Bi-Level Optimization for Movable Antenna Enabled UAV MU-MIMO Communications: Joint Positioning and Beamforming

Abstract

With the rapid development of the low-altitude economy, unmanned aerial vehicle (UAV) has become a key platform for diverse aerial services due to its high mobility, flexible deployment, and line-of-sight communication links. However, UAV trajectory optimization has significant issues of energy consumption and latency. By contrast, movable antenna (MA) technology adaptively adjusts antenna positions to achieve flexible beamforming, thereby improving communication performance, with ultra-low energy cost and millisecond-level response. This paper investigates the MA enabled UAV multi-user multiple-input multiple-output (MU-MIMO) communication scenario, in which a UAV acts as an aerial base station serving multiple mobile users. The objective is to maximize the average sum rate by jointly optimizing the MA positions and the transmit-receive beamforming, which is challenging due to its non-convex nature and coupled optimization variables. To address this challenge, a bi-level improved CMAES–WMMSE algorithm is developed: on the upper level, the improved covariance matrix adaptation evolution strategy (CMA-ES) incorporating cross-slot warm starting and displacement-aware step-size adaptation conducts an evolutionary search over the MA positions; on the lower level, the weighted minimum mean-squared error (WMMSE) framework efficiently solves the beamforming subproblem via alternating optimization. Simulation results demonstrate that the proposed algorithm achieves substantial gains over benchmark schemes under various system configurations, confirming the effectiveness of the algorithm and validating the promising application potential of MA technology in UAV MU-MIMO communications.