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This paper is devoted to the study of the performance of the Linear MinimumMean-Square Error receiver for (receive) correlated Multiple-InputMultiple-Output systems. By the random matrix theory, it is well-known that theSignal-to-Noise Ratio (SNR) at the output of this receiver behavesasymptotically like a Gaussian random variable as the number of receive andtransmit antennas converge to +$\infty$ at the same rate. However, thisapproximation being inaccurate for the estimation of some performance metricssuch as the Bit Error Rate and the outage probability, especially for smallsystem dimensions, Li et al. proposed convincingly to assume that the SNRfollows a generalized Gamma distribution which parameters are tuned bycomputing the first three asymptotic moments of the SNR. In this article, thistechnique is generalized to (receive) correlated channels, and closed-formexpressions for the first three asymptotic moments of the SNR are provided. Toobtain these results, a random matrix theory technique adapted to matrices withGaussian elements is used. This technique is believed to be simple, efficient,and of broad interest in wireless communications. Simulations are provided, andshow that the proposed technique yields in general a good accuracy, even forsmall system dimensions.

BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels