Antenna Selection for Multiantenna Over-the-Air Computation

Over-the-air computation (AirComp) integrates wireless communication and data processing in sensor networks. Multiple antennas have been used at the sink to improve its performance. In massive MIMO for conventional wireless communication, it is known that not all antennas contribute equally, and antenna selection is studied for the scenario where there are more antennas than RF chains. In this letter, we show that antenna selection also applies to AirComp. But here the problem is more complex in that antenna selection is coupled with the optimization of the Rx-scaling vector. We show that when optimizing the Rx-scaling vector by the matrix lifting technique, the selection of antennas corresponds to sparsifying the diagonal of the lifted matrix, and on this basis, propose a new algorithm to gradually sparsify the diagonal of the lifted matrix, which both solves the Rx-scaling vector and selects the antennas simultaneously. This is applied to both the case where all signals share the same magnitude, and the case where the misalignment occurs in some signals.