Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart (CW) matrix ${\bf{W}}(t)$ as it varies along a certain dimension $t$. We characterize the second-order joint cdf of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ($N_T$) and receive ($N_R$) antennas is similar. However, as $N_T$ is increased while keeping $N_R$ fixed, we see how the best and worst channels tend to have a similar rate of change.Comment: 15 pages, 9 figures and 1 table. This work has been accepted for publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Modeling and Analysis of Cellular Networks Using Stochastic Geometry: A Tutorial

This paper presents a tutorial on stochastic geometry (SG)-based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. This paper starts by modeling and analyzing the baseband interference in a baseline single-tier downlink cellular network with single antenna base stations and universal frequency reuse. Then, it characterizes signal-to-interference-plus-noise-ratio and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and transmission rate analysis is presented. Although the main focus of this paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. This paper then extends the unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. To this end, this paper highlights the state-of-the-art research and points out future research directions

Wireless networks physical layer security : modeling and performance characterization

Intrigued by the rapid growth and expand of wireless devices, data security is increasingly playing a significant role in our daily transactions and interactions with different entities. Possible examples, including e-healthcare information and online shopping, are becoming vulnerable due to the intrinsic nature of wireless transmission medium and the widespread open access of wireless links. Traditionally, the communication security is mainly regarded as the tasks at the upper layers of layered protocol stack, security techniques, including personal access control, password protection, and end-to-end encryption, have been widely studied in the open literature. More recently, plenty of research interests have been drawn to the physical layer forms of secrecy. As a new but appealing paradigm at physical layer, physical layer security is based on two pioneering works: (i) Shannon’s information-theoretic formulation and (ii) Wyner’s wiretap formulation. On account of the fundamental of physical layer security and the different nature of various wireless network, this dissertation is supposed to further fill the lacking of the existing research outcomes. To be specific, the contributions of this dissertation can be summarized as three-fold:(i) exploration of secrecy metrics to more general fading channels; (ii) characterization a new fading channel model and its reliability and security analysis in digital communication systems; and (iii) investigation of physical layer security over the random multiple-input multiple-output (MIMO) α −μ fading channels. Taking into account the classic Alice-Bob-Eve wiretap model, the first contribution can be divided into four aspects: (i) we have investigated the secrecy performance over single-input single-output (SISO) α −μ fading channels. The probability of non-zero (PNZ) secrecy capacity and the lower bound of secrecy outage probability (SOP) are derived for the special case when the main channel and wiretap channel undergo the same non-linearity fading parameter, i.e., α. Later on, for the purpose of filling the gap of lacking closed-form expression of SOP in the open literature and extending the obtained results in chapter 2 to the single-input multiple-output (SIMO) α − μ wiretap fading channels, utilizing the fact that the received signal-tonoise ratios (SNRs) at the legitimate receiver and eavesdropper can be approximated as new α −μ distributed random variables (RVs), the SOP metric is therefore derived, and given in terms of the bivariate Fox’s H-function; (ii) the secrecy performance over the Fisher-Snedecor F wiretap fading channels is initially considered. The SOP, PNZ, and ASC are finalized in terms of Meijer’s G-function; (iii) in order to generalize the obtained results over α −μ and Fisher-Snedecor F wiretap fading channels, a more flexible and general fading channel, i.e., Fox’s H-function fading model, are taken into consideration. Both the exact and asymptotic analysis of SOP, PNZ, and average secrecy capacity (ASC), are developed with closed-form expressions; and (iv) finally, motivated by the fact that the mixture gamma (MG) distribution is an appealing tool, which can be used to model the received instantaneous SNRs over wireless fading channels, the secrecy metrics over wiretap fading channels are derived based on the MG approach. Due to the limited transmission power and communication range, cooperative relays or multi-hop wireless networks are usually regarded as two promising means to address these concerns. Inspired by the obtained results in Chapters 2 and 3, the second main contribution is to propose a novel but simple fading channel model, namely, the cascaded α −μ. This new distribution is advantageous since it encompasses the existing cascaded Rayleigh, cascaded Nakagami-m, and cascaded Weibull with ease. Based on this, both the reliability and secrecy performance of a digital system over cascaded α −μ fading channels are further evaluated. Closed-form expressions of reliability metrics (including amount of fading (AF), outage probability, average channel capacity, and average symbol error probability (ABEP).) and secrecy metrics (including SOP, PNZ, and ASC) are respectively provided. Besides, their asymptotic behaviors are also performed and compared with the exact results. Considering the impacts of users’ densities, spatial distribution, and the path-loss exponent on secrecy issue, the third aspect of this thesis is detailed in Chapter 8 as the secrecy investigation of stochastic MIMO system over α −μ wiretap fading channels. Both the stochastic geometry and conventional space-time transmission (STT) scheme are used in the system configuration. The secrecy issue is mathematically evaluated by three metrics, i.e., connection outage, the probability of non-zero secrecy capacity and the ergodic secrecy capacity. Those three metrics are later on derived regarding two ordering scheme, and further compared with Monte-Carlo simulations

Secrecy Performance Analysis of SIMO Systems over Correlated κ-µ Shadowed Fading Channels

In this paper, the secrecy performance of single-input-multiple-output systems over correlated κ-μ shadowed fading channels is investigated. In particular, based on the classic Wyner's wiretap model, we derive analytical expressions for secure outage probability (SOP) and the probability of strictly positive secrecy capacity (SPSC) over correlated κ-μ shadowed fading channels. In order to further study the impact of channel parameters on the secrecy performance, novel SOP and the probability of SPSC over independent and identically distributed κ-μ shadowed fading channels are also obtained. In addition, we discuss the asymptotic expressions of the SOP and the SPSC. The match between the analytical results and simulations is excellent for all parameters under considerations. It is interesting to find that the results show that when the signal-to-noise ratio of the main channel is lower than that of the eavesdropping channel, the larger value of correlation coefficient is helpful to improve the secrecy performance and vice versa

