  Linear receivers offer a low complexity option for multi-antenna
communication systems. Therefore, understanding the outage behavior of the
corresponding SINR is important in a fading mobile environment. In this paper
we introduce a large deviations method, valid nominally for a large number M of
antennas, which provides the probability density of the SINR of Gaussian
channel MIMO Minimum Mean Square Error (MMSE) and zero-forcing (ZF) receivers,
with arbitrary transmission power profiles and in the presence of receiver
antenna correlations. This approach extends the Gaussian approximation of the
SINR, valid for large M asymptotically close to the center of the distribution,
obtaining the non-Gaussian tails of the distribution. Our methodology allows us
to calculate the SINR distribution to next-to-leading order (O(1/M)) and
showcase the deviations from approximations that have appeared in the
literature (e.g. the Gaussian or the generalized Gamma distribution). We also
analytically evaluate the outage probability, as well as the uncoded
bit-error-rate. We find that our approximation is quite accurate even for the
smallest antenna arrays (2x2).
