0.9999 0.9999 Queretaro 0.9797 0.9925 0.9998 0.9999 0.9999 Cancun 0.9752 0.9897 0.9997 0.9999 0.9999 Oaxaca 0.9738 0.9888 0.9996 0.9999 0.9999 La Habana 0.9729 0.9882 0.9996 0.9999 0.9999 Tegucigalpa 0.9728 0.9881 0.9996 0.9999 0.9999 Tuxtla, Gtz. 0.9727 0.9881 0.9996 0.9999 0.9999 Guadalajara 0.9723 0.9878 0.9996 0.9999 0.9999 Kingston 0.9714 0.9872 0.9995 0.9999 0.9999 Veracruz 0.9709 0.9868 0.9995 0.9999 0.9999 St. Domingo 0.9671 0.9842 0.9994 0.9999 0.9999 Operation Probability, [%] 70.97% 87.06% 99.50% 99.85% 99.91% CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 113 Meanwhile, the Markov chain is irreducible when the state si of the Markov chain is accessible from another state sj by a finite sequence of the transition of si to sj with positive probability [83]. In summary, Figure 6.6 depicts the obtained schemes N̄ + P̄ in terms of system outage probability, Pout. Here, it is possible to appreciate the best schemes that outperform the reference 1⇥ 103, which are: 4 + 2, 8 + 3, 12 + 3, and 16 + 4. Figure 6.6: Performance of the N̄ + P̄ schemes, as a function of system outage probability, Pout, and the number of P̄ . 6.5 Discussions There are remarkable differences between the availabilities and probabilities of each GW. For instance, the sorted list of Table 6.3 is different in comparison with the sorted list of Table 6.12. Naturally, the difference lies in the methods to define the availability (deterministic approach) and probability (probabilistic approach) at each GW. Nevertheless, this difference is not a big problem as the analysis of each feeder uplink was rigorous, following the steps aforementioned of both methods. Therefore, both sorted lists are theoretically reliable according to their mathematical nature. In both smart predictive and Markov chain 1 + P̄ strategy methods, the first PGW backs up the most of feeder uplink outages of NGWs. For this reason, the mechanism has a direct approach when an NGW feeder uplink is in an outage in terms of assignation, backing up immediately the affected NGW with the first PGW. On the other hand, if the first PGW has its feeder uplink in an outage or busy with another NGW, then the mechanism picks out the next available PGW. Motivated by this, the method encourages to avoid correlated rain in two or more GWs at the same time by a separation between them based on the correlation coefficient ⇢a obtained CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 114 from ITU-R P.1815. As a result, all GWs are separated by a distance > 80 km, reducing the risk of simultaneous rain in two or more sites at the same time, and increasing the chances of the first PGW is available in most of the time. Moreover, it was necessary to assume spatially independent and identically distributed (i.i.d) feeder uplinks. The main aim of this study is to define the most suitable ground network to manage a satellite system of 1 Tb/s and beyond. According to Table 6.2, 12 NGWs are needed to manage a satellite system of about 1 Tb/s. In a sense, for capacities of 1 Tb/s and beyond, we have coined the term Ultra High Throughput Satellite Systems (UHTS). To be specific, the ground networks of 4 and 8 NGWs are for HTS systems, whereas the ground networks of 12 and 16 NGWs are for UHTS systems. In this context, these 4 configurations of NGWs were tested by both switching strategies to determine their effectiveness, as