Sharp Analysis of RLS-based Digital Precoder with Limited PAPR in Massive MIMO

This paper focuses on the performance analysis of a class of limited peak-to-average power ratio (PAPR) precoders for downlink multi-user massive multiple-input multiple-output (MIMO) systems. Contrary to conventional precoding approaches based on simple linear precoders maximum ratio transmission (MRT) and regularized zero forcing (RZF), the precoders in this paper are obtained by solving a convex optimization problem. To be specific, for the precoders we analyze in this paper, the power of each precoded symbol entry is restricted, which allows them to present a reduced PAPR at each antenna. By using the Convex Gaussian Min-max Theorem (CGMT), we analytically characterize the empirical distribution of the precoded vector and the joint empirical distribution between the distortion and the intended symbol vector. This allows us to study the performance of these precoders in terms of per-antenna power, per-user distortion power, signal to interference and noise ratio, and bit error probability. We show that for this class of precoders, there is an optimal transmit power that maximizes the system performance.