Flexible WMMSE Beamforming for MU-MIMO Movable Antenna Communications

Movable antennas offer new potential for wireless communication by introducing degrees of freedom in antenna positioning, which has recently been explored for improving sum rates. In this paper, we aim to fully leverage the capabilities of movable antennas (MAs) by assuming that both the transmitter and receiver can optimize their antenna positions in multi-user multiple-input multiple-output (MU-MIMO) communications. Recognizing that WMMSE beamforming is a highly effective method for maximizing the MU-MIMO sum rate, we modify it to integrate antenna position optimization for MA systems, which we refer to as flexible WMMSE (F-WMMSE) beamforming. Importantly, we reformulate the subproblems within WMMSE to develop regularized sparse optimization frameworks to achieve joint beamforming (antenna coefficient optimization) and element movement (antenna position optimization). We then propose a regularized least squares-based simultaneous orthogonal matching pursuit (RLS-SOMP) algorithm to address the resulting sparse optimization problem. To enhance practical applications, the low-complexity implementation of the proposed framework is developed based on the pre-calculations and matrix inverse lemma. The overall F-WMMSE algorithm converges similarly to WMMSE, and our findings indicate that F-WMMSE achieves a significant sum rate improvement compared to traditional WMMSE, exceeding 20% under appropriate simulation conditions