deterministically (smart predictive method) as probabilistically (Markov chain method). Figure 6.7 shows the results of both proposed methods in this study to find N̄ + P̄ schemes, in addition to Gharanjik’s method [25]. The results obtained from the smart predictive method were highly superior compared with the Markov Chain method and the Gharanjik’s method. That is, the smart predictive method gave the following results: 4+1, 8+1, 12 + 1, and 16 + 2, whereas the Markov Chain method: 4 + 2, 8 + 3, 12 + 3, and 16 + 4. Gharanjik’s method provided linear results, that is, N̄/P̄ = 4, so that the scheme results are the following: 4 + 1, 8 + 2, 12 + 3, and 16 + 4. Figure 6.7: N̄ + P̄ configuration schemes obtained from the three aforementioned methods. The efficiency of the smart predictive method is, on average, 41.67% and 58.34% better than Gharanjik’s model and Markov chain model, respectively. Therefore, the 1 + P̄ switching strategy based on the smart method for forecasting rain attenuation and CNIR at each GW is highly efficient and reliable, optimizing the ground segment network as much as possible. Indeed, for a 1 Tb/s UHTS, the optimized ground CHAPTER 6. GROUND SEGMENT OPTIMIZATION BY USING . . . 115 network is 12 + 1, rather than 12 + 3 obtained from Gharanjik’s method, reducing the network complexity and generating economic savings on the ground segment. Despite the ground network could be not optimized by the Markov chain method, each stationary distribution obtained from this method gave us a panorama on the switching probability between the affected NGW and the first PGW. No doubt, this parameter could help to get more information about the ground network behavior when there is a switching between an NGW and PGW under different weather conditions. In other words, the switching probability could be determinant to define the most suitable technology to implement on the ground network, that is, the network infrastructure to communicate GWs to each other. 6.6 Contributions of the Research The proposed methods and found results in this chapter will be submitted to a IEEE Transactions on Reliability Journal to be reviewed and published later. Furthermore, the previous study was exposed to a specialized conference: "2020 IEEE 11th Latin American Symposium on Circuits and Systems, LASCAS 2020," at San Jose, Costa Rica. • Andres Cornejo, Salvador Landeros-Ayala, Jose M. Matias, and Ramon Martinez. Applying Learning Methods to Optimize the Ground Segment for HTS Systems. 2020 IEEE 11th Lat. Am. Symp. Circuits Syst. LASCAS 2020, pages 1–4, 2020 Chapter 7 Conclusions, Future Work, and Contributions 7.1 Conclusions In this thesis, we designed, allocated, and optimized the ground segment by using novel methods and procedures with excellent results. The obtained feeder link was designed in the Q/V band, whose performance was determined by numerical evaluations. Further, the designed satellite antenna was based on an offset-parabolic-reflector antenna to evaluate the interferences that could influence the satellite links, directly or indirectly. As a result, we found excellent levels of the carrier-to-noise and interference (CNIR) of each analyzed feeder uplink in clear-sky conditions, which reached out to the uplink expectations for our system. However, for a more realistic scenario, each feeder uplink was evaluated by applying a dynamic rain attenuation based on the