SINR Distribution of MIMO MMSE Receiver

Linear MMSE reception offers a low complexity option for multi-antenna communication systems. Understanding the outage behavior of the corresponding signal-to-interference-and-noise ratio (SINR) and per-antenna throughput r is important in a quasistatic mobile environment. In this paper we introduce a large deviations method, valid nominally for large antenna numbers N, which calculates the probability density of the SINR and r of Gaussian channel MIMO MMSE receivers, with arbitrary transmission power profiles and in the presence of transmitter antenna correlations. This approach extends the Gaussian approximation of the SINR, valid only very close to the center of the distribution, demonstrating the non-Gaussian tails of the distribution. Our methodology allows us to calculate the correct leading order (O(N)) of the SINR distribution and showcase the deviations from approximations that have appeared in the literature (e. g. the Gaussian or the generalized Gamma distribution). We are also able to calculate next-to-leading order corrections to the distribution, thereby making the approximation quite accurate even for the smallest antenna arrays (2 x 2).