We consider a two-way relay channel in which two transmitters want to exchange information through a central relay. The relay observes a superposition of the trans- mitted signals from which a function of the transmitted messages is computed for broadcast. We consider the design of codebooks which permit the recovery of a function at the relay and derive information-theoretic bounds on the rates for reliable decoding at the relay. In the spirit of compute-and-forward, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be decoded is chosen at the relay depending on the channel realization. We define such a class of reliably computable functions for the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme permits substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields. Our numerical results indicate that it is favorable to allow the relay to attempt both compute-and-forward and decode-and-forward decoding. Indeed, either method considered separately is suboptimal for computation over general channels. However, we obtain a converse result when the transmitters are restricted to using identical binary linear codebooks generated uniformly at random. We show that it is impossible for this code ensemble to achieve any rate higher than the maximum of the rates achieved using compute-and-forward and decode-and-forward decoding. Finally, we turn our attention to the design of low density parity check (LDPC) ensembles which can practically achieve these information rates with joint-compute- and-forward message passing decoding. To this end, we construct a class of two-way erasure multiple access channels for which we can exactly characterize the performance of joint-compute-and-forward message passing decoding. We derive the processing rules and a density evolution like analysis for several classes of LDPC ensembles. Utilizing the universally optimal performance of spatially coupled LDPC ensembles with message passing decoding, we show that a single encoder and de- coder with puncturing can achieve the optimal rate region for a range of channel parameters.

In wireless communication systems, relays are widely used to extend coverage. Over the past years, relays have evolved from simple repeaters to more sophisticated units that perform signal processing to improve signal to interference plus noise ratio (SINR) or throughput (or both) at the destination receiver. There are various types of relays such as amplify and forward (AF), decode and forward (DF), and compress and forward (CF) (or estimate and forward (EF)) relays. In addition, recently there has been a growing interest in two-way relays (TWR). By utilizing the concept of analog network coding (ANC), TWRs can improve the throughput of a wireless sys- tem by reducing the number of time slots needed to complete a bi-directional message exchange between two destination nodes. It’s well known that the performance of a TWR system greatly depends on its ability to apply signal processing techniques to effectively mitigate the self-interference and noise accumulation, thereby improving the SINR. We study a TWR system that is equipped with multiple antennas at the relay node and a single antenna at the two destination nodes. Different from traditional work on TWR, we focus on the case with imperfect knowledge of channel state information (CSI). For such a TWR, we formulate a robust optimization problem that takes into ac- count norm-bounded estimation errors in CSI and designs an optimal beamforming matrix. Realizing the fact that this problem is extremely hard to solve globally, we derive two different methods to obtain either optimal or efficient suboptimal beam- forming matrix solutions. The first method involves solving the robust optimization problem using the S-procedure and semidefinite programming (SDP) with rank-one relaxation. This method provides an optimal solution when the rank-one relaxation condition for the SDP is satisfied. In cases where the rank-one condition cannot be satisfied, it’s necessary to resort to sub-optimal techniques. The second approach presented here reformulates the robust non-convex quadratically constrained quadratic programming (QCQP) into a robust linear programming (LP) problem by using first-order perturbation of the optimal non-robust beamforming solution (which assumes no channel estimation error). Finally, we view the TWR robust beamforming problem from a practical standpoint and develop a set of iterative algorithms based on Newton’s method or the steepest descent method that are practical for hardware implementation.

