Enhancing the Efficiency of WMMSE and FP for Beamforming by Minorization-Maximization

Weighted minimum mean squared error (WMMSE) and fractional programming (FP) constitute two common approaches to the weighted sum-rate maximization in communication system design. One subtle issue with WMMSE and FP lies in the tuning of a Lagrange multiplier for the power constraint when it comes to the multi-antenna transmission. To obtain the optimal Lagrange multiplier, we must repeatedly inverse an $M\times M$ matrix, where $M$ is the number of transmit antennas, which incurs considerable complexity. To address the above issue, this work explores the connection of WMMSE and FP to minorization-maximization (MM), thereby modifying the two methods to get rid of the Lagrange multiplier. The proposed algorithm enables a parameter-free iterative optimization of the beamforming vectors with the power constraint enforced automatically. Numerical results demonstrate the faster convergence of the proposed beamforming method as compared to the conventional WMMSE and FP methods.