  In this study, we propose an over-the-air computation (AirComp) scheme for
federated edge learning (FEEL) without channel state information (CSI) at the
edge devices (EDs) or the edge server (ES). The proposed scheme relies on
non-coherent communication techniques for achieving distributed training by
majority vote (MV). In this work, the votes, i.e., the signs of the local
gradients, from the EDs are represented with the pulse-position modulation
(PPM) symbols constructed with discrete Fourier transform (DFT)-spread
orthogonal frequency division multiplexing (OFDM) (DFT-s-OFDM). By taking the
delay spread and time-synchronization errors into account, the MV at the ES is
obtained with an energy detector. Hence, the proposed scheme does not require
CSI at the EDs and ES. We also prove the convergence of the distributed
training when the MV is obtained with the proposed scheme under fading channel.
Through simulations, we show that the proposed scheme provides a high test
accuracy in fading channels while resulting in lower peak-to-mean envelope
power ratio (PMEPR) symbols.
