A Single-Loop Algorithm for Weighted Sum Rate Maximization in Multiuser MIMO Systems With Per-Antenna Power Constraints

This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.