Nonsmooth optimization for joint multicast beamforming and user scheduling in massive MIMO systems

Abstract

Wireless multicast is a key enabling technology for efficient distribution of high-rate multimedia services in future wireless communication systems. When there are a massive number of users in the system, it is impractical or inefficient to serve all users with a single multicast beamformer and within a single channel. We therefore study the joint multicast beamforming and user scheduling problem, with the objective of minimizing the total transmitting power across multiple channels by jointly assigning each user to appropriate channel and designing multicast beamformer for each channel. The problem of interest is first formulated as a mixed binary quadratically constrained quadratic program, and then reformulated as a highly structured nonsmooth optimization problem. We propose a sequential approximation scheme for the nonsmooth formulation to yield a series of parallel smooth convex subproblems, and devise a dual fast gradient projection method for the subproblem. The overall algorithm is an efficient matrix-free algorithm, which is based solely on matrix-vector multiplications and comparison operations and costs O(MK) arithmetic operations per iteration with M being the number of antennas and K being the number of users, and therefore is well suited for massive MIMO systems with a large number of users. The proposed algorithm is guaranteed to converge to a critical point to the nonsmooth formulation problem. Finally, simulation results demonstrate the advantage of the proposed co-design scheme over conventional fixed scheduling and random scheduling.