Achievable Sum Rate of Linear MIMO Receivers with Multiple Rayleigh Scattering

We study the performance of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) or zero-forcing (ZF) processing at the receiver. In particular, we focus on a source-destination pair communicating through a multiple scattering channel affected by Rayleigh fading. This is an especially relevant case, as it can well represent the communication between a pico-base station and a user in 5G cellular networks. In this scenario, we investigate the system performance in terms of achievable sum rate. In the case of MMSE receiver, we provide a closed-form expression, exploiting the relationship derived by McKay et al. [1] between the achievable sum rate and the ergodic mutual information corresponding to optimal nonlinear receivers. For ZF receivers, instead, we leverage the result derived by Matthaiou et al. [2], and derive compact upper and lower bounds to the sum rate. We validate the obtained expression through numerical results.