  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.
