Performance of Rayleigh-Product MIMO Channels with Linear Receivers

This paper presents an analytical investigation on the performance of Rayleigh-product MIMO channels with linear minimum mean-square-error (MMSE) or zero-forcing (ZF) receivers. For MMSE receivers, exact closed-form expressions for the ergodic sum-rate of the system are derived. In addition, simplified expressions are obtained for the key parameters dictating the sum-rate performance of the system in the high signal-to-noise ratio (SNR) regime (i.e., high SNR slope and power offset) and low SNR regime (i.e., minimum energy per information bit required to convey any positive rate and the wideband slope). While for ZF receivers, tight closed-form upper and lower bounds for the ergodic sum-rate of the system are derived. It is analytically proven that the ZF and MMSE receivers achieve the same sum rate performance in the high SNR regime. Moreover, for both MMSE and ZF receivers, the achievable diversity-multiplexing tradeoff (DMT) of Rayleigh-product MIMO channels is characterized. The findings suggest that a larger number of scatterers will improve the the performance of Rayleigh-product MIMO channels with linear receivers, and the ZF receivers achieve the same performance as the MMSE receivers in Rayleigh-product MIMO channels in the high SNR regime. Moreover, it is demonstrated that as long as the number of the scatterers is greater than the number of receive antennas, linear receivers achieve the optimal DMT.