基于MiLAC辅助波束成形的MIMO空中计算
MiLAC-Aided Beamforming for MIMO Over-the-Air Computation
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中文总结 AI 辅助
本文针对MIMO空中计算的硬件负担问题，提出MiLAC辅助波束成形方法，通过联合优化预编码与聚合矩阵，在减少射频链数量的同时，性能接近全数字波束成形且优于混合波束成形。
中文摘要 AI 辅助
空中计算（AirComp）可实现低延迟无线数据聚合，但其精度受衰落信道上的信号对齐缺陷和接收机噪声限制。全数字波束成形可提升多输入多输出（MIMO）AirComp系统的聚合精度，但要求每天线配备一个射频（RF）链。为降低硬件负担，本文研究微波线性模拟计算机（MiLAC）辅助的MIMO AirComp波束成形。在无损且互易的MiLAC模型下，联合优化发射端数字预编码矩阵与接收端MiLAC聚合矩阵以最小化均方误差（MSE）。提出一种交替优化算法：利用Karush-Kuhn-Tucker条件与二分法最优更新预编码矩阵，采用投影梯度下降全局求解凸聚合矩阵子问题。数值结果验证了算法的收敛性，表明MiLAC辅助波束成形在RF链数量大幅减少的情况下，性能接近全数字波束成形的MSE表现，且在相同RF链预算下优于基于移相器的混合波束成形。
英文摘要
Over-the-air computation (AirComp) enables low-latency wireless data aggregation, but its accuracy is limited by imperfect signal alignment over fading channels and receiver noise. Fully digital beamforming improves aggregation accuracy in multiple-input multiple-output (MIMO) AirComp systems but requires one radio-frequency (RF) chain per antenna. To reduce this hardware burden, we investigate microwave linear analog computer (MiLAC)-aided beamforming for MIMO AirComp. Under a lossless and reciprocal MiLAC model, we jointly optimize the transmit digital precoding matrices and the receive-side MiLAC aggregation matrix to minimize the mean squared error (MSE). An alternating optimization algorithm is developed, in which the precoding matrices are optimally updated using the Karush--Kuhn--Tucker conditions and bisection, while the resulting convex aggregation matrix subproblem is solved globally using projected gradient descent. Numerical results verify the algorithm's convergence and demonstrate that MiLAC-aided beamforming approaches the MSE performance of fully digital beamforming with substantially fewer RF chains and outperforms phase-shifter-based hybrid beamforming under the same RF-chain budget.