ITU Recommendation P.1853, defining the upper and lower limits of feeder uplinks operation under the rain conditions. For this purpose, we have successfully developed a method to generate, train, and validate rain-attenuation prediction models based on LSTM networks. Two Experiments were carried out to determine the best models, where Experiment 2 was found to be the most complete and accurate. In this sense, Machine Learning methods can be beneficial for solving a specific problem whether the adaptation is correct. In this case, deep learning networks based on LSTM regression models were adequately adapted to our study, thereby, they were able to predict rain attenuation events more accurately. In order to validate our proposal, this method was compared with other predictive methods, where our proposal obtained a higher accuracy and a better performance. Furthermore, real rain-attenuation data were difficult to obtain due to the lack of historical database, however, ITU Recommendation (ITU-R P.1853) was able to compute artificial rain-attenuation, providing a plethora of data. Indeed, a lot of data is required to train LSTM networks due to they are notably ubiquitous. Here, it was possible to split data into both training and validation subsets because each rain attenuation time series had hundreds of thousands of samples. 116 CHAPTER 7. CONCLUSIONS, FUTURE WORK, AND CONTRIBUTIONS 117 The processing of data was essential for obtaining good results as the answer lies in the data. For this reason, subsets were carefully processed in terms of normalization, partitioning, training, and validation. Thus, the model accuracy, on average, is about 87.83%, where the best model reaches out to the accuracy of 92.24%. All evaluated GW-sites indicate good performance, giving solid predictions of rain attenuation. In this context, the found results are successful to determine in advance how the feeder uplink will be affected by weather impairments. This certainly leads to better decision-making under rain-attenuation events, thereby, mechanisms such as ULPC, traffic switching between GWs with extra resources, and satellite-link switching towards backup gateway stations, can be improved by CNIR predictions obtained from this proposal in order to assure high availability on satellite links. To be precise, we focus on the optimization of the ground network by the switching strategies of traffic between GWs. In this context, two switching strategy mechanisms were proposed by a smart-predictive-method based on the deep learning model and a Markov chain method. As a result, the proposed smart-predictive method reaches a superior efficiency, on average, of 41.67% vs Gharanjik’s method, and 58.34% vs the proposed Markov chain method, optimizing the ground network with excellent performance. For instance, for a UHTS system of 1 Tb/s, Gharanjik’s method provided a ground network scheme of 12 + 3 to operate above the required network availability of 99.9%. Meanwhile, the proposed smart-predictive method gave, as a result, an optimized scheme of 12 + 1, which was 66.67% more efficient than the previous configuration scheme. In other words, the success of the smart-predictive method lies in the ability to detect, in advance, a feeder uplink in outage due to the rain, anticipating the switching between the affected NGW and an available PGW. To sum up, this prediction method leads to optimizing the ground segment by the smart gateway diversity, reducing the number of gateway stations, that is, the network complexity. 