Codebook based Precoding for Multiuser MIMO Broadcast Systems: An MM Approach

The goal of this paper is to propose a novel, principled approach to solve non-convex optimization problems that arise in multiuser (MU) multiple input multiple output (MIMO) cellular wireless communication systems. We explore a minorization-maximization (MM) optimization approach, which is guaranteed to converge to a stationary point starting from any initialization. One of the important problems in wireless communications is sum rate maximization in MU MIMO broadcast systems, in which multiple data streams are simultaneously transmitted to all users. In this paper, we adopt a codebook based precoding method, where each data stream is beamformed using a vector selected from a predetermined codebook. Our objective is to determine the selection of beamforming vectors and power allocation to each beam to maximize the achievable sum rate. We reformulate the problem to facilitate the application of MM procedure in a nested fashion. The outcome is a novel, iterative, and computationally efficient solution, which we call the inverse-MM (IMM) algorithm. We illustrate the superior performance of our algorithm compared to existing approaches through Monte Carlo simulations. The advantages of computational efficiency, simple implementation, and structured approach makes the MM framework a good candidate for solving non convex optimization problems in wireless communications.