Orthogonal Delay-Doppler Division Multiplexing Modulation with Tomlinson-Harashima Precoding

TL;DR

This paper introduces a time domain Tomlinson-Harashima precoding scheme for orthogonal delay-Doppler division multiplexing, significantly reducing equalization complexity and improving bit error rate performance in high-mobility communication channels.

Contribution

It proposes a novel THP design with an adaptive modulo operation for ODDM, enabling single-tap equalization and enhanced BER performance over LTV channels.

Findings

Reduced equalization complexity in ODDM systems.

Analytical BER bounds for 4-QAM and 16-QAM modulations.

Numerical validation showing improved BER performance over traditional systems.

Abstract

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.