Exact and Closed-Form Error Performance Analysis for Hard MMSE Detection in MIMO Systems

Abstract-We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection in multipleinput multiple-output (MIMO) systems. To facilitate the analysis, we first conduct error analysis for a general system with decision statistic, z = ax + u, where a >; 0, x is the transmitted signal, and u is the arbitrarily distributed noise component which is independent of x. For this general system, we derive the exact and closed-form bit-error rate (BER) expressions for M-ary pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) signalings, which include the well-known BER result in [12] as a special case. For the first time in the literature (to the best of our knowledge), we then derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for hard MMSE detection. Finally, the validity of the derived error probability expressions is verified through our own Monte Carlo simulations and the simulation results reported in the literature.