Orthogonal Delay-Doppler Division Multiplexing Modulation with Hierarchical Mode-Based Index Modulation

The orthogonal time frequency space with index modulation (OTFS-IM) offers flexible tradeoffs between spectral efficiency (SE) and bit error rate (BER) in doubly selective fading channels. While OTFS-IM schemes demonstrated such potential, a persistent challenge lies in the detection complexity. To address this problem, we propose the hierarchical mode-based index modulation (HMIM). HMIM introduces a novel approach to modulate information bits by IM patterns, significantly simplifying the complexity of maximum a posteriori (MAP) estimation with Gaussian noise. Further, we incorporate HMIM with the recently proposed orthogonal delay-Doppler division multiplexing (ODDM) modulation, namely ODDM-HMIM, to exploit the full diversity of the delay-Doppler (DD) channel. The BER performance of ODDM-HMIM is analyzed considering a maximum likelihood (ML) detector. Our numerical results reveal that, with the same SE, HMIM can outperform conventional IM in terms of both BER and computational complexity. In addition, we propose a successive interference cancellation-based minimum mean square error (SIC-MMSE) detector for ODDM-HMIM, which enables low-complexity detection with large frame sizes.