Diversity of MMSE MIMO receivers

This work settles a long-standing open problem by providing a complete characterization of the diversity of the MMSE MIMO receiver for all fixed rates (spectral efficiencies). The MMSE MIMO receivers exhibit a complicated behavior in the fixed-rate regime that cannot be obtained via DMT analysis. Specifically, we show that in a system with M transmit antennas, N receive antennas, and rate R, the diversity is given by d = ⌈M2^-R/M⌉² + (N - M)⌈M2^-R/M⌉. This verifies and refines earlier results that were obtained only for two extremal operating points: diversity MN at very low rates and diversity N - M + 1 at very high rates.