A Matrix-Inverse-Free WMMSE Algorithm to MISO Beamforming Based on Quasi-Newton

This letter propose a quasi-Newton based weighted minimum mean square error (WMMSE) algorithm without matrix inverse to solve the weighted sum rate (WSR) maximization problem in multi-user multi-input single-output (MU-MISO) beamforming. On one hand, the quasi-Newton method can replace the first-order optimal condition to solve the extremum problem of the convex quadratic function, without involving matrix inverse. One the other hand, compared to projected gradient descent (PGD) approach, it can achieve a faster convergence under the guidance of approximate Hessian matrix and avoid performance loss under the condition of high transmit power. Furthermore, a learning strategy is adopted to replace the linear searching process to obtain the optimal step size that satisfies the Wolfe condition. Simulation results validate that the proposed algorithm can achieve the same performance as WMMSE, but with a reduced computation complexity.