Federated Learning via Over-the-Air Computation With Statistical Channel State Information

Federated learning (FL) is a popular distributed learning paradigm, in which a global model at a server learns private data of clients without data shared among clients or the server. In this paper, we consider FL over a noisy fading multiple access channel (MAC) via over-the-air computation (AirComp). Benefiting from waveform-superposition propriety of wireless signals, AirComp is able to achieve fast aggregations in FL and improve spectral efficiency. However, most of the schemes exploiting AirComp require intensive channel estimations as the demands from precoders, which results in considerable communication overheads. For this reason, we propose two novel FL schemes with statistical channel state information (FL-SCSI-A and FL-SCSI-B) to reduce the efforts required by channel estimations. In FL-SCSI-A, precoders adjust phases of transmitted signals with phases of instant channel state information (CSI), and scale transmitted signal powers based on statistical CSI. The precoder design has the following two advantages. First, phases of instant CSI can be easier to estimate than complete instant CSI. Second, since clients only need to estimate phases of their own instant CSI (instead of CSI of all clients), with channel reciprocity, this can be easily achieved by letting the server broadcast pilots to all clients. The server in FL-SCSI-A is also efficient. It only needs to estimate the sum of channel gains of all clients, which can be easily achieved by letting clients transmit pilots simultaneously. To further reduce the communication overhead, FL-SCSI-B is proposed. The precoders in FL-SCSI-B are similar to FL-SCSI-A, while the server does not require any knowledge of instant CSI, which reduces the demands of channel estimations. For both schemes, we prove that the distortion caused by the noisy fading MAC is bounded, and the convergences of the learning processes are guaranteed for strongly smooth losses with heterogeneous data assumptions. Experimental results show that the proposed schemes perform better than benchmark schemes while reducing efforts required by channel estimation.