Movable Antenna Assisted Dual-Polarized Multi-Cell Cooperative AirComp: An Alternating Optimization Approach

Abstract: Over-the-air computation (AirComp) is a key enabler for distributed optimization, since it leverages analog waveform superposition to perform aggregation and thereby mitigates the communication bottleneck caused by iterative information exchange. However, AirComp is sensitive to wireless environment and conventional systems with fixed single-polarized base-station arrays cannot fully exploit spatial degrees of freedom while also suffering from polarization mismatch. To overcome these limitations, this paper proposes a multi-cell cooperative air-computation framework assisted by dual-polarized movable antennas (D-PMA), and formulates a mean squared error (MSE) minimization problem by jointly optimizing the combining matrix, polarization vectors, antenna positions, and user transmit coefficients. The resulting problem is highly nonconvex, so an alternating algorithm is developed in which closed-form updates are obtained for the combining matrix and transmit coefficients. Then a method based on successive convex approximation (SCA) and semidefinite relaxation (SDR) is proposed to refine polarization vectors, and the antenna positions are updated using a gradient-based method. In addition, we develop a statistical-channel-based scheme for optimizing the antenna locations, and we further present the corresponding algorithm to efficiently obtain the solution. Numerical results show that the proposed movable dual-polarized scheme consistently outperforms movable single-polarized and fixed-antenna baselines under both instantaneous and statistical channels.