Asymptotic Performance Analysis of the Regularized Least Squares Precoding with Restricted Transmit Power in Multi-User Massive MIMO

This paper characterizes the regularized least squares (RLS) precoding scheme in multi-user massive multiple-input multiple-output (MU-mMIMO) communication systems. To allow for the use of cheap power amplifiers (PAs) with very limited dynamic ranges, the studied precoder is formulated as a non-closed form solution of a convex problem in which the power at each antenna is constrained below a predefined maximum power. By leveraging the convex Gaussian min-max theorem (CGMT), we characterize the statistics of the precoded symbols and the distortion error at each user under the assumption of Gaussian channels. Based on this, the bit error rate (BER) and a tight lower bound of the signal-to-noise and distortion ratio (SINADlb) are asymptotically approximated. As a major outcome of our analysis, we establish that there is an average transmit power that asymptotically optimizes the SINADlb and the BER performance. Such a value can be achieved by properly tuning the power control parameter. Numerical simulations are provided to support the accuracy of our theoretical predictions.