Half-Duplex Relaying for the Multi-User Channel: Capacity Bounds, Fading Channel Performance and Asymptotical Behaviour

Multiple-input multiple-output (MIMO) scheme is able to improve the modern communications system performance in terms of increased throughput or reliability. As a virtually distributed antenna scheme, the relaying can enhance the communication system performance while there is no physical size limitation at the end user. Through decades, many relaying schemes have been extensively investigated for different channels. When the relay is close to the destination in a static channel and perfect channel state information (CSI) is available at the relay in a slow fading channel, the compress-and-forward (CF) scheme is often applied since it performs better than other relaying schemes. However, the CF scheme requires the relay to perform two-step operation (quantization and WZ binning), which increases the cost of implementing such scheme. In addition, having perfect CSI at the relay is not always possible in a wireless channel. To address these problems caused by the nature of the CF scheme, the generalized quantize-and-forward (GQF) scheme is proposed in this dissertation for the half-duplex (HD) multi-user channel. In this dissertation, the first part focuses on studying the half-duplex (HD) relaying in the Multiple Access Relay Channel (MARC) and the Compound Multiple Access Channel with a Relay (cMACr). A GQF scheme has been proposed to establish the achievable rate regions. Such scheme is developed based on the variation of the Quantize-and-Forward (QF) scheme and single block with two slots coding structure. The achievable rates results obtained can also be considered as a significant extension of the achievable rate region of Half-Duplex Relay Channel (HDRC). Furthermore, the rate regions based on GQF scheme are extended to the Gaussian channel case. The scheme performance is shown through some numerical examples. In contrast to conventional Full-Duplex (FD) MARC and Interference Relay Channel (IRC) rate achieving schemes which apply the block Markov encoding and decoding in a large number of communication blocks, the GQF developed are based on the single block coding strategies, which are more suitable for the HD channels. When the relay has no access to Channel State Information (CSI) of the relay-destination link, the GQF is implemented in the slow Rayleigh fading HD-MARC. Based on the achievable rates inequalities, the common outage probability and the expected sum rates are derived. Through numerical examples, we show that in the absence of CSI at the relay, the GQF scheme outperforms other relaying schemes. When the end users have different quality-of-service (QoS) requirements for slow fading channel, it is more precise to use the individual outage related parameters to quantify the scheme performance. The individual outage probability and total throughput are characterized for the HD-MARC. The numerical examples show that the outage probability of the individual users is lower than that of classic Compress-and-Forward (CF) scheme. The Diversity Multiplexing Tradeoff (DMT) is often applied as a figure of merit for different communication schemes in the asymptotically high SNR slow fading channels. The CF scheme achieves the optimal DMT for high multiplexing gains when the CSI of the relay-destination (R-D) link is available at the relay. However, having the CSI of R-D link at relay is not always possible due to the practical considerations of the wireless system. In this dissertation, the DMT of the GQF scheme is derived without R-D link CSI at the relay. Moreover, the GQF scheme achieves the optimal DMT for the entire range of multiplexing gains

