Design of Per-Antenna Constant-Envelope Precoding for Massive MIMO Communications With Beyond Diagonal Reconfigurable Intelligent Surface

This paper addresses the design of per-antenna constant-envelope precoding for massive MIMO communications, where a beyond diagonal reconfigurable intelligent surface (BD-RIS) is considered to be involved. The primary goal of the design is to mitigate the multi-user interference for communications, and the reflection-coefficient matrix of the BD-RIS is required to be both unitary and symmetric. Meanwhile, we also impose constant-modulus constraints for the precoding at each antenna. These considerations culminate in a non-convex optimization problem characterized by a min-max type objective and multiple intricate constraints. To solve the design problem, we propose a cyclic alternating framework for finding solutions. For each subproblem arising from the alternating optimization framework, we reformulate the min-max problem into a tractable form, and subsequently devise a fixed-point iteration scheme via proximal splitting. These enable us to obtain a closed-form solution at each iteration. Furthermore, we provide a theoretical analysis that demonstrates convergence to stable points for the developed update procedures. Simulation results confirm that the proposed approach outperforms existing methods across various aspects.