Low-Complexity and High-Performance Combiners for Over the Air Computing

We consider the design of successive convex approximation (SCA)-based mean square error (MSE) minimization combiners for over-the-air-computation (AirComp) schemes operating over the uplink of a system with one multiple-antenna access point (AP) and multiple single-antenna edge devices (EDs). Within that context, we contribute with two different initial combiner designs alternative to the state-of-the-art (SotA) combiner based on semi-definite relaxation (SDR). The first is a low-complexity design, whereby the SDR formulation of the MSE minimization problem is replaced by a rank-one Rayleigh quotient (RQ) method, whose closed-form solution is obtained with linear complexity; and the second is a highperformance design obtained by enforcing a low-rank solution of the SDR-based MSE minimization problem. Numerical results demonstrate that the low-complexity RQ design can be up to 1000-times less costly than the SotA uniform-forcing (UF)/SDR scheme; while the high-performance regularized SDR design is found to be about 4-times faster than the latter, at a comparable complexity.