Asymptotic Analysis of RZF over Double Scattering Channels with MMSE Estimation

Abstract : This paper studies the ergodic sum rate performance of regularized zero-forcing (RZF) precoding in the downlink (DL) of a multiuser multiple-input single-output (MISO) system, where the channel between the base station (BS) and each user is modeled by the double scattering model. This non-Gaussian channel model is a function of both the antenna correlation and the structure of scattering in the propagation environment. This paper first makes the preliminary contribution of deriving the minimum-mean-square-error (MMSE) channel estimate for this model. The system model accounts for channel estimation errors and per-group channel correlation matrices for the users. The analysis assumes that the number of BS antennas, the number of single-antenna users and the number of scatterers in each group grow large while their ratio remains bounded. Under this setting, this paper derives deterministic equivalents of the signal-to-interference plus noise ratio (SINR) and the sum rate which are almost surely tight in the large system limit. The derived approximations are expressed in a closed-form for the special case of multi-keyhole channel. We show that the performance of a massive MIMO system does not scale linearly with the number of antennas under uncorrelated channel conditions and is actually limited by the number of scatterers in the propagation environment. Simulation results confirm the close match provided by the asymptotic analysis for moderate system dimensions.