Bayesian Optimization Aided Low-Complexity Beamforming Design for Over-the-Air-Computing

We consider the design of low complexity and high-performing mean square error (MSE) minimization combiners for over-the-air-computing (AirComp) applications operating over the uplink of a system with one multiple-antenna access point (AP) and multiple single-antenna edge devices (EDs). Within that paradigm, we offer two contributions, namely, a simple initial combiner based on a Rayleigh quotient (RQ) design, and a low-complexity refinement stage based on a convex concave procedure (CCP). The new refinement stage algorithm is further enriched with an efficient (offline) hyperparameter tuning mechanism via Bayesian optimization (BO) and acceleration method based on a half-space constrained least square problem reformulation solved via the adaptive moment estimation (Adam) algorithm. The low complexity and good performance of the proposed method help address typical limitations of edge devices. Numerical results demonstrate that the proposed design can achieve (MSE) performances equivalent to those of the best state-of-the-art (SotA) alternatives currently known, at about 200-times less complexity than the highest-performing SotA, and about 4-times less complexity than its low-complexity counterpart.