Miso: Misalignment Allowed Optimization for Multiantenna Over-the-Air Computation

Abstract

Over-the-air computation (AirComp), as an effective method to wireless data aggregation, has attracted much attention recently. It helps to improve network efficiency and scalability by integrating communication and computation in the air. In AirComp, both signal magnitude misalignment and noise lead to computation error. In the single antenna case, by allowing misalignment in signal magnitude, a good tradeoff can be achieved between signal distortion and noise power, which leads to a minimal error. In the multi-antenna case, usually the zeroforcing policy is used to enforce signal magnitude alignment (no distortion), which, however, increases noise and affects the overall computation error. To better exploit multiple antennas at the sink, in this paper, we propose a misalignment allowed optimization (Miso) method for AirComp. Specifically, a group of nodes whose signals may be misaligned are dynamically selected, and other signals are aligned to a higher level with higher quality. On this basis, the optimization of multi-antenna AirComp is converted to a difference of convex problem and is solved iteratively. Simulations confirm that the proposed method greatly reduces computation error and scales better with the number of nodes, compared with previous methods.