Closed form analysis of Poisson cellular networks: a stochastic geometry approach

Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into network densification. Fundamental issues, however, remain open in order to use stochastic geometry tools for the optimization of wireless networks, with the biggest challenge being the lack of tractable closed form expressions for the derived figures of merit. To this end, the present thesis revisits stochastic geometry and provides a novel stochastic geometry framework with a twofold contribution. The first part of the thesis focuses on the derivation of simple, albeit accurate closed form approximations for the ergodic rate of Poisson cellular networks under a noise limited, an interference limited and a general case scenario. The ergodic rate constitutes the most sensible figure of merit for characterizing the system performance, but due to the inherent intractability of the available stochastic geometry frameworks, had not been formulated in closed form hitherto. To demonstrate the potential of the aforementioned tractable expressions with respect to network optimization, the present thesis proposes a flexible connectivity paradigm and employs part of the developed expressions to optimize the network connectivity. The proposed flexible connectivity paradigm exploits the downlink uplink decoupling (DUDe) configuration, which is a promising framework providing substantial capacity and outage gains in UDNs and introduces the DUDe connectivity gains into the 5G era and beyond. Subsequently, the last part of the thesis provides an analytical formulation of the probability density function (PDF) of the aggregate inter-cell interference in Poisson cellular networks. The introduced PDF is an accurate approximation of the exact PDF that could not be analytically formulated hitherto, even though it constituted a crucial tool for the analysis and optimization of cellular networks. The lack of an analytical expression for the PDF of the interference in Poisson cellular networks had imposed the use of intricate formulas, in order to derive sensible figures of merit by employing only the moment generating function (MGF). Hence, the present thesis introduces an innovative framework able to simplify the analysis of Poisson cellular networks to a great extent, while addressing fundamental issues related to network optimization and design.Las redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red

Closed form analysis of Poisson cellular networks: a stochastic geometry approach

Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into network densification. Fundamental issues, however, remain open in order to use stochastic geometry tools for the optimization of wireless networks, with the biggest challenge being the lack of tractable closed form expressions for the derived figures of merit. To this end, the present thesis revisits stochastic geometry and provides a novel stochastic geometry framework with a twofold contribution. The first part of the thesis focuses on the derivation of simple, albeit accurate closed form approximations for the ergodic rate of Poisson cellular networks under a noise limited, an interference limited and a general case scenario. The ergodic rate constitutes the most sensible figure of merit for characterizing the system performance, but due to the inherent intractability of the available stochastic geometry frameworks, had not been formulated in closed form hitherto. To demonstrate the potential of the aforementioned tractable expressions with respect to network optimization, the present thesis proposes a flexible connectivity paradigm and employs part of the developed expressions to optimize the network connectivity. The proposed flexible connectivity paradigm exploits the downlink uplink decoupling (DUDe) configuration, which is a promising framework providing substantial capacity and outage gains in UDNs and introduces the DUDe connectivity gains into the 5G era and beyond. Subsequently, the last part of the thesis provides an analytical formulation of the probability density function (PDF) of the aggregate inter-cell interference in Poisson cellular networks. The introduced PDF is an accurate approximation of the exact PDF that could not be analytically formulated hitherto, even though it constituted a crucial tool for the analysis and optimization of cellular networks. The lack of an analytical expression for the PDF of the interference in Poisson cellular networks had imposed the use of intricate formulas, in order to derive sensible figures of merit by employing only the moment generating function (MGF). Hence, the present thesis introduces an innovative framework able to simplify the analysis of Poisson cellular networks to a great extent, while addressing fundamental issues related to network optimization and design.Las redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red.Postprint (published version

Closed-form capacity bounds for downlink and uplink decoupling

©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Downlink (DL) and uplink (UL) decoupling (DUDe) is a new architectural paradigm where DL and UL are not constrained to be associated to the same base station (BS). Thus, a user having access to multiple BSs within a dense cellular network can receive the DL traffic from one BS and send its UL traffic through another. Building upon this architectural paradigm, the present paper provides tight analytical bounds in closed form for the UL ergodic capacity that depend solely on the density of the infrastructure. The devised bounds account for the backbone network congestion and the synchronization of the acknowledgments of the decoupled channels. The proposed bounds are compared against extensive numerical simulations demonstrating the tractability and accuracy of the expressions.Peer ReviewedPostprint (author's final draft

