Compressed Sensing-Based Channel Estimation and Position Optimization for Movable Antenna Systems

Movable Antenna (MA) systems enhance channel capacity by leveraging antenna mobility within a continuous spatial region. However, practical performance depends on accurate Channel State Information (CSI) and effective position optimization. This paper proposes a two-stage framework to optimize MA systems under imperfect CSI. First, we design a pilot position optimization method to improve channel estimation accuracy using Compressed Sensing (CS). The estimated channel then provides the necessary CSI for a joint antenna position and precoding optimization scheme. By employing an analytic gradient-based Coordinate Descent approach with binary-search-driven distance constraint handling, we optimize all antenna positions simultaneously to avoid local optima. Furthermore, the Weighted Minimum Mean Square Error (WMMSE) algorithm is integrated to refine the precoders. Simulation results demonstrate that the proposed scheme achieves an approximate 15% performance gain over baseline methods in low-overhead regimes.