Closed-formed distribution for the SINR of MMSE-detected MIMO systems and performance analysis

In this paper, we investigate the error performance of multiple-input multiple-output (MIMO) wireless communications systems using minimum mean-square error (MMSE) detection. Particularly, a new closed-form statistical distribution for the output signal-to-interference-plus-noise ratio (SINR) of MMSE receiver is derived, for independent Rayleigh fading channels. The expression for the distribution of SINR is shown to be a linear combination of gamma distributions and polynomial of 11+x, where x is the SINR. Base on the derived distribution for the SINR, closed-form and approximated expressions for the symbol error probability (SEP) of quadrature amplitude modulation (QAM) and phase shift keying (PSK) signaling are obtained, respectively. The derived SINR density and SEP are valid for arbitrary number of transmit and receive antennas. Furthermore, a reduced complexity approximation is introduced to obtain the SINR distribution and SEP performance of MMSE-Detected MIMO Systems with a large number of antennas. The provided simulation results confirm the validity of our theoretical analysis for both the SINR and SEP.