Closed form analysis of Poisson cellular networks: a stochastic geometry approach

Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into network densification. Fundamental issues, however, remain open in order to use stochastic geometry tools for the optimization of wireless networks, with the biggest challenge being the lack of tractable closed form expressions for the derived figures of merit. To this end, the present thesis revisits stochastic geometry and provides a novel stochastic geometry framework with a twofold contribution. The first part of the thesis focuses on the derivation of simple, albeit accurate closed form approximations for the ergodic rate of Poisson cellular networks under a noise limited, an interference limited and a general case scenario. The ergodic rate constitutes the most sensible figure of merit for characterizing the system performance, but due to the inherent intractability of the available stochastic geometry frameworks, had not been formulated in closed form hitherto. To demonstrate the potential of the aforementioned tractable expressions with respect to network optimization, the present thesis proposes a flexible connectivity paradigm and employs part of the developed expressions to optimize the network connectivity. The proposed flexible connectivity paradigm exploits the downlink uplink decoupling (DUDe) configuration, which is a promising framework providing substantial capacity and outage gains in UDNs and introduces the DUDe connectivity gains into the 5G era and beyond. Subsequently, the last part of the thesis provides an analytical formulation of the probability density function (PDF) of the aggregate inter-cell interference in Poisson cellular networks. The introduced PDF is an accurate approximation of the exact PDF that could not be analytically formulated hitherto, even though it constituted a crucial tool for the analysis and optimization of cellular networks. The lack of an analytical expression for the PDF of the interference in Poisson cellular networks had imposed the use of intricate formulas, in order to derive sensible figures of merit by employing only the moment generating function (MGF). Hence, the present thesis introduces an innovative framework able to simplify the analysis of Poisson cellular networks to a great extent, while addressing fundamental issues related to network optimization and design.Las redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red

Κατανομή πόρων σε δορυφορικά συστήματα πολλαπλών δεσμών

125 σ.Multi-beam satellite systems offer higher throughput due to frequency reuse and multiple levels of flexibility and allow the use of smaller earth terminals due to their higher directivity. At a high-level multi-beam satellite operation resembles to that of cellular mobile communications. As the lifetime of a satellite is about 15 years efficient communication satellites must take into account current as well as future demands. To improve satellite efficiency and reduce operational risk, design flexibility is imperative. Among others, multibeam satellites, offer significant flexibility both with regard to coverage area and resources allocation. Coverage area flexibility is achieved by adjusting the position of the spots adaptively to communications traffic. Resource allocation flexibility is made possible by adaptively adjusting the power and bandwidth to the various beams according to traffic. In the present thesis, we focus on resource allocation flexibility offered by multi-beam satellites. In particular, for a specific satellite payload (number of beams, available power, bandwidth etc.,) the first part of the thesis deals with the problem of allocating power to different beams to satisfy the demand as closely as possible. Based on a model relating the power allocated to the data rate offered, we explore the suitability of using/ modifying existing optimization algorithms. Among exact methods as well as approximate methods that are initially considered, a scheme is selected based on complexity, convergence, scalability and other issues. The selected algorithm is then used to optimize the resource allocation. The advantages obtained over other existing methods are presented. Next, an attempt is made to minimize the DC power consumption of a multi-beam satellite. In this course, the optimized resource allocation obtained in the first part of the thesis is further enhanced, with the aim to minimize the system power consumption. This task is deal with employing a multi-objective optimization algorithm that aims at meeting the traffic demand as closely as possible while minimizing the system power consumption. The benefits from using such multiple.Αλέξιος Ι. Αραβανή

Analysis of downlink and uplink decoupling in dense cellular networks

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Decoupling uplink (UL) and downlink (DL) is a new architectural paradigm where DL and UL are not constrained to be associated to the same base station (BS). Building upon this paradigm, the goal of the present paper is to provide lower, albeit tight bounds for the ergodic UL capacity of a decoupled cellular network. The analysis is performed for a scenario consisting of a macro BS and a set of small cells (SCs) whose positions are selected randomly according to a Poisson point process of a given spatial density. Based on this analysis simple bounds in closed form expressions are defined. The devised bounds are employed to compare the performance of the decoupled case versus a set of benchmark cases, namely the coupled case, and the situations of having either a single macro BS or only SCs. This comparison provides valuable insights regarding the behavior and performance of such networks, providing simpler expressions for the ergodic UL capacity as a function of the distances to the macro BS and the density of SCs. These expressions constitute a simple guide to the minimum degree of densification that guarantees the Quality of Service (QoS) objectives of the network, thus, providing a valuable tool to the network operator of significant practical and commercial value.Peer ReviewedPostprint (published version

