CSI-Free Over-The-Air Decentralized Learning Over Frequency Selective Channels

We propose a novel physical layer scheme for decentralized learning over wirelessly connected, serverless systems operating under frequency-selective channels. To achieve scalability with respect to the number of devices, we exploit the waveform superposition properties of wireless channels: devices map their local optimization signals to energy levels across OFDM subcarriers, and transmit simultaneously; each receiver then computes the energy received on each subcarrier, and leverages a non-coherent energy-superposition technique to estimate the weighted disagreement signal, used in conjunction with a decentralized gradient descent algorithm. To enable CSI-free operation over a broad class of frequency-selective channels, including static ones as a special case, we propose two mechanisms: independent phase shifts and coordinated subcarrier shifts at the transmitters. We show that these mechanisms ensure an unbiased estimate of the weighted disagreement signal, with weights given by the average channel gain across subcarriers. We also provide a bound on the variance of this estimate.