Baseband-Efficient WMMSE Precoding: From a Signal Weighting Cost Perspective

Abstract

For downlink transmission in massive multi-user multiple-input multiple-output (MU-MIMO) systems, conventional precoding research heavily focuses on reducing the computational complexity of precoding matrix design, while largely overlooking another critical bottleneck: the substantial signal weighting cost incurred by repeatedly applying the precoder to high-speed data streams. To address both challenges simultaneously, this paper proposes a novel sparse precoding framework tailored for fully-digital architectures. Within this framework, from the sum-rate maximization perspective, we design two sparse precoding architectures: a common-support row-sparse architecture and a user-specific row-sparse architecture, so as to reduce the number of multiplication operations required in baseband signal weighting while largely preserving the achievable sum-rate. For the formulated mixed-integer non-linear programming (MINLP) problem, we rigorously prove that the optimal precoder under both sparse architectures strictly resides in a specific low-dimensional subspace determined by the channel matrices, thereby reducing the dimensionality of the optimization variables. Based on this insight, an alternating optimization algorithm is developed within the weighted minimum mean square error (WMMSE) framework to jointly optimize sparse beam selection and low-dimensional precoding coefficients. The combinatorial beam selection problem is handled using an efficient penalty-based majorize-minimization (MM) method, yielding a low-complexity closed-form solution. Simulation results demonstrate that the proposed schemes achieve sum-rate performance close to that of full-dimensional WMMSE precoding without sparsity constraints, while substantially reducing the overall signal-weighting cost.