The use of multiple-antenna arrays in both transmission and reception promises huge increases in the throughput of wireless communication systems. It is therefore important to analyze the capacities of such systems in realistic situations, which may include spatially correlated channels and correlated noise, as well as correlated interferers with known channel at the receiver. Here, we present an approach that provides analytic expressions for the statistics, i.e., the moments of the distribution, of the mutual information of multiple-antenna systems with arbitrary correlations, interferers, and noise. We assume that the channels of the signal and the interference are Gaussian with arbitrary covariance. Although this method is valid formally for large antenna numbers, it produces extremely accurate results even for arrays with as few as two or three antennas. We also develop a method to analytically optimize over the input signal covariance, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel (i.e., the channel covariance). In many cases of interest, this capacity is very close to the full closed-loop capacity, in which the transmitter has instantaneous channel knowledge. We apply this analytic approach to a number of examples and we compare our results with simulations to establish the validity of this approach. This method provides a simple tool to analyze the statistics of throughput for arrays of any size. The emphasis of this paper is on elucidating the novel mathematical methods used.

Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of a MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear receiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.Comment: 48 pages, Submitted to IEEE Transactions on Information Theor

4G systems are expected to support data rates of the order of 100 Mbps in the outdoor environment and 1 Gbps in the indoor/stationary environment. In order to support such large payloads, the radio physical layer must employ receiver algorithms that provide a significant increase in spectrum efficiency (and hence capacity) over current wireless systems. Recently an explosion of MIMO studies have appeared with many journals presenting special issues on this subject. This has occured dur to the potential of MIMO to provide a linear increase in capacity with antenna numbers. Environmental conciderations and tower loads will often restrict the placing of large antenna spans on base stations. Similarly, customer device form factors also place a limit on the antenna numbers that can be placed with a mutual spacing of 0.5 wavelength. The use of cross-polarized antennas is widely used in modern cellular installtions as it reduces spacing needs and tower loads on base stations. Hence, this approach is also receiving considerable attention in MIMO systems. In order to study and compare various receiver architectures that are based on MIMO techniques, one needs to have an accurate knowledge of the MIMO channel. However, very few studies have appeared that characterize the cross-polarized MIMO channel. Recently, the third generation partnership standards bodies (3GPP/3GPP2) have defined a cross-polarized channel model for MIMO systems but this model neglects the elevation spectrum. In this paper we provide a deeper understanding of the channel model for cross-polarized systems for different environments and propose a composite channel impulse model for the cross-polarized channel that takes into account both azimuth and elevation spectrum. We use the resulting channel impulse response to derive closed form expressions for the spatial correlation. We also present models to describe the dependence of cross-polarization discrimination (XPD) on distance, azimuth and elevation and delay spread. In addition, we study the impact of array width, SNR and antenna slant angle on the mutual information (MI) of the system. In particular we present an analytical model for large system mean mutual information values and consider the impact of elevation spectrum on MI. Finally, the impace of multipath delays on XPD and MI is also explored. IEEE Journal on Selected Areas in CommunicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, ...

Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.The ongoing communications revolution has motivated researchers to look for novel ways to transmit information (1, 2). One recent development (3, 4) is the suggestion that, contrary to long-held beliefs, random scattering of microwave or radio signals may enhance the amount of information that can be transmitted on a particular channel. Prompted by this suggestion, we introduce a realistic physical model for a scattering environment and analytically evaluate the amount of information that can be transmitted between two antenna arrays for a number of example cases. On the one hand, this lays a new foundation for complex microwave signal modeling, an important task in a world with ever-increasing demand for wireless communication, and, on the other, introduces a new arena for physicists to test ideas concerning disordered media.From information theory (5), the capacity of a channel between a transmitter and a receiver, that is, the maximum rate of information transfer at a given frequency, can be described in terms of the average power of the signal S and the noise N at the receiver: C = log 2 (1+S/N ). More generally (2), the communication channel connecting several transmitters and receivers is described by a matrix G iα giving the amplitude of the received signal α due to transmitter i. The information carried by the channel can be characterized using several quantities, such as the capacity or mutual information, which are typically functionals of the matrix G, which must be known in order to predict these quantities. Often G cannot be predicted for actual systems, such as wireless communication networks or optical fibers, because of the complicated scattering and interference of waves that is involved. It is crucial, therefore, to develop physical models for the signal propagation, as it is only through such models that one can understand the real effects of scattering and interference on the amount of information that can be communicated.In many cases, only partial information is available for prediction; in these situations, one only has a statistical description of G. Instead of making assumptions about G directly, the usual procedure in information theory, we introduce statistical models for the physical environment from which we derive the properties of G. The adv...

