Movable Antenna-Enabled Phase Shifting: Performance Analysis and Position Optimization

Abstract

High-gain analog beamforming in wireless systems conventionally employs analog phase shifters to coherently combine signals. However, this reliance on active hardware components introduces substantial costs, power consumption, and signal insertion losses, all of which increase with the size of the antenna array. This paper presents a novel framework that replaces phase adjustments with the positional optimization of Movable Antennas (MAs). The core idea is to emulate the function of phase shifters by leveraging the fact that the movement of antennas inherently alter the phase of the wireless channel. To realize this framework, we develop a computationally efficient method, named Derivative Matching Optimization (DMO). Unlike conventional iterative algorithms, DMO is a non-iterative approach that directly determines the optimal MA positions by leveraging a novel geometric detection strategy that decouples the optimization problem. In theoretical analysis, we prove the global optimality of the DMO method under practical MA placement constraints and derive a closed-form expression for the Normalized Mean Square Error (NMSE) to characterize its asymptotic convergence behavior. Simulation results indicate that our DMO-based system substantially outperforms both conventional Fixed-Position Antenna (FPA) arrays and the MA systems that rely on phase shifters, validating its superiority in performance, energy efficiency, and cost-effectiveness.