Nonlinear Precoders for Massive MIMO Systems with General Constraints

Abstract

We introduce a class of nonlinear least square error precoders with a general penalty function for multiuser massive MIMO systems. The generality of the penalty function allows us to consider several hardware limitations including transmitters with a predefined constellation and restricted number of active antennas. The large-system performance is then investigated via the replica method under the assumption of replica symmetry. It is shown that the least square precoders exhibit the ``marginal decoupling property'' meaning that the marginal distributions of all precoded symbols converge to a deterministic distribution. As a result, the asymptotic performance of the precoders is described by an equivalent single-user system. To address some applications of the results, we further study the asymptotic performance of the precoders when both the peak-to-average power~ratio~and number of active transmit antennas are constrained. Our~numerical~investigations show that for a desired distortion at the receiver side, proposed forms of the least square precoders need to employ around $35\%$ fewer number of active antennas compared to cases with random transmit antenna selection.