A closed-form approximation of correlated multiuser MIMO ergodic capacity with antenna selection and imperfect channel estimation

Abstract—Antenna selection (AS) is a promising technology to substantially reduce the complexity of massive multiple-input multiple-output (MIMO) systems. However, spatial correlation and imperfect estimation of channel state information (CSI) are well known to have a direct impact on the capacity of feasible MIMO schemes. In this paper, a tight closed-form approximation of the ergodic capacity for correlated Rayleigh fading multiuser MIMO channels with receive AS and imperfect CSI is presented. The derived expression takes into account the spatial correlation at both link sides and channel estimation error at the receiver. It can be used for arbitrary numbers of users, antennas, and receive RF chains. Furthermore, a concise analytical capacity formula is derived in the high signal-to-noise ratio (SNR) region. Numerical results validate the accuracy of our closed-form expressions over different channel conditions and SNRs. The new capacity approximation extends the state-of-the-art and enables efficient performance evaluation of varied multiantenna applications including massive MIMO for 5G systems

Some fundamental issues in receiver design and performance analysis for wireless communication

Ph.DDOCTOR OF PHILOSOPH

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

Algorithms and architecture for multiusers, multi-terminal, multi-layer information theoretic security

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 161-164).As modern infrastructure systems become increasingly more complex, we are faced with many new challenges in the area of information security. In this thesis we examine some approaches to security based on ideas from information theory. The protocols considered in this thesis, build upon the "wiretap channel," a model for physical layer security proposed by A. Wyner in 1975. At a higher level, the protocols considered here can strengthen existing mechanisms for security by providing a new location based approach at the physical layer.In the first part of this thesis, we extend the wiretap channel model to the case when there are multiple receivers, each experiencing a time varying fading channel. Both the scenario when each legitimate receiver wants a common message as well as the scenario when they all want separate messages are studied and capacity results are established in several special cases. When each receiver wants a separate independent message, an opportunistic scheme that transmits to the strongest user at each time, and uses Gaussian codebooks is shown to achieve the sum secrecy capacity in the limit of many users. When each receiver wants a common message, a lower bound to the capacity is provided, independent of the number of receivers. In the second part of the thesis the role of multiple antennas for secure communication studied. We establish the secrecy capacity of the multi antenna wiretap channel (MIMOME channel), when the channel matrices of the legitimate receiver and eavesdropper are fixed and known to all the terminals. To establish the capacity, a new computable upper bound on the secrecy capacity of the wiretap channel is developed, which may be of independent interest. It is shown that Gaussian codebooks suffice to attain the capacity for this problem. For the case when the legitimate receiver has a single antenna (MISOME channel) a rank one transmission scheme is shown to attain the capacity.(CONT.) In the high signal-to-noise ratio (SNR) regime, it is shown that a capacity achieving scheme involves simultaneous diagonalization of the channel matrices using the generalized singular value decomposition and independently coding accross the resulting parallel channels. Furthermore a semi-blind masked beamforming scheme is studied, which transmits signal of interest in the subspace of the legitimate receiver's channel and synthetic noise in the orthogonal subspace. It is shown that this scheme is nearly optimal in the high SNR regime for the MISOME case and the performance penalty for the MIMOME channel is evaluated in terms of the generalized singular values. The behavior of the secrecy capacity in the limit of many antennas is also studied. When the channel matrices have i.i.d. CN(O, 1) entries, we show that (1) the secrecy capacity for the MISOME channel converges (almost surely) to zero if and only if the eavesdropper increases its antennas at a rate twice as fast as the sender (2) when a total of T >> 1 antennas have to be allocated between the sender and the receiver, the optimal allocation, which maximizes the number of eavesdropping antennas for zero secrecy capacity is 2 : 1. In the final part of the thesis, we consider a variation of the wiretap channel where the sender and legitimate receiver also have access to correlated source sequences. They use both the sources and the structure of the underlying channel to extract secret keys. We provide general upper and lower bounds on the secret key rate and establish the capacity for the reversely degraded case.by Ashish Khisti.Ph.D

Local to global geometric methods in information theory

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 201-203).This thesis treats several information theoretic problems with a unified geometric approach. The development of this approach was motivated by the challenges encountered while working on these problems, and in turn, the testing of the initial tools to these problems suggested numerous refinements and improvements on the geometric methods. In ergodic probabilistic settings, Sanov's theorem gives asymptotic estimates on the probabilities of very rare events. The theorem also characterizes the exponential decay of the probabilities, as the sample size grows, and the exponential rate is given by the minimization of a certain divergence expression. In his seminal paper, A Mathematical Theory of Communication, Shannon introduced two influential ideas to simplify the complex task of evaluating the performance of a coding scheme: the asymptotic perspective (in the number of channel uses) and the random coding argument. In this setting, Sanov's theorem can be used to analyze ergodic information theoretic problems, and the performance of a coding scheme can be estimated by expressions involving the divergence. One would then like to use a geometric intuition to solve these problems, but the divergence is not a distance and our naive geometric intuition may lead to incorrect conclusions. In information geometry, a specific differential geometric structure is introduced by means of "dual affine connections". The approach we take in this thesis is slightly different and is based on introducing additional asymptotic regimes to analyze the divergence expressions. The following two properties play an important role. The divergence may not be a distance, but locally (i.e., when its arguments are "close to each other"), the divergence behaves like a squared distance.(cont.) Moreover, globally (i.e., when its arguments have no local restriction), it also preserves certain properties satisfied by squared distances. Therefore, we develop the Very Noisy and Hermite transformations, as techniques to map our global information theoretic problems in local ones. Through this localization, our global divergence expressions reduce in the limit to expressions defined in an inner product space. This provides us with a valuable geometric insight to the global problems, as well as a strong tool to find counter-examples. Finally, in certain cases, we have been able to "lift" results proven locally to results proven globally.(cont.) Therefore, we develop the Very Noisy and Hermite transformations, as techniques to map our global information theoretic problems in local ones. Through this localization, our global divergence expressions reduce in the limit to expressions defined in an inner product space. This provides us with a valuable geometric insight to the global problems, as well as a strong tool to find counter-examples. Finally, in certain cases, we have been able to "lift" results proven locally to results proven globally. We consider the following three problems. First, we address the problem of finding good linear decoders (maximizing additive metrics) for compound discrete memoryless channels. Known universal decoders are not linear and most of them heavily depend on the finite alphabet assumption. We show that by using a finite number of additive metrics, we can construct decoders that are universal (capacity achieving) on most compound sets. We then consider additive Gaussian noise channels. For a given perturbation of a Gaussian input distribution, we define an operator that measures how much variation is induced in the output entropy. We found that the singular functions of this operator are the Hermite polynomials, and the singular values are the powers of a signal to noise ratio. We show, in particular, how to use this structure on a Gaussian interference channel to characterize a regime where interference should not be treated as noise. Finally, we consider multi-input multi-output channels and discuss the properties of the optimal input distributions, for various random fading matrix ensembles. In particular, we prove Telatar's conjecture on the covariance structure minimizing the outage probability for output dimension one and input dimensions less than one hundred.by Emmanuel Auguste Abbe.Ph.D