7.2 Future Work As a result of this thesis, some interesting topics have been branched for future research work in both Machine Learning and Satellite Communication fields, which comprise, • Although the artificial data were useful to develop this proposal, rain attenuation from a historical database could help to tune up and to improve models. Further studies are necessary to determine much more accurate models by employing real and artificial data together. • By using Cloud Computing, the prediction method could be accessed from any GW station, to be specific, the prediction method could be implemented by software as a service (SaaS). No doubt that the prediction method as a cloud service will guarantee to manage data in real-time, in addition to providing flexibility and security. CHAPTER 7. CONCLUSIONS, FUTURE WORK, AND CONTRIBUTIONS 118 • Finally, the stationary distributions obtained from the Markov chain method provide worth information (the switching rate) to define the best infrastructure capable of transferring data traffic between GWs, reducing latency and delays. In this context, the best option is the network infrastructure based on optical fiber, but it is not the cheapest choice. Hence, other options could be considered to simplify the terrestrial network and reduce costs by the analysis of the switching probability and rate, e.g., microwave links. 7.3 Contributions and Production The research results of each topic of this thesis have been published or have been submitted for publications in journals and conference proceedings, as indicated in the following. It is worth to mention that the main ideas, the problem formulations, the analysis, simulations, and numerical assessments for all publications are contributions of the author of this thesis. Journals • [103] Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez, and Jose M Matias. Analysis to Quantify and Optimize Spot Beams for a High Throughput Satellite in Ka and Q/V Bands. IEEE Lat. Am. Trans., 17(02):219–227, feb 2019 • [104] Andres Cornejo, Salvador Landeros-Ayala, Ramon Martínez Rodríguez-Osorio, and Jose M Matias. A method for designing an offset-parabolic-reflector antenna for a ultra-high throughput satellite. In Rev. Tecnol. e Inf., volume 16, pages 84–87, Lima, Peru, 2018. Universidad Inca Garcilaso de la Vega • [105] Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez-Rodriguez, and Jose M Matias. Interference Evaluations in Frequency Reuse by Using Offset- Parabolic-Reflector Antennas for a UHTS System. Int. J. Eng. Sci., 7(8):34–45, 2018 • Andres Cornejo, Salvador Landeros-Ayala, Jose M. Matias, Flor Ortiz-Gomez, Ramon Martinez, and Miguel Salas-Natera. Method of Rain Attenuation Prediction Based On Long-Short Term Memory Network. In Review., 1(1):1–35, 2020 • Andres Cornejo, Salvador Landeros-Ayala, and Jose Maria Matias. Optimization of the Ground Network Segment by Implementing Machine Learning. To be Submitted, 1(1):30, 2020 Conferences • [106] Andres Cornejo, Salvador Landeros-Ayala, Ramon Martinez Rodriguez-Osorio, and Jose Maria Matias. Optimization of the Ground Segment for an UHTS System through Neural Networks. In XXXIII Simp. CHAPTER 7. CONCLUSIONS, FUTURE WORK, AND CONTRIBUTIONS 119 Nac. la Unión Científica Int. Radio (URSI 2018), pages 1–5, Granada, Spain, 2018 • [107] Andres Cornejo, Salvador Landeros-Ayala, Jose M. Matias, and Ramon Martinez. Applying Learning Methods to Optimize the Ground Segment for HTS Systems. 