Eigenvalue Distributions of Wishart-Type Random Matrices with Application to the Performance Analysis of MIMO MRC Systems

Abstract

In this paper, we characterize the eigenvalue distribution of Hermitian matrices generated from a set of independent zero-mean proper complex Gaussian random (PCGR) vectors with an arbitrary common covariance matrix. Such random matrices follow the so-called Wishart-type distribution, a generic designation for both Wishart and pseudo-Wishart distributions. More specifically, we propose new simple expressions for the probability density function (PDF) and derive the cumulative distribution function (CDF) of any subset of unordered eigenvalues of Wishart-type random matrices with arbitrary finite dimensions. Many interesting results can be deduced from the foregoing distributions. In particular, one can straightforwardly deduce the statistics of the largest eigenvalue of Wishart-type random matrices, thereby paving the way for the second contribution of this paper, namely, analyzing the average error probability of dual multiple-input multiple-output (MIMO) systems using maximum-ratio transmission (MRT), subject to frequency-nonselective semicorrelated Rayleigh fading. Furthermore, Monte Carlo simulations are carried out and shown to be in perfect match with the corresponding analytical results, thereby illustrating their validity.