On the Achievable Rates of Pairwise Multiway Relay Channels

In this paper, we study the effect of users' transmission ordering on the common rate and sum rate of pairwise multiway relay channels (MWRCs) with functional-decode-forward strategy. To this end, we first develop a graphical model for the data transmission in a pairwise MWRC. Using this model, we then find the optimal orderings that achieve the maximum common rate and sum rate of the system. The achieved maximum common and sum rate are also found. Moreover, we show that the performance gap between optimal orderings and a random ordering vanishes when SNR increases. Computer simulations are presented for better illustration of the results.Comment: Extended version of "On the Achievable Rates of Pairwise Multiway Relay Channels" accepted for ISIT 201

Wireless MIMO Switching: Weighted Sum Mean Square Error and Sum Rate Optimization

This paper addresses joint transceiver and relay design for a wireless multiple-input-multiple-output (MIMO) switching scheme that enables data exchange among multiple users. Here, a multi-antenna relay linearly precodes the received (uplink) signals from multiple users before forwarding the signal in the downlink, where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed. The problem of optimizing the precoder based on various design criteria is typically non-convex and difficult to solve. The main contribution of this paper is a unified approach to solve the weighted sum mean square error (MSE) minimization and weighted sum rate maximization problems in MIMO switching. Specifically, an iterative algorithm is proposed for jointly optimizing the relay's precoder and the users' receive filters to minimize the weighted sum MSE. It is also shown that the weighted sum rate maximization problem can be reformulated as an iterated weighted sum MSE minimization problem and can therefore be solved similarly to the case of weighted sum MSE minimization. With properly chosen initial values, the proposed iterative algorithms are asymptotically optimal in both high and low signal-to-noise ratio (SNR) regimes for MIMO switching, either with or without self-interference cancellation (a.k.a., physical-layer network coding). Numerical results show that the optimized MIMO switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature.Comment: This manuscript is under 2nd review of IEEE Transactions on Information Theor

Non-Regenerative Multi-Way Relaying: Combining the Gains of Network Coding and Joint Processing

In this paper, we consider a non-regenerative multi-group multi-way relaying scenario in which each group consists of multiple half-duplex nodes. Each node wants to share its data with all other nodes within its group. The transmissions are performed via an intermediate non-regenerative half-duplex multi-antenna relay station, termed RS, which spatially separates the different groups. In our proposal, all nodes simultaneously transmit to RS during a common multiple access phase and RS retransmits linearly processed versions of the received signals back to the nodes during multiple broadcast (BC) phases. We propose a novel transmit strategy which exploits analog network coding (ANC) and efficiently combines spatial transceive processing at RS with joint receive processing at each node over multiple BC phases. A closed-form solution for an ANC aware relay transceive filter is introduced and closed-form solutions for the joint receive processing filters at the nodes are presented. Furthermore, self-interference cancellation and successive interference cancellation are exploited at the nodes to improve the joint receive processing. By numerical results, it is shown that the proposed transmit strategy significantly outperforms existing multi-way strategies

Analysis and design of physical-layer network coding for relay networks

Physical-layer network coding (PNC) is a technique to make use of interference in wireless transmissions to boost the system throughput. In a PNC employed relay network, the relay node directly recovers and transmits a linear combination of its received messages in the physical layer. It has been shown that PNC can achieve near information-capacity rates. PNC is a new information exchange scheme introduced in wireless transmission. In practice, transmitters and receivers need to be designed and optimized, to achieve fast and reliable information exchange. Thus, we would like to ask: How to design the PNC schemes to achieve fast and reliable information exchange? In this thesis, we address this question from the following works: Firstly, we studied channel-uncoded PNC in two-way relay fading channels with QPSK modulation. The computation error probability for computing network coded messages at the relay is derived. We then optimized the network coding functions at the relay to improve the error rate performance. We then worked on channel coded PNC. The codes we studied include classical binary code, modern codes, and lattice codes. We analyzed the distance spectra of channel-coded PNC schemes with classical binary codes, to derive upper bounds for error rates of computing network coded messages at the relay. We designed and optimized irregular repeat-accumulate coded PNC. We modified the conventional extrinsic information transfer chart in the optimization process to suit the superimposed signal received at the relay. We analyzed and designed Eisenstein integer based lattice coded PNC in multi-way relay fading channels, to derive error rate performance bounds of computing network coded messages. Finally we extended our work to multi-way relay channels. We proposed a opportunistic transmission scheme for a pair-wise transmission PNC in a single-input single-output multi-way relay channel, to improve the sum-rate at the relay. The error performance of computing network coded messages at the relay is also improved. We optimized the uplink/downlink channel usage for multi-input multi-output multi-way relay channels with PNC to maximize the degrees of freedom capacity. We also showed that the system sum-rate can be further improved by a proposed iterative optimization algorithm

