  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 such as 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,
these precoders are designed so that the power of each precoded symbol entry is
restricted, and the PAPR at each antenna is tunable. 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-noise and distortion ratio (SINAD), and bit error
probability. We show that for this class of precoders, there is an optimal
transmit per-antenna power that maximizes the system performance in terms of
SINAD and bit error probability.
