Fast Algorithm Design for the Constant-Envelope Precoding in Massive Mimo Communications with Interference Exploitation

We study the problem of constant-envelope precoding in massive MIMO communications with interference exploitation, whose main challenge lies in the non-convexity introduced by its constant-modulus constraints. Different from conventional approaches that typically involve constant-modulus approximations, we devise a new method with direct phase manipulations for precoding. To this end, we first formulate the precoding design into an unconstrained phase optimization with a "min-max" scheme, based on which we then apply the majorization-minimization (MM) technique to transform it into a convex minimization problem. For the sake of efficient solutions to this convex optimization, we focus on dealing with its dual problem, whose objective is further transformed into a simple quadratic form by means of elaborating the surrogate for MM. Finally, we arrive to a fast gradient-based solution for iteration. Simulation results show the superiority of our proposed algorithm over the existing methods in terms of different aspects, especially in the context of large-scale optimization.