Information Theoretic Limits of MIMO Interference and Relay Networks

In this thesis, the information theoretic performance limits of two important building blocks of the general multi-user wireless network, namely, the interference channel and the relay channel, are characterized. We consider both time-invariant and time-varying or fading channel. In the first part, we focus on the 2-user interference channel with time-invariant channel coefficients. First, we characterize the capacity region of a class of MIMO IC called strong in partial order ICs. It turns out that for this class of channels decoding both the messages at both the receivers is optimal, i.e., the capacity region is identical to that of the compound multiple access channel (MAC). The defining constraints on the channel coefficients for the class of strong in partial order ICs enable us to derive a novel tight upper bound to the sum rate of the channel --- a problem that is very difficult for general channel coefficients. To avoid this difficulty for the general IC, we next derive upper and lower bounds which are not identical but are within a constant number of bits to each other which characterizes the capacity region of the 2-user multi-input multi-output (MIMO) Gaussian interference channel (IC) with an arbitrary number of antennas at each node to within a constant gap that is independent of the signal-to-noise ratio (SNR) and all channel parameters. In contrast to an earlier result in [Telatar and Tse, ISIT, 2007], where both the achievable rate region and upper bounds to the capacity region of a general class of interference channels was specified as the union over all possible input distributions here we provide, a simple and an explicit achievable coding scheme for the achievable region and an explicit outer bound. We also illustrate an interesting connection of the simple achievable coding scheme to MMSE estimators at the receivers. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC. We also analyze the channel\u27s performance in the high SNR regime, which is obtained from the explicit expressions of the approximate capacity region and the resulting asymptotic rate region is known as the generalized degrees of freedom (GDoF) region. A close examination of the super position coding scheme which is both GDoF and approximate capacity optimal reveals that joint signal-space and signal-level interference alignment is necessary to achieve the GDoF region of the channel. The admissible DoF-splits between the private and common messages of the HK scheme are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques (at high SNR) on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time-sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime - where single-user DoF performance can be achieved simultaneously for both users- depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the SISO case. For asymmetric numbers of antennas at the four nodes the shape of the symmetric GDoF curve can be a \u22distorted W\u22 curve to the extent that for certain MIMO ICs it is a \u22V\u22 curve. In the second part of the thesis, we concentrate on time varying fading channels. We first characterize the fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading MIMO Z interference channel (ZIC) with channel state information at the transmitters (CSIT) and arbitrary number of antennas at each node. A short-term average power constraint is assumed. It is shown that a variant of the superposition coding scheme described above, where the 2nd transmitter\u27s signal depends on the channel matrix to the first receiver and the 1st user\u27s transmit signal is independent of CSIT, can achieve the full CSIT DMT of the ZIC. We also characterize the achievable DMT of a transmission scheme, which does not utilize any CSIT and show that for some range of multiplexing gains, the full CSIT DMT of the ZIC can be achieved by it. The size of this range of multiplexing gains depends on the system parameters such as the number of antennas at the four nodes (referred to hereafter as “antenna configuration”), signal-to-noise ratios (SNR) and interference-to-noise ratio (INR) of the direct links and cross link, respectively. Interestingly, for certain special cases such as when the interfered receiver has a relatively larger number of antennas than that at the other nodes or when the INR is stronger than the SNRs, the No-CSIT scheme can achieve the F-CSIT DMT for all multiplexing gains. Thus, under these circumstances, the optimal DMT of the MIMO ZIC with F-CSIT is same as the DMT of the corresponding ZIC with No-CSIT. For other channel configurations, the DMT achievable by the No-CSIT scheme serves as a lower bound to the fundamental No-CSIT DMT of the MIMO ZIC. We also characterize the fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward (DCF) protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information (CSI) at the relay. In this work, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this work enables the in-depth comparisons herein of full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes

A Critical Review of Physical Layer Security in Wireless Networking

Wireless networking has kept evolving with additional features and increasing capacity. Meanwhile, inherent characteristics of wireless networking make it more vulnerable than wired networks. In this thesis we present an extensive and comprehensive review of physical layer security in wireless networking. Different from cryptography, physical layer security, emerging from the information theoretic assessment of secrecy, could leverage the properties of wireless channel for security purpose, by either enabling secret communication without the need of keys, or facilitating the key agreement process. Hence we categorize existing literature into two main branches, namely keyless security and key-based security. We elaborate the evolution of this area from the early theoretic works on the wiretap channel, to its generalizations to more complicated scenarios including multiple-user, multiple-access and multiple-antenna systems, and introduce not only theoretical results but practical implementations. We critically and systematically examine the existing knowledge by analyzing the fundamental mechanics for each approach. Hence we are able to highlight advantages and limitations of proposed techniques, as well their interrelations, and bring insights into future developments of this area

Cooperative diversity in wireless networks : algorithms and architectures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 179-187).To effectively combat multipath fading across multiple protocol layers in wireless networks, this dissertation develops energy-efficient algorithms that employ certain kinds of cooperation among terminals, and illustrates how one might incorporate these algorithms into various network architectures. In these techniques, sets of terminals relay signals for each other to create a virtual antenna array, trading off the costs-in power, bandwidth, and complexity-for the greater benefits gained by exploiting spatial diversity in the channel. By contrast, classical network architectures only employ point-to-point transmission and thus forego these benefits. After summarizing a model for the wireless channel, we present various practical cooperative diversity algorithms based upon different types of relay processing and re-encoding, both with and without limited feedback from the ultimate receivers. Using information theoretic tools, we show that all these algorithms can achieve full spatial diversity, as if each terminal had as many transmit antennas as the entire set of cooperating terminals. Such diversity gains translate into greatly improved robustness to fading for the same transmit power, or substantially reduced transmit power for the same level of performance. For example, with two cooperating terminals, power savings as much as 12 dB (a factor of sixteen) are possible for outage probabilities around one in a thousand. Finally, we discuss how the required level of complexity in the terminals makes different algorithms suitable for particular network architectures that arise in, for example, current cellular and ad-hoc networks.by J. Nicholas Laneman.Ph.D