MiLAC-Aided Beamforming for MIMO Over-the-Air Computation

2026-08-13

AI Summary

This work addresses the challenges in MIMO over-the-air computation (AirComp) posed by signal misalignment due to channel fading and noise, as well as the high hardware cost of fully digital beamforming. To tackle these issues, the paper introduces, for the first time, a microwave linear analog computer (MiLAC)-assisted beamforming architecture that drastically reduces the number of radio-frequency chains. It jointly optimizes the transmit digital precoding matrix and the receive MiLAC aggregation matrix to minimize the mean-square error. An alternating optimization algorithm is developed: the precoding subproblem is solved via KKT conditions combined with bisection search, while the convex MiLAC subproblem is globally optimized using projected gradient descent. Under identical hardware budgets, the proposed scheme outperforms conventional phase-shifter-based hybrid beamforming and approaches the performance of fully digital beamforming. Numerical experiments confirm the convergence and efficacy of the algorithm.

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.

Problem

• Over-the-air computation
• MIMO
• beamforming
• RF chain reduction
• aggregation accuracy

Innovation

• MiLAC
• MIMO AirComp
• hybrid beamforming
• alternating optimization
• mean squared error