On the Distribution of MIMO Mutual Information: An In-Depth Painlev\'{e} Based Characterization

This paper builds upon our recent work which computed the moment generating function of the MIMO mutual information exactly in terms of a Painlev\'{e} V differential equation. By exploiting this key analytical tool, we provide an in-depth characterization of the mutual information distribution for sufficiently large (but finite) antenna numbers. In particular, we derive systematic closed-form expansions for the high order cumulants. These results yield considerable new insight, such as providing a technical explanation as to why the well known Gaussian approximation is quite robust to large SNR for the case of unequal antenna arrays, whilst it deviates strongly for equal antenna arrays. In addition, by drawing upon our high order cumulant expansions, we employ the Edgeworth expansion technique to propose a refined Gaussian approximation which is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and for moderate deviations into the tails (where the Gaussian approximation fails remarkably). For stronger deviations where the Edgeworth expansion becomes unwieldy, we employ the saddle point method and asymptotic integration tools to establish new analytical characterizations which are shown to be very simple and accurate. Based on these results we also recover key well established properties of the tail distribution, including the diversity-multiplexing-tradeoff.Comment: Submitted to IEEE Transaction on Information Theory (under revision

Multiple-antenna systems in ad-hoc wireless networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (leaves 223-229).The increasing demand for wireless communication services has resulted in crowding of the electromagnetic spectrum. The "spectral-commons" model, where a portion of the electromagnetic spectrum is public and used on an ad-hoc basis, has been proposed to free up spectrum that has been allocated but underutilized. Ad-hoc wireless networks (networks with no central control) are also interesting in their own right as they do not require costly infrastructure, are robust to single-node failures, and can be deployed in environments where it is difficult to deploy infrastructure. The main contributions of this thesis are expressions for the mean and in some cases the variance of the spectral efficiency (bits/second/Hz) of single-hop links in random wireless networks as a function of the number of antennas per node, link-length, interferer density, and path-loss-exponent (an environmental parameter that determines signal decay with distance), under assumptions chosen for realistic implementability in the near future. These results improve our understanding of such systems as they indicate the data rates achievable as a function of tangible parameters like user density and environmental characteristics, and are useful for designers of wireless networks to trade-off hardware costs, data-rates, and user densities. We found that constant mean spectral efficiencies can be maintained in wireless networks with increasing user density by linearly increasing the number of antenna elements per user, or by maintaining a constant fraction of nodes connected to high capacity infrastructure like optical fiber, equipped with antenna arrays. These are promising ways to serve an increasing density of users without increasing bandwidth. Additionally, several interesting features of such networks have been highlighted.(cont.) For instance we found that the mean and variance of spectral efficiencies can be characterized in terms of a parameter called the link rank, which on average equals the number of interferers whose signal power is stronger at a representative receiver than its target transmitter. Rank thus combines the effects of node density and link lengths. Another interesting finding is that mean spectral efficiency in networks with rank-1 links, and equal numbers of antennas at transmit and receive sides can be improved if nodes turn off two thirds of their transmit antennas. These results were derived using infinite random matrix theory and validated using Monte Carlo simulations which were also used to characterize the distribution of spectral efficiencies in such networks.by Siddhartan Govindasamy.Ph.D