2020 IEEE 11th Lat. Am. Symp. Circuits Syst. LASCAS 2020, pages 1–4, 2020 • [108] Andres Cornejo, Flor Ortiz-Gomez, Jose M. Matias, Ramon Martinez, and Miguel Salas-Natera. Quantum Cryptography for Satellite Communication Systems. In Congr. Nac. Act. Espac. 2020-Agencia Espac. Mex., Mexico City, 2020 Finally, all code scripts employed in this thesis will remain in the Github repository permanently, https://github.com/KunaCornejo. All code scripts were developed by the author of this thesis using Python® and Matlab®, except for the ITU-R P.1853 script, which was written in Matlab by ONERA®, French Aerospace Lab. Appendix A List of Geographic Coordinates for Gateway (GW) Locations A.1 List of Geographic Coordinates for Gateway (GW) Locations, Chapter 3 A.2 List of Geographic Coordinates for Gateway (GW) Locations, Chapter 5 The clear sky carrier-to-noise ratio (cs) for each feeder uplink was calculated by using the geographic coordinates regarding its location, geostationary satellite position at 92.0 West, roll-off of 5%, and the frequency band at 50 GHz (V-band). Furthermore, the transmitter power of each GW is about 16.0 W, and the antenna diameter of 5.0 m, as can be seen in Chapter 3. A.3 Distance Matrix Between Pairs of Locations, Chapter 6 The distance between a pair of gateway locations was calculated by their geographic coordinates. For this purpose, the geographic coordinates for each GW location were provided by Table A.2. Finally, each computed value was stored in the distance matrix D. 120 APPENDIX A. LIST OF GEOGRAPHIC COORDINATES FOR GW . . . 121 Table A.1: List of Geographic Coordinates for GW Locations, Chapter 3 Location Country Latitude [deg] Longitude [deg] Height (a.m.s.l.) [m] Buenos Aires Argentina -34.611758 -58.430232 25.0 Santiago Chile -33.458205 -70.666972 567.0 Montevideo Uruguay -34.81721 -56.188972 43.0 Asuncion Paraguay -25.298939 -57.636595 43.0 La Paz Bolivia -16.503502 -68.124903 3625.0 Sao Paulo Brazil -23.572845 -46.623028 760.0 Lima Peru -12.052542 -77.043969 154.0 Guayaquil Ecuador -2.185092 -79.908501 4.0 Quito Ecuador -0.178182 -78.482904 2700.0 Rio de Janeiro Brazil -22.904847 -43.219689 11.0 Bogota Colombia 4.696189 -74.077603 2640.0 Caracas Venezuela 10.474799 -66.905474 900.0 Panama Panama 9.010642 -79.509318 2.0 San Jose Costa Rica 9.924622 -84.094463 1300.0 Tegucigalpa Guatemala 14.069427 -87.201883 1000.0 Mexico City Mexico 19.336688 -99.165822 2250.0 Monterrey Mexico 25.707672 -100.334175 530.0 Guadalajara Mexico 20.65853 -103.347001 1556.0 Cordoba Argentina -31.408778 -64.196749 390.0 Iquique Chile -20.232089 -70.134301 1.0 Manaus Brazil -3.11014 -60.000065 92.0 Belo Horizonte Brazil -19.925298 -43.940535 760.0 Tijuana Mexico 32.505354 -116.971508 31.0 Arequipa Peru -16.405163 -71.541072 2335.0 Cuzco Peru -13.527847 -71.964484 3399.0 Mar del Plata Argentina -38.030257 -57.604656 38.0 Rosario Argentina -32.953004 -60.687002 25.0 Porto Alegre Brazil -30.079685 -51.231157 10.0 Valdivia Chile -39.838558 -73.23594 14.0 Cali Colombia 3.4074 -76.533906 1018.0 Cartagena Colombia 10.401403 -75.51452 2.0 Pto. Concordia Colombia 1.252249 -70.232856 201.0 Maracaibo Venezuela 10.6808 -71.635416 15.0 Barinas Venezuela 8.603336 -70.229713 200.0 La Habana Cuba 23.104927 -82.286028 59.0 St. Domingo Dominican. Rep. 18.48892 -69.935325 14.0 Chiclayo Peru -6.784283 -79.858654 27.0 San Salvador El Salvador 13.697313 -89.219673 658.0 San Juan Puerto Rico 18.401754 -66.036714 7.9 Brasilia Brazil -15.811467 -47.874582 1172.0 Ushuaia Argentina -54.817684 -68.329799 58.0 Recife Brazil -8.043475 -34.955255 58.0 Pto. Baquerizo Ecuador -0.907203 -89.604353 2.0 APPENDIX A. LIST OF GEOGRAPHIC COORDINATES FOR GW . . . 