Multi-way relay networks: characterization, performance analysis and transmission scheme design

Multi-way relay networks (MWRNs) are a growing research area in the field of relay based wireless networks. Such networks provide a pathway for solving the ever in- creasing demand for higher data rate and spectral efficiency in a general multi-user scenario. MWRNs have potential applications in video conferencing, file sharing in a social network, as well as satellite networks and sensor networks. Recent research on MWRNs focuses on efficient transmission protocol design by harnessing different network coding schemes, higher dimensional structured codes and advanced relaying protocols. However, the existing research misses out the characterization and analysis of practical issues that influence the performance of MWRNs. Moreover, the existing transmission schemes suffer some significant limitations, that need to be solved for maximizing the benefits of MWRNs. In this thesis, we investigate the practical issues that critically influence the perfor- mance of a MWRN and propose solutions that can outperform existing schemes. To be specific, we characterize error propagation phenomenon for additive white Gaus- sian noise (AWGN) and fading channels with functional decode and forward (FDF) and amplify and forward (AF) relaying protocols, propose a new pairing scheme that out- performs the existing schemes for lattice coded FDF MWRNs in terms of the achievable rate and error performance and finally, analyze the impact of imperfect channel state information (CSI) and optimum power allocation on MWRNs. At first, we analyze the error performance of FDF and AF MWRNs with pair- wise transmission using binary phase shift keying (BPSK) modulation in AWGN and Rayleigh fading channels. We quantify the possible error events in an L-user FDF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) other users. We show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a FDF MWRN. We derive the average BER of a user in a FDF or AF MWRN under high SNR conditions and provide simulation results to verify them. Next, we propose a novel user pairing scheme for lattice coded FDF MWRNs. Lattice codes can achieve the capacity of AWGN channels and are used in digital communica- tions as high-rate signal constellations. Our proposed pairing scheme selects a common user with the best average channel gain and thus, allows it to positively contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. In addition, considering M-ary QAM with square constellation as a special case of lattice codes, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates and error performance, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. Finally, we investigate lattice coded FDF and AF MWRNs with imperfect CSI. Con- sidering lattice codes of sufficiently large dimension, we obtain the bounds on the com- mon rate and sum rate. In addition, considering M-ary quadrature amplitude mod- ulation (QAM) with square constellations, we obtain expressions for the average SER in FDF MWRNs. For AF MWRNs, considering BPSK modulation as the simplest case of lattice codes, we obtain the average BER. Moreover, we obtain the optimum power allocation coefficients to maximize the sum rate in AF MWRN. For both FDF and AF relaying protocols, the average common rate and sum rate are decreasing functions of the estimation error. The analysis shows that the error performance of a FDF MWRN is an increasing function of both the channel estimation error and the number of users, whereas, for AF MWRN, the error performance is an increasing function of only the channel estimation error. Also, we show that to achieve the same sum rate in AF MWRN, optimum power allocation requires 7 − 9 dB less power compared to equal power allocation depending upon users’ channel conditions

