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 picobase 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. between the achievable sum rate and the ergodic mutual information corresponding to optimal nonlinear receivers. For ZF receivers, instead, we leverage the results derived by Matthaiou et al. and Jiang et al., and derive compact upper and lower bounds to the sum rate. We validate the obtained expressions through numerical results.