Eigenvalue Distributions of Wishart-Type Random Matrices and Error Probability Analysis of Dual Maximum-Ratio Transmission in Semicorrelated Rayleigh Fading

In this paper, we characterize the eigenvalue distribution of Hermitian matrices generated from a set of independent zero-mean proper complex Gaussian random 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 joint probability density function and cumulative distribution function of any subset of unordered eigenvalues of Wishart-type random matrices with arbitrary finite dimensions. We further show how one can extract many interesting results from the foregoing distributions such as the statistics of the extreme eigenvalues. In particular, we focus on 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 bit/symbol error probability of dual multiple-input multiple-output systems employing maximum-ratio transmission, subject to frequency-nonselective semicorrelated Rayleigh fading.