Adaptive Communication for Wireless Massive MIMO Systems

The demand for high data rates in wireless communications is increasing rapidly. One way to provide reliable communication with increased rates is massive multiple-input multiple-output (MIMO) systems where a large number of antennas is deployed. We analyze three systems utilizing a large number of antennas to provide enhancement in the performance of wireless communications. First, we consider a general form of spatial modulation (SM) systems where the number of transmitted data streams is allowed to vary and we refer to it as generalized spatial modulation with multiplexing (GSMM). A Gaussian mixture model (GMM) is shown to accurately model the transmitted spatially modulated signal using a precoding framework. Using this transmit model, a general closed-form expression for the achievable rate when operating over Rayleigh fading channels is evaluated along with a tight upper and a lower bounds for the achievable rate. The obtained expressions are flexible enough to accommodate any form of SM by adjusting the precoding set. Followed by that, we study quantized distributed wireless relay networks where a relay consisting of many geographically dispersed nodes is facilitating communication between unconnected users. Due to bandwidth constraints, distributed relay networks perform quantization at the relay nodes, and hence they are referred to as quantized distributed relay networks. In such systems, users transmit their data simultaneously to the relay nodes through the uplink channel that quantize their observed signals independently to a few bits and broadcast these bits to the users through the downlink channel. We develop algorithms that can be employed by the users to estimate the uplink channels between all users and all relay nodes when the relay nodes are performing simple sign quantization. This setup is very useful in either extending coverage to unconnected regions or replacing the existing wireless infrastructure in case of disasters. Using the uplink channel estimates, we propose multiple decoders that can be deployed at the receiver side. We also study the performance of each of these decoders under different system assumptions. A different quantization framework is also proposed for quantized distributed relay networking where the relay nodes perform vector quantization instead of sign quantization. Applying vector quantization at the relay nodes enables us to propose an algorithm that allocates quantization resources efficiently among the relay nodes inside the relay network. We also study the beamforming design at the users’ side in this case where beamforming design is not trivial due to the quantization that occurs at the relay network. Finally, we study a different setup of distributed communication systems called cell-free massive MIMO. In cell-free massive MIMO, regular cellular communication is replaced by multiple access points (APs) that are placed randomly over the coverage area. All users in the coverage area are sharing time and frequency resources and all APs are serving all UEs while power allocation is done in a central processor that is connected to the APs through a high speed backhaul network. We study the power allocation in cell-free massive MIMO system where APs are equipped with few antennas and how the distribution of the available antennas among access points affects both the performance and the infrastructure cost

