  Inspired by providing reliable communications for high-mobility scenarios, in
this letter, we investigate the channel estimation and signal detection in
integrated sensing and communication~(ISAC) systems based on the orthogonal
delay-Doppler multiplexing~(ODDM) modulation, which consists of a pulse-train
that can achieve the orthogonality with respect to the resolution of the
delay-Doppler~(DD) plane. To enhance the communication performance in the
ODDM-based ISAC systems, we first propose a low-complexity approximation
algorithm for channel estimation, which addresses the challenge of the high
complexity from high resolution in the ODDM modulation, and achieves
performance close to that of the maximum likelihood estimator scheme. Then, we
employ the orthogonal approximate message-passing scheme to detect the symbols
in the communication process based on the estimated channel information.
Finally, simulation results show that the detection performance of ODDM is
better than other multi-carrier modulation schemes. Specifically, the ODDM
outperforms the orthogonal time frequency space scheme by 2.3 dB when the bit
error ratio is $10^{-6}$.
