SINR Distribution for MIMO MMSE Receivers in Transmit-Correlated Rayleigh Channels: SER Performance and High-SNR Power Allocation

In this paper, a multiple-input-multiple-output (MIMO) system with a precoder is considered in transmit-correlated Rayleigh channels. We specifically target the MIMO system employing minimum-mean-square-error (MMSE) receivers. Based on the random matrix theory, we first present a direct and generalized formulation for deriving a probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR). Then, we derive accurate closed-form SINR pdfs for a small number of transmit and receive antennas. Based on the SINR pdfs, tight closed-form approximations of the symbol error rate (SER) are derived. In the high-signal-to-noise-ratio (SNR) regime, we also propose high-SNR power allocation (HPA) by minimizing the modified global SER approximation. At high SNRs, the computationally efficient HPA performing similar to optimal power allocation (PA) shows noticeable performance gain over the equal PA, particularly at the high transmit correlation. Moreover, the performance gain of the proposed HPA increases with the diversity order.