Weighted Sum-Rate Maximization for Beamforming Design Using Minorization-Maximization: Convergence Rate and Deep Unfolding

Weighted sum-rate (WSR) maximization is a fundamental yet generally NP-hard problem in communication system design. Existing optimization-based methods, such as weighted sum-minimum mean-square error (WMMSE), often suffer from high computational overhead in the subproblem, such as matrix inversion. Recent studies [1], [2] have reinterpreted WMMSE within the minorization-maximization (MM) framework, yielding matrix-inversion-free algorithms with improved efficiency. In this paper, we analyze the landscape of the WSR objective and show that all optimal solutions lie on the boundary of the beamforming constraint set. Moreover, we prove that the WSR function is globally L-smooth, which enables us to establish a global sublinear convergence rate for the MM-based algorithm proposed in [1], [2]. To further accelerate computation, we propose a neural network architecture inspired by the MM algorithm, termed MM-Net, which learns to predict a tighter upper-bound constant by exploiting a key matrix in the algorithm. Simulation results demonstrate that MM-Net achieves faster convergence than both WMMSE and MM, while also offering lower complexity compared to state-of-the-art deep learning-based methods.