  For doubly-selective channels, delay-Doppler (DD) modulation, mostly known as
orthogonal time frequency space (OTFS) modulation, enables simultaneous
compensation of delay and Doppler shifts. However, OTFS modulated signal has
high peak-to-average power ratio (PAPR) because of its precoding operation
performed over the DD domain. In order to deal with this problem, we propose a
single-carrier transmission with delay-Doppler domain equalization (SC-DDE). In
this system, the discretized time-domain SC signal is converted to the DD
domain by discrete Zak transform (DZT) at the receiver side, followed by
delay-Doppler domain equalization (DDE). Since equalization is performed in the
DD domain, the SC-DDE receiver should acquire the channel delay-Doppler
response. To this end, we introduce an embedded pilot-aided channel estimation
scheme designed for SC-DDE, which does not affect the peak power property of
transmitted signals. Through computer simulation, distribution of PAPR and bit
error rate (BER) performance of the proposed system are compared with those of
the conventional OTFS and SC with frequency-domain equalization (SC-FDE). As a
result, our proposed SC-DDE significantly outperforms SC-FDE in terms of BER at
the expense of additional computational complexity at the receiver.
Furthermore, SC-DDE shows much lower PAPR than OTFS even though they achieve
comparable coded BER performance.
