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

TL;DR

This work tackles the detection complexity of OTFS-IM in doubly selective channels by introducing hierarchical mode-based index modulation (HMIM) and integrating it with orthogonal delay-Doppler division multiplexing (ODDM). It delivers a HQC-based HMIM transmitter, a DD-domain input–output model, and three detectors: ML, a Gaussian-noise MAP with linear block-length complexity, and a SIC-MMSE detector with iterative MAP refinement. Theoretical BER analysis and extensive simulations show HMIM achieving comparable or better BER than conventional IM at the same spectral efficiency, with significantly reduced complexity, especially for large frames; SIC-MMSE further boosts performance with modest complexity. The approach also generalizes to OTFS, offering a practical, high-SE reliable DD-domain communication solution for high-mobility scenarios.

Abstract

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.

Figures (7)

• Figure 1: ODDM-HMIM frame structure with $M=N=32,N_b=4$, and $Q_2=4$.
• Figure 2: Block diagram of the transmitter of ODDM-HMIM system.
• Figure 3: Normalized HQC diagram of $\mathbf{\Lambda}$ with $Q_1=4,Q_2=4,\rho=2$.
• Figure 4: BER performance of ODDM-HMIM with ML detection (SE = 1.5 bps/Hz, $M=N=2$, $P=2$).
• Figure 5: Factor graph of the block-wise MAP estimator for ODDM-HMIM with Gaussian noise.

Theorems & Definitions (1)

• Definition 1: Hierarchical QAM constellation