Relay-Aided Communication in Large Interference Limited Wireless Networks

In recent years, the number of active wireless devices increases exponentially and it is, therefore, to expect that the interference increases as well. Interference between communication links is the major performance limiting factor in today's communication networks. Hence, the handling of the overall interference in a network is one major challenge in wireless communication networks of the future. If the interference signals are weak in comparison to the useful signal, they can be simply treated as noise. If the interference signals are strong in comparison to the useful signal, they can be reliably decoded and subtracted from the received signal at the receivers. However, in multiuser communication networks, the interference and the useful signal are often of comparable signal strength. The conventional approach to handle these interference signals is to orthogonalize the useful signal and the interference signals using, e.g., time division multiple access (TDMA) or frequency division multiple access (FDMA). In the past few years, instead of orthogonalization, interference alignment (IA) has been developed as an efficient technique to handle interference signals, especially in the high signal to noise ratio (SNR) region. The basic idea of IA is to align multiple interference signals in a particular subspace of reduced dimension at each receiver. The objective is to minimize the signal dimensions occupied by interference at each receiver. In order to perform IA, the receive space is divided into two disjoint subspaces, the useful signal subspace and the interference signal subspace. Each transmitting node designs its transmit filters in such a way that at each receiving node, all interference signals are within the interference subspace and only the useful signal is in the useful subspace. In this thesis, the focus is on large interference limited wireless communication networks. In contrast to the conventional use of relays, for extending the coverage, in this thesis, the relays are used to manipulate the effective end-to-end channel between the transmitters and receivers to perform IA in the network. Since the relays are used to assist the process of IA and not interested in the data streams transmitted by the nodes, amplify-and-forward relays are sufficient to support the process of IA. Therefore, the main focus of this thesis is on amplify-and-forward relays. Throughout this thesis, it is assumed that all nodes and relays are multi-antenna half-duplex devices. When considering large networks, the assumption that all nodes are connected to all relays does not hold due to physical propagation phenomena, e.g., high path loss and shadowing. In such large networks, the distances between different nodes may differ a lot, leading to links of considerably different signal strengths, where sufficiently weak links may be neglected. Hence, large networks are in general partially connected. In this thesis, three important interference-limited relay aided wireless network topologies are investigated, the partially connected relay aided multi-pair pair-wise communication network, the fully connected multi-group multi-way relaying network and the partially connected multi-group multi-way relaying network. For each of these topologies, new algorithms to perform IA are developed in this thesis. First, a large partially connected relay aided pair-wise communication network is considered. The concept of an appropriate partitioning of a partially connected network into subnetworks which are themselves fully connected is introduced. Each of these subnetworks contains a single relay and all nodes being connected to this relay. Some nodes or even communication pairs may be connected to multiple relays. The bidirectional pair-wise communication between the nodes takes place via the intermediate relays, using the two-way relaying protocol. Only relays which are connected to both nodes of a communication pair can serve this pair. Hence, it is assumed that all communication pairs in the entire network are served by at least one relay. The most challenging part of such a partially connected network is the handling of nodes which are connected to multiple relays. Hence, techniques called simultaneous signal alignment (SSA) and simultaneous channel alignment (SCA), are proposed to perform signal alignment (SA) and channel alignment (CA) with multiple relays simultaneously. SA means that all nodes transmit to the relay in such a way that the signals of each communicating pair are pair-wise aligned at the relay. For CA, which is dual to SA, the receive filter of each node is designed such that the effective channels between the relay and both nodes of a communicating pair span the same subspace. A closed-form solution to perform IA in this network topology is obtained and the properness conditions for SSA and SCA are derived. It is shown that local channel state information (CSI) is sufficient to perform IA in partially connected networks, whereas in fully connected relay aided networks, global CSI is required in general. Through simulations, it is shown that the proposed closed-form solution achieves more degrees of freedom (DoF) than the reference algorithms and has better sum-rate performance, especially in the high SNR-region. Especially in large wireless networks, it may happen that not both nodes of a communication pair are connected to the same relays. If a single node of a communication pair is in addition connected to a relay which, therefore, cannot assist the communication, this node receives only interference and no useful signal from this relay. Such a node suffers from inter-subnetwork interference, due to the connection by an inter-subnetwork link to the additional relay. Hence, in this thesis, a closed form algorithm which minimizes the inter-subnetwork interference power in the whole partially connected network is proposed and the properness conditions are derived. The condition under which an interference free-communication can be achieved by the proposed inter-subnetwork interference power minimization algorithm is derived. Further, it is shown that the proposed inter-subnetwork interference power minimization algorithm achieves a higher sum rate in comparison to the considered reference algorithm. Secondly, a fully connected multi-group multi-way relaying networks is considered. In such a network, multiple nodes form a group and each node wants to share its message with all other nodes in its group via an intermediate relay. The group-wise communication between the nodes inside a group takes place via the intermediate relay, using a transmission strategy considering several multiple access (MAC) phases and several multicast (MC) phases, in general. In this thesis, a multicast IA algorithm to handle the interference in such a network is proposed. The idea of the proposed algorithm is that in each of the MC phases, a multiple input multiple output (MIMO) interference multicast channel is created by separating the antennas of the relay into as many clusters as groups in the network. Each of these clusters serves a specific group of nodes and transmits in such a way that the signals transmitted from different clusters are aligned at the receiving nodes of the non-intended multicast groups. It is shown that the minimum required number of antennas at the relay is independent of the number of nodes per group, which is an important property since the number of antennas available at the relay is limited in general. Furthermore, the properness conditions for the proposed multicast IA algorithm are derived. It is shown that the proposed multicast algorithm outperforms a reference algorithm for a broad range of SNR values, while still requiring less antennas at the relay. Finally, a large partially connected multi-group multi-way relay network is considered. In contrast to the fully connected multi-group multi-way relaying network, multiple relays are considered in this partially connected network. Such a partially connected network can be partitioned into subnetworks that are themselves fully connected. Hence, such a partially connected network consists of multiple subnetworks, where each of these contains a single relay and all groups of nodes which are connected to this relay. Each group of nodes may be connected to one or multiple relays. This means that not all groups of nodes are connected to all relays in the network. However, any group is connected to at least one relay which serves this group of nodes. The group-wise exchange of data between the nodes inside a group is performed via the multi-way relaying protocol. The most challenging part of such a partially connected network is the handling of the nodes inside groups which are connected to multiple relays. To overcome this challenge, new techniques called simultaneous group signal alignment (SGSA) and simultaneous group channel alignment (SGCA) are introduced to perform SA and CA in partially connected multi-group multi-way relaying networks. A closed-form IA solution for this network topology is obtained and the properness conditions for the solvability of SGSA and SGCA are derived. It is shown that the proposed IA algorithm outperforms the reference algorithm in terms of sum rate and DoF

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Principal Component Analysis

This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as image processing, biometric, face recognition and speech processing. It also includes the core concepts and the state-of-the-art methods in data analysis and feature extraction