Asymptotic Sum-Capacity of Random Gaussian Interference Networks Using Interference Alignment

We consider a dense n-user Gaussian interference network formed by paired transmitters and receivers placed independently at random in Euclidean space. Under natural conditions on the node position distributions and signal attenuation, we prove convergence in probability of the average per-user capacity C_Sigma/n to 1/2 E log(1 + 2SNR). The achievability result follows directly from results based on an interference alignment scheme presented in recent work of Nazer et al. Our main contribution comes through the converse result, motivated by ideas of `bottleneck links' developed in recent work of Jafar. An information theoretic argument gives a capacity bound on such bottleneck links, and probabilistic counting arguments show there are sufficiently many such links to tightly bound the sum-capacity of the whole network.Comment: 5 pages; to appear at ISIT 201

Interference Mitigation in Large Random Wireless Networks

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background, including the concept of capacity. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. (See also arXiv:1002.0235 and arXiv:0907.5165.) In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We analyse the tradeoff between reducing delay and lowering the communication rate. (See also arXiv:1004.0208.) In Chapter 6, we outline a problem that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests.Comment: PhD thesis, University of Bristol, 201

MIMO Interference Alignment Over Correlated Channels with Imperfect CSI

Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the post-processing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Hybrid Channel Pre-Inversion and Interference Alignment Strategies

In this paper we consider strategies for MIMO interference channels which combine the notions of interference alignment and channel pre-inversion. Users collaborate to form data-sharing groups, enabling them to clear interference within a group, while interference alignment is employed to clear interference between groups. To improve the capacity of our schemes at finite SNR, we propose that the groups of users invert their subchannel using a regularized Tikhonov inverse. We provide a new sleeker derivation of the optimal Tikhonov parameter, and use random matrix theory to provide an explicit formula for the SINR as the size of the system increases, which we believe is a new result. For every possible grouping of K = 4 users each with N = 5 antennas, we completely classify the degrees of freedom available to each user when using such hybrid schemes, and construct explicit interference alignment strategies which maximize the sum DoF. Lastly, we provide simulation results which compute the ergodic capacity of such schemes.Comment: Submitted to ICC 201