Closed-form capacity bounds for downlink and uplink decoupling

©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Downlink (DL) and uplink (UL) decoupling (DUDe) is a new architectural paradigm where DL and UL are not constrained to be associated to the same base station (BS). Thus, a user having access to multiple BSs within a dense cellular network can receive the DL traffic from one BS and send its UL traffic through another. Building upon this architectural paradigm, the present paper provides tight analytical bounds in closed form for the UL ergodic capacity that depend solely on the density of the infrastructure. The devised bounds account for the backbone network congestion and the synchronization of the acknowledgments of the decoupled channels. The proposed bounds are compared against extensive numerical simulations demonstrating the tractability and accuracy of the expressions.Peer Reviewe

Analysis of downlink and uplink decoupling in dense cellular networks

Decoupling uplink (UL) and downlink (DL) is a new architectural paradigm where DL and UL are not constrained to be associated to the same base station (BS). Building upon this paradigm, the goal of the present paper is to provide lower, albeit tight bounds for the ergodic UL capacity of a decoupled cellular network. The analysis is performed for a scenario consisting of a macro BS and a set of small cells (SCs) whose positions are selected randomly according to a Poisson point process of a given spatial density. Based on this analysis simple bounds in closed form expressions are defined. The devised bounds are employed to compare the performance of the decoupled case versus a set of benchmark cases, namely the coupled case, and the situations of having either a single macro BS or only SCs. This comparison provides valuable insights regarding the behavior and performance of such networks, providing simpler expressions for the ergodic UL capacity as a function of the distances to the macro BS and the density of SCs. These expressions constitute a simple guide to the minimum degree of densification that guarantees the Quality of Service (QoS) objectives of the network, thus, providing a valuable tool to the network operator of significant practical and commercial value.Peer Reviewe

On the coordination of base stations in ultra dense cellular networks

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. However, recent findings have demonstrated that the reduction of inter-site distances after a certain threshold, has a detrimental effect on the network performance. In such cases, interference mitigation strategies to counteract the effect of primarily the line of sight (LOS) interference are imperative. In this course, the present paper investigates a minimum coordination strategy among immediate neighbors. The adopted scheme realizes the interference mitigation objective, enhancing system capacity, while being implementable in practice. Building upon this scheme, the present paper provides tractable closed form expressions for the downlink (DL) ergodic capacity of a reference user under the examined coordination scheme. The analysis is performed for a scenario consisting of base stations (BSs) whose positions follow a Poisson point process of a given spatial density. The tractability and accuracy of the derived expressions renders them ideal for quantifying the performance of additional coordination strategies and for revealing trends in complex optimization problems. Thus, constituting a valuable tool for network operators, toward assessing different interference mitigation techniques and coordination schemes in UDNs.Peer Reviewe

A tractable closed form approximation of the ergodic rate in Poisson cellular networks

The employment of stochastic geometry for the analysis and design of ultra dense networks (UDNs) has provided significant insights into network densification. In addition to the characterization of the network performance and behavior, these tools can also be exploited toward solving complex optimization problems that could maximize the capacity benefits arising in UDNs. However, this is preconditioned on the existence of tractable closed form expressions for the considered figures of merit. In this course, the present paper introduces an accurate approximation for the moment generating function (MGF) of the aggregate other-cell interference created by base stations whose positions follow a Poisson point process of given spatial density. Given the pivotal role of the MGF of the aggregate interference in stochastic geometry and the tractability of the derived MGF, the latter can be employed to substantially simplify ensuing stochastic geometry analyses. Subsequently, the present paper employs the introduced MGF to provide closed form expressions for the downlink ergodic capacity for the interference limited case, and validates the accuracy of these expressions by the use of extensive Monte Carlo simulations. The derived expressions depend on the density of users and base stations, setting out a densification road map for network operators and designers of significant value.Peer Reviewe