This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

There has been phenomenal interest in applying space-time coding techniques in wireless communications in the last two decades. In general, the benefit of applying space-time codes in multiple-input, multiple-output (MIMO) wireless channels is an increase in transmission reliability or system throughput (capacity). However, such a benefit cannot be obtained in some wireless systems where size or other constraints preclude the use of multiple antennas. As such, wireless relay communications has recently been proposed as a means to provide spatial diversity in the face of this limitation. In this approach, some users or relay nodes assist the transmission of other users information. This dissertation contributes to the advancement of wireless relay communications by investigating the performance of various relaying signal processing methods under different practical fading environments. In particular, it examines two main relaying methods, namely decode-and-forward (DF) and amplify-and-forward (AF).<p> For DF, the focus is on the diversity analysis of relaying systems under various practical protocols when detection error at relays is taken into account. In order to effectively mitigate the phenomenon of error propagation, the smart relaying technique proposed by Wang et al. in [R1] is adopted. First, diversity analysis of a single-relay system under the scenario that only the relay is allowed to transmit in the second time slot (called Protocol II) is carried out. For Nakagami and Hoyt generalized fading channels, analytical and numerical results are provided to demonstrate that the system always obtains the maximal diversity when binary phase shift keying (BPSK) modulation is used. Second, a novel and low-complexity relaying system is proposed when smart relaying and equal gain combing (EGC) techniques are combined. In the proposed system, the destination requires only the phases of the channel state information in order to detect the transmitted signals. For the single-relay system with M-ary PSK modulation, it is shown that the system can achieve the maximal diversity under Nakagami and Hoyt fading channels. For the K-relay system, simulation results suggest that the maximal diversity can also be achieved. Finally, the diversity analysis for a smart relaying system under the scenario when both the source and relay are permitted to transmit in the second time slot (referred to as Protocol I) is presented. It is shown that Protocol I can achieve the same diversity order as Protocol II for the case of 1 relay. In addition, the diversity is very robust to the quality of the feedback channel as well as the accuracy of the quantization of the power scaling implemented at the relay.<p> For AF, the dissertation considers a fixed-gain multiple-relay system with maximal ratio combining (MRC) detection at the destination under Nakagami fading channels. Different from the smart relaying for DF, all the channel state information is assumed to be available at the destination in order to perform MRC for any number of antennas. Upperbound and lowerbound on the system performance are then derived. Based on the bounds, it is shown that the system can achieve the maximal diversity. Furthermore, the tightness of the upperbound is demonstrated via simulation results. With only the statistics of all the channels available at the destination, a novel power allocation (PA) is then proposed. The proposed PA shows significant performance gain over the conventional equal PA.

Several emerging wireless communication systems require direct transmission between mobile terminals to support efficient data transfer and user mobility. Such mobile-to-mobile communication systems differ from the conventional cellular systems where only the user unit is mobile. In addition, there might be a relay, also called a repeater, between the original transmitter and the final receiver to improve the network range and coverage. Potential applications for mobile-to-mobile systems include Intelligent Highways for coordinated traffic control and ad-hoc networks meant for military and disaster management. Relays may be deployed in cellular networks and IEEE 802.16 mesh networks for wireless broadband access. Extensive research in cellular radio channels has led to the successful deployment of cellular networks. However, our knowledge of the radio channels encountered in mobile-to-mobile and relay-based systems is still inadequate. This forms the primary motivation behind our research in addressing wireless channel modeling, simulation, and estimation issues for these systems. Specifically, we investigate frequency-flat mobile-to-mobile channels and develop simulation models by using the sum-of-sinusoids method, which is widely used for cellular channels. In addition, we present the properties of amplify and forward relay channels via theoretical analysis. This analysis, to the best of our knowledge, is the first of its kind. Further, we address the unique challenges, which arise because of the different underlying channel model, for channel estimation in amplify and forward relay systems. Our work would provide other researchers the necessary tools for the design and testing of these emerging communication systems.

