Chirp-Based Over-the-Air Computation for Long-Range Federated Edge Learning

In this study, we propose circularly-shifted chirp (CSC)-based majority vote (MV) (CSC-MV), a power-efficient over-the-air computation (OAC) scheme, to achieve long-range federated edge learning (FEEL). The proposed approach maps the votes (i.e., the sign of the local gradients) from the edge devices (EDs) to the linear CSCs constructed with a discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM) transmitter. At the edge server (ES), the MV is calculated with an energy detector. We compare our proposed scheme with one-bit broadband digital aggregation (OBDA) and show that the output-power back-off (OBO) requirement of the transmitters with an adjacent-channel-leakage ratio (ACLR) constraint for CSC-MV is lower than the one with OBDA. For example, with an ACLR constraint of -22 dB, CSC-MV can have an OBO requirement of 6-7 dB less than the one with OBDA. When the power amplifier (PA) non-linearity is considered, we demonstrate that CSC-MV outperforms OBDA in terms of test accuracy for both homogeneous and heterogeneous data distributions, without using channel state information (CSI) at the ES and EDs.

Multi-cell Non-coherent Over-the-Air Computation for Federated Edge Learning

In this paper, we propose a framework where over-the-air computation (OAC) occurs in both uplink (UL) and downlink (DL), sequentially, in a multi-cell environment to address the latency and the scalability issues of federated edge learning (FEEL). To eliminate the channel state information (CSI) at the edge devices (EDs) and edge servers (ESs) and relax the time-synchronization requirement for the OAC, we use a non-coherent computation scheme, i.e., frequency-shift keying (FSK)-based majority vote (MV) (FSK-MV). With the proposed framework, multiple ESs function as the aggregation nodes in the UL and each ES determines the MVs independently. After the ESs broadcast the detected MVs, the EDs determine the sign of the gradient through another OAC in the DL. Hence, inter-cell interference is exploited for the OAC. In this study, we prove the convergence of the non-convex optimization problem for the FEEL with the proposed OAC framework. We also numerically evaluate the efficacy of the proposed method by comparing the test accuracy in both multi-cell and single-cell scenarios for both homogeneous and heterogeneous data distributions.