abstract: This dissertation considers two different kinds of two-hop multiple-input multiple-output (MIMO) relay networks with beamforming (BF). First, "one-way" amplify-and-forward (AF) and decode-and-forward (DF) MIMO BF relay networks are considered, in which the relay amplifies or decodes the received signal from the source and forwards it to the destination, respectively, where all nodes beamform with multiple antennas to obtain gains in performance with reduced power consumption. A direct link from source to destination is included in performance analysis. Novel systematic upper-bounds and lower-bounds to average bit or symbol error rates (BERs or SERs) are proposed. Second, "two-way" AF MIMO BF relay networks are investigated, in which two sources exchange their data through a relay, to improve the spectral efficiency compared with one-way relay networks. Novel unified performance analysis is carried out for five different relaying schemes using two, three, and four time slots in sum-BER, the sum of two BERs at both sources, in two-way relay networks with and without direct links. For both kinds of relay networks, when any node is beamforming simultaneously to two nodes (i.e. from source to relay and destination in one-way relay networks, and from relay to both sources in two-way relay networks), the selection of the BF coefficients at a beamforming node becomes a challenging problem since it has to balance the needs of both receiving nodes. Although this "BF optimization" is performed for BER, SER, and sum-BER in this dissertation, the solution for optimal BF coefficients not only is difficult to implement, it also does not lend itself to performance analysis because the optimal BF coefficients cannot be expressed in closed-form. Therefore, the performance of optimal schemes through bounds, as well as suboptimal ones such as strong-path BF, which beamforms to the stronger path of two links based on their received signal-to-noise ratios (SNRs), is provided for BERs or SERs, for the first time. Since different channel state information (CSI) assumptions at the source, relay, and destination provide different error performance, various CSI assumptions are also considered. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

Physical layer network coding (PNC) was proposed under the two-way relay hannel (TWRC) scenario, where two sources exchange information aided by a relay. PNC allows the two sources to transmit to the relay simultaneously, where superimposed signals at the relay can be mapped to network-coded symbols and then be broadcast to both sources instead of being treated as interference. Concurrent transmissions using PNC achieve a higher spectrum efficiency compared to time division and network coding solutions. Existing research mainly focused on the symmetric PNC designs, where the same channel coding and modulation configurations are applied by both sources. When the channel conditions of the two source-relay links are asymmetric or unequal amount of data are exchanged, heterogeneous modulation PNC designs are necessary. In additional, the design and optimization of multi-hop PNC, where multiple relays forming a multi-hop path between the two sources, remains an open issue. The above issues motivate the study of this dissertation. This dissertation investigates the design of heterogeneous modulation physical layer network coding (HePNC), the integration of channel error control coding into HePNC, the combination of HePNC with hierarchical modulation, and the design and generalization of multi-hop PNC. The contributions of this dissertation are four-fold. First, under the asymmetric TWRC scenario, where the channel conditions of the two source-relay links are asymmetric, we designed a HePNC protocol, including the optimization of the adaptive mapping functions and the bit-symbol labeling, to minimize the end-to-end BER. In addition, we developed an analytical framework to derive the BER of HePNC. HePNC can substantially enhance the throughput compared to the existing symmetric PNC under the asymmetric TWRC scenario. Second, we investigated channel coded HePNC and integrated the channel error control coding into HePNC in a link-to-link coding, where the relay tries to decode the superimposed codewords in the multi-access stage. A full-state sum-product decoding algorithm is proposed at the relay based on the repeat-accumulate codes to guarantee reliable end-to-end communication. Third, we proposed hierarchical modulation PNC (H-PNC) under asymmetric TWRC, where additional data exchange between the relay and the source with the relatively better channel condition is achieved in addition to that between the two end sources, benefiting from superimposing the additional data flow on the PNC transmission. When the relay also has the data exchange requirement with the source with a better source-relay channel, H-PNC outperforms HePNC and PNC in terms of the system sum throughput. Fourth, we designed and generalized multi-hop PNC, where multiple relays located in a linear topology are scheduled to support the data exchange between two end sources. The impact of error propagation and mutual interference among the nodes are addressed and optimized. The proposed designs outperform the existing ones in terms of end-to-end BER and end-to-end throughout. / Graduate