122 Table A.2: List of Geographic Coordinates for GW Locations, Chapter 5 i Location Country Latitude [deg] Longitude [deg] Height (a.m.s.l.) [m] cs [dB] 1 Panama Panama 9.010642 -79.509318 2.0 32.44 2 San Jose Costa Rica 9.924622 -84.094463 1300.0 32.46 3 Tegucigalpa Guatemala 14.069427 -87.201883 1000.0 32.45 4 Mexico City Mexico 19.336688 -99.165822 2250.0 32.39 5 Monterrey Mexico 25.707672 -100.334175 530.0 32.31 6 Guadalajara Mexico 20.65853 -103.347001 1566.0 32.36 7 Tijuana Mexico 32.505354 -116.971508 31.0 32.09 8 La Habana Cuba 23.104927 -82.286028 59.0 32.34 9 St. Domingo Dominican Rep. 18.48892 -69.935325 14.0 32.29 10 San Salvador El Salvador 13.697313 -89.219673 658.0 32.45 11 San Juan Puerto Rico 18.401754 -66.036714 7.9 32.24 12 Torreon Mexico 25.560636 -103.374418 1120.0 32.30 13 La Paz, B.C. Mexico 24.129867 -110.292943 27.0 32.27 14 Veracruz Mexico 19.170373 -96.181209 10.0 32.40 15 Cancun Mexico 21.12228 -86.840371 11.0 32.38 16 Queretaro Mexico 20.614965 -100.411033 2017.0 32.37 17 Tuxtla, Gtz. Mexico 16.705306 -93.173516 522.0 32.43 18 Cd. Juarez Mexico 31.761652 -106.526185 1137.0 32.19 19 San Pedro Sula Honduras 15.517251 -87.992356 83.0 32.43 20 Belmopan Belize 17.265146 -88.768523 76.0 32.42 21 Kingston Jamaica 18.013036 -76.811471 9.0 32.36 22 Merida Mexico 20.970434 -89.608201 10.0 32.39 23 Pto. Cabezas Nicaragua 14.047875 -83.407334 7.0 32.43 24 Oaxaca Mexico 17.113126 -96.74277 1555.0 32.42 APPENDIX A. LIST OF GEOGRAPHIC COORDINATES FOR GW . . . 123 D =                                            P a n a m a S a n J o s e T e g u c ig a lp a M e x ic o C it y M o n t e r r e y G u a d a la ja r a T ij u a n a L a H a b a n a S t . D o m in g o S a n S a lv a d o r S a n J u a n T o r r e o n P a n a m a 5 1 3 .0 6 1 0 0 9 .0 8 2 4 0 6 .6 7 2 8 7 7 .8 5 2 8 6 5 .1 4 4 6 4 9 .5 6 1 5 9 4 .8 8 1 4 7 5 .4 9 1 1 7 9 .5 9 1 7 8 9 .5 7 3 1 2 1 .0 0 S a n J o s e 5 1 3 .0 6 5 7 1 .4 8 1 9 2 7 .8 3 2 4 5 1 .3 5 2 3 8 1 .3 1 4 2 0 1 .7 8 1 4 7 8 .1 4 1 7 9 7 .3 6 6 9 7 .8 7 2 1 6 0 .7 4 2 6 7 4 .7 8 T e g u c ig a lp a 1 0 0 9 .0 8 5 7 1 .4 8 1 4 0 1 .6 7 1 8 8 4 .2 2 1 8 6 1 .9 3 3 6 4 5 .4 0 1 1 3 0 .0 9 1 9 0 6 .2 8 2 2 1 .7 1 2 3 0 8 .7 3 2 1 1 6 .4 6 M e x ic o C it y 2 4 0 6 .6 7 1 9 2 7 .8 3 1 4 0 1 .6 7 7 1 8 .5 0 4 6 0 .9 3 2 2 9 9 .1 8 1 7 9 7 .8 9 3 0 7 2 .6 4 1 2 3 1 .3 1 3 4 8 2 .0 9 8 1 5 .9 3 M o n t e r r e y 2 8 7 7 .8 5 2 4 5 1 .3 5 1 8 8 4 .2 2 7 1 8 .5 0 6 4 0 .2 8 1 7 8 1 .4 8 1 8 4 8 .7 7 3 2 2 4 .9 4 1 7 6 9 .1 7 3 6 1 5 .8 0 3 0 5 .2 2 G u a d a la ja r a 2 8 6 5 .1 4 2 3 8 1 .3 1 1 8 6 1 .9 3 4 6 0 .9 3 6 4 0 .2 8 1 8 8 6 .1 8 2 1 8 8 .1 7 3 5 0 2 .8 1 1 6 8 7 .3 2 3 9 0 9 .7 2 5 4 5 .1 0 T ij u a n a 4 6 4 9 .5 6 4 2 0 1 .7 8 3 6 4 5 .4 0 2 2 9 9 .1 8 1 7 8 1 .4 8 1 8 8 6 .1 8 3 5 5 0 .1 5 4 9 2 7 .5 6 3 5 0 6 .1 1 5 2 9 6 .0 2 1 5 2 8 .9 8 L a H a b a n a 1 5 9 4 .8 8 1 4 7 8 .1 4 1 1 3 0 .0 9 1 7 9 7 .8 9 1 8 4 8 .7 7 2 1 8 8 .1 7 3 5 5 0 .1 5 1 3 8 1 .9 0 1 2 7 5 .8 5 1 7 6 7 .3 6 2 1 5 1 .6 8 S t . D o m in g o 1 4 7 5 .4 9 1 7 9 7 .3 6 1 9 0 6 .2 8 3 0 7 2 .6 4 3 2 2 4 .9 4 3 5 0 2 .8 1 4 9 2 7 .5 6 1 3 8 1 .9 0 2 1 2 6 .6 1 4 1 1 .3 4 3 5 2 5 .3 5 S a n S a lv a d o r 1 1 7 9 .5 9 6 9 7 .8 7 2 2 1 .7 1 1 2 3 1 .3 1 1 7 6 9 .1 7 1 6 8 7 .3 2 3 5 0 6 .1 1 1 2 7 5 .8 5 2 1 2 6 .6 1 2 5 2 9 .8 5 1 9 8 1 .3 4 S a n J u a n 1 7 8 9 .5 7 2 1 6 0 .7 4 2 3 0 8 .7 3 3 4 8 2 .0 9 3 6 1 5 .8 0 3 9 0 9 .7 2 5 2 9 6 .0 2 1 7 6 7 .3 6 4 1 1 .3 4 2 5 2 9 .8 5 3 9 1 8 .0 1 T o r r e o n 3 1 2 1 .0 0 2 6 7 4 .7 8 2 1 1 6 .4 6 8 1 5 .9 3 3 0 5 .2 2 5 4 5 .1 0 1 5 2 8 .9 8 2 1 5 1 .6 8 3 5 2 5 .3 5 1 9 8 1 .3 4 3 9 1 8 .0 1 L a P a z , B .C . 3 6 7 2 .7 3 3 1 9 2 .2 8 2 6 6 6 .2 5 1 2 6 6 .2 2 1 0 1 9 .2 1 8 1 1 .5 5 1 1 3 7 .1 9 2 8 5 0 .9 5 4 2 1 3 .3 0 2 4 9 7 .0 5 4 6 1 1 .5 6 7 1 5 .9 0 V e r a c r u z 2 1 2 0 .8 0 1 6 5 6 .6 4 1 1 1 1 .8 3 3 1 3 .8 5 8 4 2 .7 8 7 6 7 .1 3 2 5 4 6 .6 2 1 5 0 5 .2 3 2 7 6 0 .6 8 9 5 9 .7 1 3 1 7 0 .5 8 1 0 2 5 .2 2 C a n c u n 1 5 5 9 .0 0 1 2 7 9 .2 7 7 8 5 .1 8 1 3 0 0 .8 6 1 4 6 7 .2 4 1 7 1 4 .8 1 3 2 3 2 .3 7 5 1 8 .3 4 1 7 9 1 .7 0 8 6 3 .2 9 2 1 9 6 .2 9 1 7 5 7 .1 8 Q u e r e t a r o 2 5 8 6 .3 1 2 1 1 2 .8 5 1 5 7 8 .5 6 1 9 2 .7 1 5 6 6 .3 4 3 0 5 .5 5 2 1 0 7 .1 7 1 8 8 9 .5 8 3 1 9 7 .5 2 1 4 1 5 .2 5 3 6 0 4 .7 1 6 2 7 .8 7 T u x t la , G t z . 1 7 0 9 .3 7 1 2 3 7 .8 1 7 0 4 .0 3 6 9 7 .8 3 1 2 4 5 .5 2 1 1 5 7 .8 9 2 9 6 6 .5 5 1 3 4 1 .5 7 2 4 6 9 .3 4 5 4 0 .2 0 2 8 8 0 .5 2 1 4 4 4 .0 7 C d . J u a r e z 3 7 6 3 .3 2 3 3 5 0 .4 9 2 7 8 0 .9 4 1 5 6 5 .3 4 9 0 3 .8 4 1 2 7 4 .4 8 9 8 6 .6 1 2 5 7 1 .2 8 3 9 4 4 .6 9 2 6 7 2 .3 6 4 3 1 0 .3 1 7 5 4 .8 7 S a n P e d r o S u la 1 1 7 1 .3 1 7 5 1 .8 7 1 8 2 .0 4 1 2 5 8 .7 6 1 7 1 0 .8 2 1 7 1 9 .6 0 3 4 7 8 .3 7 1 0 3 4 .2 5 1 9 4 7 .3 7 2 4 1 .6 4 2 3 5 5 .5 8 1 9 4 9 .7 0 B e lm o p a n 1 3 5 8 .5 3 9 5 9 .6 9 3 9 2 .9 3 1 1 2 1 .3 4 1 5 1 9 .4 9 1 5 7 8 .1 2 3 2 9 4 .9 0 9 3 7 .4 3 1 9 9 6 .7 9 3 9 9 .6 6 2 4 0 7 .9 8 1 7 6 9 .0 3 K in g s t o n 1 0 4 2 .5 5 1 1 9 3 .8 4 1 1 9 3 .4 7 2 3 5 7 .8 0 2 5 6 9 .0 7 2 7 9 6 .5 8 4 3 1 6 .7 4 8 0 3 .1 9 7 2 8 .0 1 1 4 1 0 .7 8 1 1 3 8 .7 7 2 8 6 2 .1 0 M e r id a 1 7 1 4 .5 8 1 3 6 2 .5 2 8 0 8 .6 0 1 0 1 3 .9 1 1 2 1 4 .5 3 1 4 2 7 .9 7 2 9 9 2 .6 4 7 9 1 .0 1 2 0 7 6 .1 4 8 0 9 .7 8 2 4 8 2 .0 4 1 4 9 4 .9 8 P t o . C a b e z a s 7 0 2 .8 2 4 6 4 .5 3 4 0 9 .3 0 1 7 7 7 .3 4 2 1 9 0 .0 3 2 2 3 7 .9 6 3 9 6 8 .9 2 1 0 1 3 .9 9 1 5 1 9 .7 9 6 2 8 .6 4 1 9 1 5 .6 6 2 4 4 4 .7 6 O a x a c a 2 0 7 0 .7 9 1 5 8 2 .9 0 1 0 7 6 .2 3 3 5 5 .8 3 1 0 2 5 .2 6 7 9 8 .7 1 2 6 5 5 .0 0 1 6 4 8 .7 0 2 8 3 9 .7 1 8 9 1 .2 7 3 2 5 1 .0 4 1 1 6 3 .0 9                                            APPENDIX A. LIST OF GEOGRAPHIC COORDINATES FOR GW . . . 124 D =                                            L a P a z , B .C . V e r a c r u z C a n c u n Q u e r e t a r o T u x t la , G t z . C d . J u a r e z S a n P e d r o S u la B e lm o p a n K in g s t o n M e r id a P t o . C a b e z a s O a x a c a P a n a m a 3 6 7 2 .7 3 2 1 2 0 .8 0 1 5 5 9 .0 0 2 5 8 6 .3 1 1 7 0 9 .3 7 3 7 6 3 .3 2 1 1 7 1 .3 1 1 3 5 8 .5 3 1 0 4 2 .5 5 1 7 1 4 .5 8 7 0 2 .8 2 2 0 7 0 .7 9 S a n J o s e 3 1 9 2 .2 8 1 6 5 6 .6 4 1 2 7 9 .2 7 2 1 1 2 .8 5 1 2 3 7 .8 1 3 3 5 0 .4 9 7 5 1 .8 7 9 5 9 .6 9 1 1 9 3 .8 4 1 3 6 2 .5 2 4 6 4 .5 3 1 5 8 2 .9 0 T e g u c ig a lp a 2 6 6 6 .2 5 1 1 1 