Orthogonal Delay–Doppler Division Multiplexing with Frequency-domain Tomlinson–Harashima Precoding

Abstract

Orthogonal delay-Doppler (DD) division multiplexing (ODDM) has been recently proposed as a promising candidate for communication in high-mobility scenarios. This work investigates the application of Tomlinson-Harashima precoding (THP) in ODDM systems to simplify equalization. To align the transceiver architecture with conventional orthogonal frequency division multiplexing (OFDM) systems, we propose applying THP to the frequency-domain (FD) symbols. To address the structural challenge of the banded and non-causal FD channel with Doppler-induced wrap-around, we first introduce virtual Doppler alignment at the receiver and zero padding at the transmitter. These operations make the effective FD channel into a strictly lower-triangular form, thus enabling efficient symbolwise precancellation and modulo operation in the FD at the transmitter, as well as single-tap equalization at the receiver. We then analytically model the bit-error rate (BER) lower bound of our system by characterizing three losses, namely power, modulo noise, and modulo signal losses. Simulation results are finally presented to show the significance of our proposed FD-THP design under high-mobility condition, and also to validate the analysis. The findings establish a practical pathway for nonlinear precoding in the FD for DD modulations.