In this thesis, we proposed a precoding scheme for semi-blind channel estimation in amplify-and-forward (AF) multipath two-way relay networks (TWRN), where two terminals exchange their information through multi-relays. The precoding scheme, which diminishes computational complexity of semi-blind channel estimator, is used to distinguish received signal at both terminals from multi-relays. By applying a non-redundant linear precoding scheme at multi-relays, we proposed a semi-blind channel estimation to estimate the channel impulse response (CIR) of direct link and the cascaded source-relay-terminal links. Firstly, semi-blind channel estimation adopts least-square (LS) estimation to find the CIR of direct link between both terminals using a smaller number of training symbols. Secondly, the CIR of the cascaded source-relay-terminal links are obtained through second-order statistics (SOS) of received signals at both terminals. Consequently, the proposed scheme can effectively reduce the computational complexity and enhance the spectral efficiency in overall system. Simulation results corroborate the effectiveness of the proposed scheme.

abstract: There are many wireless communication and networking applications that require high transmission rates and reliability with only limited resources in terms of bandwidth, power, hardware complexity etc.. Real-time video streaming, gaming and social networking are a few such examples. Over the years many problems have been addressed towards the goal of enabling such applications; however, significant challenges still remain, particularly, in the context of multi-user communications. With the motivation of addressing some of these challenges, the main focus of this dissertation is the design and analysis of capacity approaching coding schemes for several (wireless) multi-user communication scenarios. Specifically, three main themes are studied: superposition coding over broadcast channels, practical coding for binary-input binary-output broadcast channels, and signalling schemes for two-way relay channels. As the first contribution, we propose an analytical tool that allows for reliable comparison of different practical codes and decoding strategies over degraded broadcast channels, even for very low error rates for which simulations are impractical. The second contribution deals with binary-input binary-output degraded broadcast channels, for which an optimal encoding scheme that achieves the capacity boundary is found, and a practical coding scheme is given by concatenation of an outer low density parity check code and an inner (non-linear) mapper that induces desired distribution of "one" in a codeword. The third contribution considers two-way relay channels where the information exchange between two nodes takes place in two transmission phases using a coding scheme called physical-layer network coding. At the relay, a near optimal decoding strategy is derived using a list decoding algorithm, and an approximation is obtained by a joint decoding approach. For the latter scheme, an analytical approximation of the word error rate based on a union bounding technique is computed under the assumption that linear codes are employed at the two nodes exchanging data. Further, when the wireless channel is frequency selective, two decoding strategies at the relay are developed, namely, a near optimal decoding scheme implemented using list decoding, and a reduced complexity detection/decoding scheme utilizing a linear minimum mean squared error based detector followed by a network coded sequence decoder. / Dissertation/Thesis / Ph.D. Electrical Engineering 2011

abstract: The recent proposal of two-way relaying has attracted much attention due to its promising features for many practical scenarios. Hereby, two users communicate simultaneously in both directions to exchange their messages with the help of a relay node. This doctoral study investigates various aspects of two-way relaying. Specifically, the issue of asynchronism, lack of channel knowledge, transmission of correlated sources and multi-way relaying techniques involving multiple users are explored. With the motivation of developing enabling techniques for two-way relay (TWR) channels experiencing excessive synchronization errors, two conceptually-different schemes are proposed to accommodate any relative misalignment between the signals received at any node. By designing a practical transmission/detection mechanism based on orthogonal frequency division multiplexing (OFDM), the proposed schemes perform significantly better than existing competing solutions. In a related direction, differential modulation is implemented for asynchronous TWR systems that lack the channel state information (CSI) knowledge. The challenge in this problem compared to the conventional point-to-point counterpart arises not only from the asynchrony but also from the existence of an interfering signal. Extensive numerical examples, supported by analytical work, are given to demonstrate the advantages of the proposed schemes. Other important issues considered in this dissertation are related to the extension of the two-way relaying scheme to the multiple-user case, known as the multi-way relaying. First, a distributed source coding solution based on Slepian-Wolf coding is proposed to compress correlated messages close to the information theoretical limits in the context of multi-way relay (MWR) channels. Specifically, the syndrome approach based on low-density parity-check (LDPC) codes is implemented. A number of relaying strategies are considered for this problem offering a tradeoff between performance and complexity. The proposed solutions have shown significant improvements compared to the existing ones in terms of the achievable compression rates. On a different front, a novel approach to channel coding is proposed for the MWR channel based on the implementation of nested codes in a distributed manner. This approach ensures that each node decodes the messages of the other users without requiring complex operations at the relay, and at the same time, providing substantial benefits compared to the traditional routing solution. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