1 .8 3 7 8 5 .1 8 1 5 7 8 .5 6 7 0 4 .0 3 2 7 8 0 .9 4 1 8 2 .0 4 3 9 2 .9 3 1 1 9 3 .4 7 8 0 8 .6 0 4 0 9 .3 0 1 0 7 6 .2 3 M e x ic o C it y 1 2 6 6 .2 2 3 1 3 .8 5 1 3 0 0 .8 6 1 9 2 .7 1 6 9 7 .8 3 1 5 6 5 .3 4 1 2 5 8 .7 6 1 1 2 1 .3 4 2 3 5 7 .8 0 1 0 1 3 .9 1 1 7 7 7 .3 4 3 5 5 .8 3 M o n t e r r e y 1 0 1 9 .2 1 8 4 2 .7 8 1 4 6 7 .2 4 5 6 6 .3 4 1 2 4 5 .5 2 9 0 3 .8 4 1 7 1 0 .8 2 1 5 1 9 .4 9 2 5 6 9 .0 7 1 2 1 4 .5 3 2 1 9 0 .0 3 1 0 2 5 .2 6 G u a d a la ja r a 8 1 1 .5 5 7 6 7 .1 3 1 7 1 4 .8 1 3 0 5 .5 5 1 1 5 7 .8 9 1 2 7 4 .4 8 1 7 1 9 .6 0 1 5 7 8 .1 2 2 7 9 6 .5 8 1 4 2 7 .9 7 2 2 3 7 .9 6 7 9 8 .7 1 T ij u a n a 1 1 3 7 .1 9 2 5 4 6 .6 2 3 2 3 2 .3 7 2 1 0 7 .1 7 2 9 6 6 .5 5 9 8 6 .6 1 3 4 7 8 .3 7 3 2 9 4 .9 0 4 3 1 6 .7 4 2 9 9 2 .6 4 3 9 6 8 .9 2 2 6 5 5 .0 0 L a H a b a n a 2 8 5 0 .9 5 1 5 0 5 .2 3 5 1 8 .3 4 1 8 8 9 .5 8 1 3 4 1 .5 7 2 5 7 1 .2 8 1 0 3 4 .2 5 9 3 7 .4 3 8 0 3 .1 9 7 9 1 .0 1 1 0 1 3 .9 9 1 6 4 8 .7 0 S t . D o m in g o 4 2 1 3 .3 0 2 7 6 0 .6 8 1 7 9 1 .7 0 3 1 9 7 .5 2 2 4 6 9 .3 4 3 9 4 4 .6 9 1 9 4 7 .3 7 1 9 9 6 .7 9 7 2 8 .0 1 2 0 7 6 .1 4 1 5 1 9 .7 9 2 8 3 9 .7 1 S a n S a lv a d o r 2 4 9 7 .0 5 9 5 9 .7 1 8 6 3 .2 9 1 4 1 5 .2 5 5 4 0 .2 0 2 6 7 2 .3 6 2 4 1 .6 4 3 9 9 .6 6 1 4 1 0 .7 8 8 0 9 .7 8 6 2 8 .6 4 8 9 1 .2 7 S a n J u a n 4 6 1 1 .5 6 3 1 7 0 .5 8 2 1 9 6 .2 9 3 6 0 4 .7 1 2 8 8 0 .5 2 4 3 1 0 .3 1 2 3 5 5 .5 8 2 4 0 7 .9 8 1 1 3 8 .7 7 2 4 8 2 .0 4 1 9 1 5 .6 6 3 2 5 1 .0 4 T o r r e o n 7 1 5 .9 0 1 0 2 5 .2 2 1 7 5 7 .1 8 6 2 7 .8 7 1 4 4 4 .0 7 7 5 4 .8 7 1 9 4 9 .7 0 1 7 6 9 .0 3 2 8 6 2 .1 0 1 4 9 4 .9 8 2 4 4 4 .7 6 1 1 6 3 .0 9 L a P a z , B .C . 1 5 5 8 .1 4 2 4 2 7 .3 1 1 0 8 8 .2 9 1 9 6 3 .4 2 9 2 5 .5 6 2 5 1 7 .2 7 2 3 6 2 .0 9 3 5 3 1 .1 6 2 1 5 0 .9 5 3 0 3 2 .1 9 1 6 1 0 .1 7 V e r a c r u z 1 5 5 8 .1 4 9 9 8 .7 8 4 7 0 .5 1 4 1 9 .9 4 1 7 4 0 .9 7 9 5 9 .1 7 8 1 1 .0 0 2 0 4 4 .4 3 7 1 5 .0 0 1 4 7 4 .7 6 2 3 6 .3 3 C a n c u n 2 4 2 7 .3 1 9 9 8 .7 8 1 4 1 0 .7 0 8 2 7 .4 6 2 2 8 3 .4 7 6 3 4 .9 9 4 7 4 .2 7 1 1 0 5 .8 6 2 8 7 .7 3 8 6 6 .6 0 1 1 3 1 .4 7 Q u e r e t a r o 1 0 8 8 .2 9 4 7 0 .5 1 1 4 1 0 .7 0 8 7 7 .4 8 1 3 8 0 .7 5 1 4 2 9 .2 1 1 2 7 9 .4 6 2 4 9 1 .0 9 1 1 2 3 .4 7 1 9 4 5 .2 7 5 4 8 .2 1 T u x t la , G t z . 1 9 6 3 .4 2 4 1 9 .9 4 8 2 7 .4 6 8 7 7 .4 8 2 1 4 8 .8 5 5 6 9 .0 1 4 7 2 .5 5 1 7 4 2 .0 1 6 0 4 .6 6 1 0 8 7 .7 8 3 8 2 .4 2 C d . J u a r e z 9 2 5 .5 6 1 7 4 0 .9 7 2 2 8 3 .4 7 1 3 8 0 .7 5 2 1 4 8 .8 5 2 6 0 4 .6 4 2 4 0 6 .9 7 3 3 4 8 .5 9 2 0 6 4 .4 7 3 0 6 6 .9 8 1 9 0 3 .9 3 S a n P e d r o S u la 2 5 1 7 .2 7 9 5 9 .1 7 6 3 4 .9 9 1 4 2 9 .2 1 5 6 9 .0 1 2 6 0 4 .6 4 2 1 1 .2 6 1 2 2 2 .0 7 6 2 9 .9 0 5 1 9 .3 0 9 5 0 .4 2 B e lm o p a n 2 3 6 2 .0 9 8 1 1 .0 0 4 7 4 .2 7 1 2 7 9 .4 6 4 7 2 .5 5 2 4 0 6 .9 7 2 1 1 .2 6 1 2 6 9 .5 6 4 2 1 .3 4 6 7 6 .2 8 8 4 7 .2 0 K in g s t o n 3 5 3 1 .1 6 2 0 4 4 .4 3 1 1 0 5 .8 6 2 4 9 1 .0 9 1 7 4 2 .0 1 3 3 4 8 .5 9 1 2 2 2 .0 7 1 2 6 9 .5 6 1 3 8 0 .6 0 8 3 1 .2 7 2 1 1 4 .3 1 M e r id a 2 1 5 0 .9 5 7 1 5 .0 0 2 8 7 .7 3 1 1 2 3 .4 7 6 0 4 .6 6 2 0 6 4 .4 7 6 2 9 .9 0 4 2 1 .3 4 1 3 8 0 .6 0 1 0 1 2 .0 2 8 6 3 .7 0 P t o . 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It has also been done the best effort to acknowledge data properly, opinions, and presented content in this work, so any mistakes or omissions can be totally involuntary. Mexico City, November 2020 IVAN ANDRES CORNEJO GAIBOR