  The orthogonal delay-Doppler (DD) division multiplexing(ODDM) modulation has
been recently proposed as a promising modulation scheme for next-generation
communication systems with high mobility. Despite its benefits, ODDM modulation
and other DD domain modulation schemes face the challenge of excessive
equalization complexity. To address this challenge, we propose time domain
Tomlinson-Harashima precoding (THP) for the ODDM transmitter, to make the DD
domain single-tap equalizer feasible, thereby reducing the equalization
complexity. In our design, we first pre-cancel the inter-symbolinterference
(ISI) using the linear time-varying (LTV) channel information. Second,
different from classical THP designs, we introduce a modified modulo operation
with an adaptive modulus, by which the joint DD domain data multiplexing and
timedomain ISI pre-cancellation can be realized without excessively increasing
the bit errors. We then analytically study the losses encountered in this
design, namely the power loss, the modulo noise loss, and the modulo signal
loss. Based on this analysis, BER lower bounds of the ODDM system with time
domain THP are derived when 4-QAM or 16-QAM modulations are adopted for symbol
mapping in the DD domain. Finally, through numerical results, we validate our
analysis and then demonstrate that the ODDM system with time domain THP is a
promising solution to realize better BER performance over LTV channels compared
to orthogonal frequency division multiplexing systems with single-tap equalizer
and ODDM systems with maximum ratio combining.