Le codage réseau est apparu comme une technique alternative au routage au niveau de la couche réseau permettant d'améliorer le débit et d'optimiser l'utilisation de la capacité du réseau. Récemment, le codage réseau a été appliqué au niveau de la couche physique des réseaux sans-fil pour profiter de la superposition naturelle des signaux effectuée par le lien radio. Le codage réseau peut être vue comme un traitement interne du réseau pour lequel différentes techniques de relayage peuvent être utilisées. Cette thèse étudie un ensemble de traitements ayant des compromis variés en terme de performance et complexité. Nous considérons le canal bidirectionnel à relais, un modèle de canal de communication typique dans les réseaux coopératifs, où deux terminaux s'échangent mutuellement des messages par l'intermédiaire d'un relais. La communication se déroule en deux phases, une phase à accès multiple et une phase de broadcast. Pour ce scénario, nous analysons, dans une première partie, une stratégie de "decode-and-forward". Nous considérons, pour cette étude, des alphabets de taille finie et nous calculons les probabilités moyennes d'erreur de bout-en-bout en se basant sur la métrique d'exposant d'erreur du codage aléatoire. Puis, nous dérivons les régions des débits atteignables par rapport à une probabilité d'erreur maximale tolérable au niveau de chaque nœud. Dans une deuxième partie de la thèse, nous proposons deux schémas de codage réseau pratiques, avec complexité réduite, qui se basent sur la stratégie de relayage "compress-and-forward" (CF). Le premier schéma utilise un codage en réseau de points imbriqués (nested lattices). Le deuxième schéma est une version améliorée qui permet d'atteindre des débits de données supérieurs pour l'utilisateur qui a les meilleures conditions canal. Nous construisons les régions des débits atteignables par les deux schémas proposés tout en optimisant la répartition du temps alloué à chacune des deux phases de transmission. Après l'étude du régime asymptotique, nous analysons le schéma de codage CF avec des réseaux de points de dimension finie. Nous nous concentrons sur le problème de la transmission analogique où la distorsion est optimisée. Enfin, nous étudions l'application d'un schéma de codage, basé sur la stratégie CF avec des réseaux de points imbriqués, pour le canal bidirectionnel à canaux parallèles. Ainsi, nous présentons deux régions de débits atteignables selon la technique de traitement, conjoint ou séparé, des sous-canaux par le relais. / Network coding has emerged as an alternative technique to routing that enhances the throughput at the network layer. Recently, network coding has been applied at the physical layer to take advantage of the natural signal superposition that occurs in the radio link. In this context, the physical-layer network coding can be seen as an in-network processing strategy for which multiple forwarding schemes can be proposed. This thesis investigates a set of processing schemes tailored to the network coding at the physical layer with various compromises between performance and complexity. We consider a two-way relay channel, a typical communication system in cooperative networks, where two terminals communicate with each other via a relay node. This communication occurs during two transmission phases, namely a multiple-access phase and a broadcast phase. For TWRC scenario, we first analyze a decode-and-forward strategy with finite size alphabets. We calculate the end-to-end average error probabilities based on random coding error exponents. Then, we derive the achievable rate regions with respect to a maximal probability of error allowed at each terminal. Next, we propose two low-complexity and practical schemes based on compress-and-forward relaying strategy. The first scheme employs nested lattice coding. The second is an improved version which enables higher data rates for the user experiencing the best channel conditions. We present an information-theoretic framework to reconstruct the achievable rate regions of both schemes by considering optimal time division between both transmission phases. After the asymptotic regime analysis, we study single-layer lattice coding scheme with finite dimension lattices. We focus on the analog transmission problem where the distortion is optimized. Finally, we investigate single-layer lattice coding scheme for parallel Gaussian two-way relay channel. We present two achievable rate regions based on whether the relay processes all the sub-channels jointly or separately.

