Sparsity Enabled Low-Complexity SPCG-LMMSE Detector for ODDM Modulation

Orthogonal delay-Doppler division multiplexing (ODDM) modulation enhances transmission in high-mobility scenarios but also increases detection complexity, especially when fractional Doppler shifts are present. To tackle these issues, we propose a low-complexity sparse pre-conditioned conjugate gradient-linear minimum mean square error (SPCG-LMMSE) detector, which can obtain the LMMSE solution without needing matrix inversion. Based on the sparsity and quasi-banded structure of the ODDM time-domain equalization matrix, the algorithm utilizes an improved conjugate gradient method to approach the optimal solution quickly. Simulation results demonstrate that the detector can significantly reduce complexity while maintaining excellent performance, with additional gains in multipath and high-order modulation scenarios.