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.

翻译：空中计算（AirComp）是分布式优化的关键赋能技术，它利用模拟波形叠加执行聚合操作，从而缓解由迭代信息交换引起的通信瓶颈。然而，AirComp对无线环境敏感，且采用固定单极化基站阵列的传统系统既无法充分利用空间自由度，又受极化失配问题困扰。为克服这些限制，本文提出一种由双极化可移动天线（D-PMA）辅助的多小区协作空中计算框架，并通过联合优化合并矩阵、极化向量、天线位置和用户发射系数，构建了均方误差（MSE）最小化问题。该问题具有高度非凸性，为此我们提出一种交替优化算法：首先推导出合并矩阵与发射系数的闭式更新解；随后提出基于逐次凸逼近（SCA）和半定松弛（SDR）的方法优化极化向量，并采用梯度下降法更新天线位置。此外，我们开发了基于统计信道的天线位置优化方案，并进一步提出相应算法以高效求解。数值结果表明，在瞬时信道与统计信道场景下，所提出的双极化可移动天线方案均持续优于可移动单极化方案与固定天线基线方案。