Asymptotic Performance of Linear Receivers in MIMO Fading Channels

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

On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.Comment: accepted by IEEE Trans. on Comm., 201

Performance Analysis of Project-and-Forward Relaying in Mixed MIMO-Pinhole and Rayleigh Dual-Hop Channel

In this letter, we present an end-to-end performance analysis of dual-hop project-and-forward relaying in a realistic scenario, where the source-relay and the relay-destination links are experiencing MIMO-pinhole and Rayleigh channel conditions, respectively. We derive the probability density function of both the relay post-processing and the end-to-end signal-to-noise ratios, and the obtained expressions are used to derive the outage probability of the analyzed system as well as its end-to-end ergodic capacity in terms of generalized functions. Applying then the residue theory to Mellin-Barnes integrals, we infer the system asymptotic behavior for different channel parameters. As the bivariate Meijer-G function is involved in the analysis, we propose a new and fast MATLAB implementation enabling an automated definition of the complex integration contour. Extensive Monte-Carlo simulations are invoked to corroborate the analytical results.Comment: 4 pages, IEEE Communications Letters, 201

Performance Analysis of Optimal Single Stream Beamforming in MIMO Dual-Hop AF Systems

This paper investigates the performance of optimal single stream beamforming schemes in multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) systems. Assuming channel state information is not available at the source and relay, the optimal transmit and receive beamforming vectors are computed at the destination, and the transmit beamforming vector is sent to the transmitter via a dedicated feedback link. Then, a set of new closed-form expressions for the statistical properties of the maximum eigenvalue of the resultant channel is derived, i.e., the cumulative density function (cdf), probability density function (pdf) and general moments, as well as the first order asymptotic expansion and asymptotic large dimension approximations. These analytical expressions are then applied to study three important performance metrics of the system, i.e., outage probability, average symbol error rate and ergodic capacity. In addition, more detailed treatments are provided for some important special cases, e.g., when the number of antennas at one of the nodes is one or large, simple and insightful expressions for the key parameters such as diversity order and array gain of the system are derived. With the analytical results, the joint impact of source, relay and destination antenna numbers on the system performance is addressed, and the performance of optimal beamforming schemes and orthogonal space-time block-coding (OSTBC) schemes are compared. Results reveal that the number of antennas at the relay has a great impact on how the numbers of antennas at the source and destination contribute to the system performance, and optimal beamforming not only achieves the same maximum diversity order as OSTBC, but also provides significant power gains over OSTBC.Comment: to appear in IEEE Journal on Selected Areas in Communications special issue on Theories and Methods for Advanced Wireless Relay

Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its mean (thus obtaining an asymptotically Gaussian distribution), we calculate the full distribution, including its tails which strongly deviate from the Gaussian behavior near the mean. The resulting distribution interpolates seamlessly between the Gaussian approximation for rates $R$ close to the ergodic value of the mutual information and the approach of Zheng and Tse for large signal to noise ratios $\rho$. This calculation provides us with a tool to obtain outage probabilities analytically at any point in the $(R, \rho, N)$ parameter space, as long as the number of antennas $N$ is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities, and it depends on the values of $R$ and $\rho$.Comment: Accepted for publication, IEEE Transactions on Information Theory (2010). Part of this work appears in the Proc. IEEE Information Theory Workshop, June 2009, Volos, Greec