Robust Movable Antenna Position Optimization Under Imperfect Channel Path Parameters

Abstract: Movable antenna (MA) systems can reshape the wireless channel by repositioning antenna elements in a confined region, but most existing MA optimization methods depend on perfect channel state information (CSI). This paper studies robust joint transmit beamforming and antenna-position optimization for a downlink multiple-input single-output (MISO) MA system with imperfect CSI. Instead of treating CSI errors as unstructured channel perturbations, we introduce bounded uncertainties directly into physical multipath parameters, including path- gain amplitudes and angular parameters. The resulting worst-case signal-to-noise ratio (SNR) design is approximated through discrete sam⁃ pling and a harmonic-mean surrogate that penalizes weak channel realizations. An alternating optimization algorithm is then developed, where transmit beamforming is updated on the complex sphere manifold, and antenna positions are optimized via a sequential grid search. Simulation results show that the proposed robust design yields higher SNR performance than non-robust designs and the fixed-position antenna (FPA) baseline.

Keywords: alternating optimization; harmonic mean; imperfect channel state information; movable antenna; robust optimization