The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex input alphabets, the energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of replica symmetry and a replica symmetry breaking ansatz is taken. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived for one-step replica symmetry breaking. For convex relaxations, replica symmetry is found to hold and corresponding results are obtained for comparison. Particularizing to a "zeroforcing" (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u, x, and y are the channel input, the equivalent precoder output, and the channel output, respectively. For discrete lattice-based alphabet relaxation, the impact of replica symmetry breaking is demonstrated for the energy penalty at the transmitter.An analysis of spectral efficiency is provided to compare discrete lattice-based relaxations against convex relaxations, as well as linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed compared to linear ZF precoding, for medium to high signal-to-noise ratios (SNRs). THP is shown to be outperformed as well. In addition, comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We find that vector precoding performs much better for complex than for real alphabets.As a byproduct, we find a nonlinear precoding method with polynomial complexity that outperforms NP-hard Tomlinson-Harashima precoding for binary modulation on complex channels if the number of transmit antennas is slightly larger than twice the number of receive antennas. R. Müller is with theThen, the R-transform of P(x) iswith m −1 (w) denoting the inverse of m(s) with respect to composition, i.e. m −1 (m(s)) = s.ASSUMPTION 1 (SELF-AVERAGING PROPERTY) We have

A wideband space-time channel model is defined, which captures the multiple dependencies and variability in multicell system-wide operating environments. The model provides a unified treatment of spatial and temporal parameters, giving their statistical description and dependencies across a large geographical area for three outdoor environments pertinent to third-generation cellular system simulations. Parameter values are drawn from a broad base of recently published wideband and multiple-antenna measurements. A methodology is given to generate fast-fading coefficients between a base station and a mobile user based on the summation of directional plane waves derived from the statistics of the space-time parameters. Extensions to the baseline channel model, such as polarized antennas, are given to provide a greater variety of spatial environments. Despite its comprehensive nature, the model's implementation complexity is reasonable so it can be used in simulating large-scale systems. Output statistics and capabilities are used to illustrate the main characteristics of the model. IEEE Transactions on Vehicular TechnologyThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-A wideband space-time channel model is defined, which captures the multiple dependencies and variability in multicell system-wide operating environments. The model provides a unified treatment of spatial and temporal parameters, giving their statistical description and dependencies across a large geographical area for three outdoor environments pertinent to thirdgeneration cellular system simulations. Parameter values are drawn from a broad base of recently published wideband and multiple-antenna measurements. A methodology is given to generate fast-fading coefficients between a base station and a mobile user based on the summation of directional plane waves derived from the statistics of the space-time parameters. Extensions to the baseline channel model, such as polarized antennas, are given to provide a greater variety of spatial environments. Despite its comprehensive nature, the model's implementation complexity is reasonable so it can be used in simulating large-scale systems. Output statistics and capacities are used to illustrate the main characteristics of the model.

Abstract-A large deviations approach is introduced, which calculates the probability density and outage probability of the MIMO mutual information, and is valid for large antenna numbers N . In contrast to previous asymptotic methods that only focused on the distribution close to its most probable value, this methodology obtains the full distribution, including its nonGaussian tails. The resulting distribution interpolates between the Gaussian approximation for rates R close its mean and the asymptotic distribution for large signal to noise ratios ρ [1]. For large enough N , this method provides the outage probability over the whole (R, ρ) parameter space. The presented analytic results agree very well with numerical simulations over a wide range of outage probabilities, even for small N . In addition, the outage probability thus obtained is more robust over a wide range of ρ and R than either the Gaussian or the large-ρ approximations, providing an attractive alternative in calculating the probability density of the MIMO mutual information. Interestingly, this method also yields the eigenvalue density constrained in the subset where the mutual information is fixed to R for given ρ. Quite remarkably, this eigenvalue density has the form of the Marčenko-Pastur distribution with square-root singularities.Index Terms-Diversitymultiplexing tradeoff (DMT), Gaussian approximation, information capacity, large-system limit, multiple-input multiple-output (MIMO) channels.