Over-the-Air Computation with Reciprocity Calibration: Detection and Realignment of Misaligned Devices

Over-the-Air (OtA) computation can be used to efficiently aggregate and compute functions of data from distributed devices. For coherent processing with channel-inversion-based precoding, the aggregation accuracy can be greatly affected by random phase rotation during the signal transmission. If devices are reciprocity calibrated, estimating the channel from the devices to the server becomes efficient. However, because of random unknown phase noise in device oscillators, repeated calibration of phase is necessary. In this work the aim is investigating the effects of phase noise in OtA computation systems with coherent processing. We propose a method for detecting if devices are misaligned in phase, as well as policies that balance detection and realignment of phase. The policies are tested in scenarios of distributed estimation and federated learning. Results show that if realignment generates too much resource cost, detecting misaligned devices can be beneficial.