  This paper is devoted to the study of the performance of the Linear Minimum
Mean-Square Error receiver for (receive) correlated Multiple-Input
Multiple-Output systems. By the random matrix theory, it is well-known that the
Signal-to-Noise Ratio (SNR) at the output of this receiver behaves
asymptotically like a Gaussian random variable as the number of receive and
transmit antennas converge to +$\infty$ at the same rate. However, this
approximation being inaccurate for the estimation of some performance metrics
such as the Bit Error Rate and the outage probability, especially for small
system dimensions, Li et al. proposed convincingly to assume that the SNR
follows a generalized Gamma distribution which parameters are tuned by
computing the first three asymptotic moments of the SNR. In this article, this
technique is generalized to (receive) correlated channels, and closed-form
expressions for the first three asymptotic moments of the SNR are provided. To
obtain these results, a random matrix theory technique adapted to matrices with
Gaussian elements is used. This technique is believed to be simple, efficient,
and of broad interest in wireless communications. Simulations are provided, and
show that the proposed technique yields in general a good accuracy, even for
small system dimensions.