In this thesis, we investigate cooperation by applying OFDM signals to cooperative relay networks. We consider the single path relay network and the multiple path relay network. Using the amplify-and-forward relay algorithm, we derive the input-output relations and mutual informations of both networks. Using a power constraint at each relay, we consider two relay power allocation schemes. The first is constant gain allocation, where the amplifying gain used in the amplify-and-forward algorithm is constant for all subcarriers. The second is equal power allocation, where each subcarrier transmits the same power. The former scheme does not require CSI (channel state information), while the latter one does. We simulate the mutual informations using the two relay power allocation schemes. Results indicate that equal power allocation gives a slightly higher mutual information for the single path relay network. For the multiple path network, the mutual information is practically the same for both schemes. Using the decode-and-forward relay algorithm, we derive the input-output relations for both networks. The transmitter and each relay are assumed to have uniform power distributions in this case. We simulate the BER (bit error rate) and WER (word error rate) performance for the two networks using both the amplify-and-forward and decode-and-forward relay algorithms. For the single path relay network, amplify-and-forward gives very poor performance, because as we increase the distance between the transmitter and receiver (and thus, add more relays), more noise and channel distortion enter the system. Decode-and-forward gives significantly better performance because noise and channel distortion are eliminated at each relay. For the multiple path relay network, decode-and-forward again gives better performance than amplify-and-forward. However, the performance gains are small compared to the single path relay network case. Therefore, amplify-and-forward may be a more attractive choice due to its lower complexity.

Wireless relay can be utilized to extend signal coverage, achieve spatial diversity by user cooperation, or shield mobile terminals from adverse channel conditions over the direct link. In a two-hop multi-input-multi-output (MIMO) amplify-and-forward (AF) relay system, the overall noise at the destination station (DS) consists of the colored noise forwarded from the relay station (RS) and the local white noise. We propose blind noise correlation estimation at the DS by utilizing statistics of the broadband relay channel over the RS-DS hop, which effectively improves signal detection at the DS. For further performance improvement, we also propose to estimate the two cascaded MIMO relay channels over the source-RS and the RS-DS links at the DS based on the overall channel between the source and the DS and the amplifying matrix applied at the RS. To cancel cross-talk interference at a channel-reuse-relay-station (CRRS), we utilize the random forwarded signals of the CRRS as equivalent pilots for local coupling channel estimation and achieve a much higher post signal-to-interference ratio (SIR) than the conventional dedicated pilots assisted cancellers without causing any in-band interference at the DS. When an OFDM-based RS is deployed on a high-speed train to shield mobile terminals from the high Doppler frequency over the direct link, inter-subchannel interference (ICI) mitigation is required at the RS. By utilizing statistics of the channel between the base station and the train, we develop both full-rate and reduced-rate OFDM transmission with inherent ICI self-cancellation via transmit and/or receive preprocessing, which achieve significant performance improvement over the existing ICI self-cancellation schemes.

This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

The rapid increasing interest in wireless communication has led to the continuous development of wireless devices and technologies. The modern convergence and interoperability of wireless technologies has further increased the amount of services that can be provided, leading to the substantial demand for access to the radio frequency spectrum in an efficient manner. Cognitive radio (CR) an innovative concept of reusing licensed spectrum in an opportunistic manner promises to overcome the evident spectrum underutilization caused by the inflexible spectrum allocation. Spectrum sensing in an unswerving and proficient manner is essential to CR. Cooperation amongst spectrum sensing devices are vital when CR systems are experiencing deep shadowing and in a fading environment. In this thesis, cooperative spectrum sensing (CSS) schemes have been designed to optimize detection performance in an efficient and implementable manner taking into consideration: diversity performance, detection accuracy, low complexity, and reporting channel bandwidth reduction. The thesis first investigates state of the art spectrums sensing algorithms in CR. Comparative analysis and simulation results highlights the different pros, cons and performance criteria of a practical CSS scheme leading to the problem formulation of the thesis. Motivated by the problem of diversity performance in a CR network, the thesis then focuses on designing a novel relay based CSS architecture for CR. A major cooperative transmission protocol with low complexity and overhead - Amplify and Forward (AF) cooperative protocol and an improved double energy detection scheme in a single relay and multiple cognitive relay networks are designed. Simulation results demonstrated that the developed algorithm is capable of reducing the error of missed detection and improving detection probability of a primary user (PU). To improve spectrum sensing reliability while increasing agility, a CSS scheme based on evidence theory is next considered in this thesis. This focuses on a data fusion combination rule. The combination of conflicting evidences from secondary users (SUs) with the classical Dempster Shafter (DS) theory rule may produce counter-intuitive results when combining SUs sensing data leading to poor CSS performance. In order to overcome and minimise the effect of the counter-intuitive results, and to enhance performance of the CSS system, a novel state of the art evidence based decision fusion scheme is developed. The proposed approach is based on the credibility of evidence and a dissociability degree measure of the SUs sensing data evidence. Simulation results illustrate the proposed scheme improves detection performance and reduces error probability when compared to other related evidence based schemes under robust practcial scenarios. Finally, motivated by the need for a low complexity and minmum bandwidth reporting channels which can be significant in high data rate applications, novel CSS quantization schemes are proposed. Quantization methods are considered for a maximum likelihood estimation (MLE) and an evidence based CSS scheme. For the MLE based CSS, a novel uniform and optimal output entropy quantization scheme is proposed to provide fewer overhead complexities and improved throughput. While for the Evidence based CSS scheme, a scheme that quantizes the basic probability Assignment (BPA) data at each SU before being sent to the FC is designed. The proposed scheme takes into consideration the characteristics of the hypothesis distribution under diverse signal-to-noise ratio (SNR) of the PU signal based on the optimal output entropy. Simulation results demonstrate that the proposed quantization CSS scheme improves sensing performance with minimum number of quantized bits when compared to other related approaches.

Dans les communications coopératives, deux ou plusieurs terminaux de transmissionsont combinés pour accroître la diversité et/ou la puissance des signaux arrivant à un récepteur. Récemment, l'analyse tensorielle s'est avérée une approche efficace pour l'estimation de canaux dans les systèmes coopératifs. Cependant, parmi les quelques travaux consacrés à cette tâche, l'utilisation de la décomposition tensorielle PARAFAC pour modéliser les signaux reçus ne permet pas l'estimation conjointe des symboles et des canaux de communication. Afin d'éviter l'utilisation de séquences de symboles pilotes, l'objectif de cette thèse est de fournir de nouvelles approches tensorielles, en termes de systèmes de transmission et de récepteurs semi-aveugles, pour des systèmes de communication MIMO avec relai mono-directionnels, à deux sauts. Deux systèmes de transmission sont proposés en utilisant un codage spatio-temporel du type Khatri-Rao et deux stratégies de traitement Amplify-and-Forward (AF) au relai. Pour ces systèmes, appelés PT2-AF et NP-AF, les signaux reçus au niveau de la destination satisfont respectivement des modèles tensoriels du type PARATUCK2 et nested PARAFAC. En exploitant les propriétés d'unicité de ces modèles tensoriels établies dans la thèse, plusieurs récepteurs semi-aveugles sont dérivés. Certains de ces récepteurs sont du type ALS, tandis que d'autres sont des solutions non itératives basées sur des factorisations de produits de Khatri-Rao. Des résultats de simulation sont présentés pour illustrer les performances des récepteurs proposés qui sont comparés à des estimateurs supervisés. / In cooperative communication systems, two or more transmitting terminals arecombined to increase the diversity and/or the power of the signals arriving at aparticular receiver. Recently, the so-called tensor analysis has been an efficient approach for channel estimation in systems with cooperative diversity. However, among the few works devoted to this task, the utilization of the PARAFAC tensor decomposition for modeling the received signals did not allow the development of techniques for joint symbol and channel estimation. Aiming to avoid the use of pilot-based sequences, the objective of this thesis is to provide new tensor-based strategies, including transmission systems and semi-blind receivers, for one-way two-hop relaying systems. Based on a Khatri-Rao space-time coding at the source and two different Amplify-and-Forward (AF) relaying strategies, two transmission systems are proposed. For these systems, named PT2-AF and NP-AF, the received signals at the destination node follow respectively a PARATUCK2 and a nested PARAFAC tensor model. Exploiting uniqueness properties of these tensor models which are established in the thesis, several semi-blind receivers are derived. Some of these receivers are of iterative form using an ALS algorithm, whereas some other ones are close-form solutions associated with Khatri-Rao factorizations. Some simulation results are finally presented to illustrate the performance of the proposed receivers which are compared to some state-of-the-art supervised techniques.