On the distribution of SINR for the MMSE MIMO receiver and performance analysis
IEEE Transactions on Information Theory
This paper studies the statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for the minimum mean square error (MMSE) receiver in multiple-input-multipleoutput (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flat-fading with unequal powers. The SINR can be decomposed into two independent random variables: SINR = SINR ZF + T , where SINR ZF corresponds to the SINR for a zero-forcing (ZF) receiver and has an exact Gamma
... tribution. This paper focuses on characterizing the statistical properties of T using the results from random matrix theory. First three asymptotic moments of T are derived for uncorrelated channels and channels with equicorrelations. For general correlated channels, some limiting upperbounds for the first three moments are also provided. For uncorrelated channels and correlated channels satisfying certain conditions, it is proved that T converges to a Normal random variable. A Gamma distribution and a generalized Gamma distribution are proposed as approximations to the finite sample distribution of T . Simulations suggest that these approximate distributions can be used to accurately estimate the probability of errors even for very small dimensions (e.g., 2 transmit antennas). Index Terms-Multiple-input-multiple-output system, minimum mean square error receiver, signal-to-interference-plusnoise ratio, channel correlation, random matrix, asymptotic distributions, Gamma approximation, error probability.