Yaru Wang, Deyou Zhang, Qingchao Li, Jun Liu, Chuang Shi
Abstract
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.