Physical-Layer Security in Cognitive Radio Networks

The fifth-generation (5G) communications and beyond are expected to serve a huge number of devices and services. However, due to the fixed spectrum allocation policies, the need for cognitive radio networks (CRNs) has increased accordingly. CRNs have been proposed as a promising approach to address the problem of under-utilization and scarcity of the spectrum. In CRNs, secondary users (SUs) access the licensed spectrum of the primary users (PUs) using underlay, overlay, or interweave paradigms. SUs can access the spectrum band simultaneously with the PUs in underlay access mode provided that the SUs’ transmission power does not cause interference to the PUs’ communication. In this case, SUs should keep monitoring the interference level that the PU receiver can tolerate and adjust the transmission power accordingly. However, varying the transmission power may lead to some threats to the privacy of the information transfer of CRNs. Therefore, securing data transmission in an underlay CRN is a challenge that should be addressed. Physical-layer security (PLS) has recently emerged as a reliable method to protect the confidentiality of the SUs’ transmission against attacks, especially for the underlay model with no need for sharing security keys. Indeed, PLS has the advantage of safeguarding the data transmission without the necessity of adding enormous additional resources, specifically when there are massively connected devices. Apart from the energy consumed by the various functions carried out by SUs, enhancing security consumes additional energy. Therefore, energy harvesting (EH) is adopted in our work to achieve both; energy efficiency and spectral efficiency. EH is a significant breakthrough for green communication, allowing the network nodes to reap energy from multiple sources to lengthen battery life. The energy from various sources, such as solar, wind, vibration, and radio frequency (RF) signals, can be obtained through the process of EH. This accumulated energy can be stored to be used for various processes, such as improving the users’ privacy and prolonging the energy-constrained devices’ battery life. In this thesis, for the purpose of realistic modelling of signal transmission, we explicitly assume scenarios involving moving vehicles or nodes in networks that are densely surrounded by obstacles. Hence, we begin our investigations by studying the link performance under the impact of cascaded κ−μ fading channels. Moreover, using the approach of PLS, we address the privacy of several three-node wiretap system models, in which there are two legitimate devices communicating under the threat of eavesdroppers. We begin by a three-node wiretap system model operating over cascaded κ − μ fading channels and under worst-case assumptions. Moreover, assuming cascaded κ − μ distributions for all the links, we investigate the impact of these cascade levels, as well as the impact of multiple antennas employed at the eavesdropper on security. Additionally, the PLS is examined for two distinct eavesdropping scenarios: colluding and non-colluding eavesdroppers. Throughout the thesis, PLS is mainly evaluated through the secrecy outage probability (SOP), the probability of non-zero secrecy capacity (Pnzcr ), and the intercept probability (Pint). Considering an underlay CRN operating over cascaded Rayleigh fading channel, with the presence of an eavesdropper, we explore the PLS for SUs in the network. This study is then extended to investigate the PLS of SUs in an underlay single-input-multiple-output (SIMO) CRN over cascaded κ-μ general fading channels with the presence of a multi-antenna eavesdropper. The impact of the constraint over the transmission power of the SU transmitter due to the underlay access mode is investigated. In addition, the effects of multiple antennas and cascade levels over security are well-explored. In the second part of our thesis, we propose an underlay CRN, in which an SU transmitter communicates with an SU destination over cascaded κ-μ channels. The confidentiality of the shared information between SUs is threatened by an eavesdropper. Our major objective is to achieve a secured network, while at the same time improving the energy and spectrum efficiencies with practical modeling for signals’ propagation. Hence, we presume that the SU destination harvests energy from the SU transmitter. The harvested energy is used to produce jamming signals to be transmitted to mislead the eavesdropper. In this scenario, a comparison is made between an energy-harvesting eavesdropper and a non-energy harvesting one. Additionally, we present another scenario in which cooperative jamming is utilized as one of the means to boost security. In this system model, the users are assumed to communicate over cascaded Rayleigh channels. Moreover, two scenarios for the tapping capabilities of the eavesdroppers are presented; colluding and non-colluding eavesdroppers. This study is then extended for the case of non-colluding eavesdroppers, operating over cascaded κ-μ channels. Finally, we investigate the reliability of the SUs and PUs while accessing the licensed bands using the overlay mode, while enhancing the energy efficiency via EH techniques. Hence, we assume that multiple SUs are randomly distributed, in which one of the SUs is selected to harvest energy from the PUs’ messages. Then, utilizing the gathered energy, this SU combines its own messages with the amplified PUs messages and forwards them to the destinations. Furthermore, we develop two optimization problems with the potential of maximizing the secondary users’ rate and the sum rate of both networks

MIMO Systems

In recent years, it was realized that the MIMO communication systems seems to be inevitable in accelerated evolution of high data rates applications due to their potential to dramatically increase the spectral efficiency and simultaneously sending individual information to the corresponding users in wireless systems. This book, intends to provide highlights of the current research topics in the field of MIMO system, to offer a snapshot of the recent advances and major issues faced today by the researchers in the MIMO related areas. The book is written by specialists working in universities and research centers all over the world to cover the fundamental principles and main advanced topics on high data rates wireless communications systems over MIMO channels. Moreover, the book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity