Relay Hybrid Precoding Design in Millimeter-Wave Massive MIMO Systems

This paper investigates the relay hybrid precoding design in millimeter-wave massive multiple-input multiple-output systems. The optimal design of the relay hybrid precoding is highly nonconvex, due to the six-order polynomial objective function, six-order polynomial constraint, and constant-modulus constraints. To efficiently solve this challenging nonconvex problem, we first reformulate it into three quadratic subproblems, where one of the subproblems is convex and the other two are nonconvex. Then, we propose an iterative successive approximation (ISA) algorithm to attain the high-approximate optimal solution to the original problem. Specifically, in the proposed ISA algorithm, we first convert the two nonconvex subproblems to convex ones by the relaxation of the constant-modulus constraints, and then we solve the three corresponding convex subproblems iteratively. We theoretically prove that the ISA algorithm converges to a Karush-Kuhn-Tucker point of the original problem. Simulation results demonstrate that the proposed ISA algorithm achieves good performance in terms of achievable rate in both full-connected and subconnected relay hybrid precoding systems.