Bandwidth Expansion for Over-the-Air Computation with One-Sided CSI

We consider a distributed computation problem over a multiple access channel (MAC), with N devices. It is known that over-the-air computation (OAC) can provide significant gains for this problem, but existing works are limited to the scenario with matched source and channel bandwidths. We propose OAC schemes for block-fading MACs that modulate the source to fit the available channel bandwidth in a wideband channel, while having channel state information (CSI) only at the transmitter or the receiver. Our results show that the proposed OAC scheme outperforms even ideal capacity-achieving digital schemes when the CSI is available only at the transmitter, and the distortion does not scale with the number of participating devices. We demonstrate the effectiveness of our proposed scheme in federated edge learning (FEEL), where OAC is used to aggregate model updates from the participating devices.