A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Distortion Exponent in MIMO Fading Channels with Time-Varying Source Side Information

Transmission of a Gaussian source over a time-varying multiple-input multiple-output (MIMO) channel is studied under strict delay constraints. Availability of a correlated side information at the receiver is assumed, whose quality, i.e., correlation with the source signal, also varies over time. A block-fading model is considered for the states of the time-varying channel and the time-varying side information; and perfect state information at the receiver is assumed, while the transmitter knows only the statistics. The high SNR performance, characterized by the \textit{distortion exponent}, is studied for this joint source-channel coding problem. An upper bound is derived and compared with lowers based on list decoding, hybrid digital-analog transmission, as well as multi-layer schemes which transmit successive refinements of the source, relying on progressive and superposed transmission with list decoding. The optimal distortion exponent is characterized for the single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenarios by showing that the distortion exponent achieved by multi-layer superpositon encoding with joint decoding meets the proposed upper bound. In the MIMO scenario, the optimal distortion exponent is characterized in the low bandwidth ratio regime, and it is shown that the multi-layer superposition encoding performs very close to the upper bound in the high bandwidth expansion regime.Comment: Submitted to IEEE Transactions on Information Theor

Fronthaul-Constrained Cloud Radio Access Networks: Insights and Challenges

As a promising paradigm for fifth generation (5G) wireless communication systems, cloud radio access networks (C-RANs) have been shown to reduce both capital and operating expenditures, as well as to provide high spectral efficiency (SE) and energy efficiency (EE). The fronthaul in such networks, defined as the transmission link between a baseband unit (BBU) and a remote radio head (RRH), requires high capacity, but is often constrained. This article comprehensively surveys recent advances in fronthaul-constrained C-RANs, including system architectures and key techniques. In particular, key techniques for alleviating the impact of constrained fronthaul on SE/EE and quality of service for users, including compression and quantization, large-scale coordinated processing and clustering, and resource allocation optimization, are discussed. Open issues in terms of software-defined networking, network function virtualization, and partial centralization are also identified.Comment: 5 Figures, accepted by IEEE Wireless Communications. arXiv admin note: text overlap with arXiv:1407.3855 by other author

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