Cooperative relaying is a promising diversity achieving technique to provide reliable transmission, high throughput and extensive coverage for wireless networks in a variety of applications. Two-way relaying is a spectrally efficient protocol, providing one solution to overcome the half-duplex loss in one-way relay channels. Moreover, incorporating the multiple-input-multiple-output (MIMO) technology can further improve the spectral efficiency and diversity gain. A lot of related work has been performed on the two-way relay network (TWRN), but most of them assume perfect channel state information (CSI). In a realistic scenario, however, the channel is estimated and the estimation error exists. So in this thesis, we explicitly take into account the CSI error, and investigate its impact on the performance of amplify-and-forward (AF) TWRN where either multiple distributed single-antenna relays or a single multiple-antenna relay station is exploited. For the distributed relay network, we consider imperfect self-interference cancellation at both sources that exchange information with the help of multiple relays, and maximal ratio combining (MRC) is then applied to improve the decision statistics under imperfect signal detection. The system performance degradation in terms of outage probability and average bit-error rate (BER) are analyzed, as well as their asymptotic trend. To further improve the spectral efficiency while maintain the spatial diversity, we utilize the maximum minimum (Max-Min) relay selection (RS), and examine the impact of imperfect CSI on this single RS scheme. To mitigate the negative effect of imperfect CSI, we resort to adaptive power allocation (PA) by minimizing either the outage probability or the average BER, which can be cast as a Geometric Programming (GP) problem. Numerical results verify the correctness of our analysis and show that the adaptive PA scheme outperforms the equal PA scheme under the aggregated effect of imperfect CSI. When employing a single MIMO relay, the problem of robust MIMO relay design has been dealt with by considering the fact that only imperfect CSI is available. We design the MIMO relay based upon the CSI estimates, where the estimation errors are included to attain the robust design under the worst-case philosophy. The optimization problem corresponding to the robust MIMO relay design is shown to be nonconvex. This motivates the pursuit of semidefinite relaxation (SDR) coupled with the randomization technique to obtain computationally efficient high-quality approximate solutions. Numerical simulations compare the proposed MIMO relay with the existing nonrobust method, and therefore validate its robustness against the channel uncertainty. / Graduate

Cooperative relay systems have emerged as promising techniques to boost the performance of wireless systems. Recent studies have confirmed that interferences, co-channel interferences (CCIs) and self-interferences, have a huge impact on cooperative relay systems and can cause significant performance degradation. Two problems were observed in this research. Firstly, previous studies on performance analysis of Amplify-and-Forward (AF) relay systems in presence of CCIs have only focused on a specific interference channel model. However, in practical design scenarios, such an assumption is not a realistic proposition. Secondly, analyses of overheads introduced by a time-based relay selection protocol in distributed cooperative systems have been based on an over-pessimistic assumption where all packets involved in a collision are destroyed. Nevertheless, collisions due to the protocol overheads cause the system performance to be degraded but this does not mean that the failure of end-to-end transmission certainly occurs. The thesis aims to analyse the performance of practical cooperative relay systems in the presence of CCIs and self-interferences, by developing exact mathematical methods. A new unified mathematical method for AF relay systems in presence of a random number of arbitrary non-identical CCIs was developed. The obtained new approach derived in terms of a moment generating function of the aggregate interferences' power led to the derivation of new explicit expressions. The new results greatly simplify evaluation of average error rates over diverse practical interference scenarios. Moreover, a new exact mathematical analysis for distributed cooperative relay systems employing a time-based relay selection protocol based on an accurate interference model was presented. This approach led to the derivation of new exact expressions for the spectral efficiency which accounts for both self-interferences and the protocol overheads as well as for different fading scenarios and arbitrary relay locations. This approach provided several advantages over direct approaches, one of which is that it significantly simplified averaging-out the joint random variables involved.