Channel Estimation with Hierarchical Sparse Bayesian Learning for ODDM Systems

Orthogonal delay-Doppler division multiplexing (ODDM) is a promising modulation technique for reliable communications in high-mobility scenarios. However, the existing channel estimation frameworks for ODDM systems cannot achieve both high accuracy and low complexity simultaneously, due to the inherent coupling of delay and Doppler parameters. To address this problem, a two-dimensional (2D) hierarchical sparse Bayesian learning (HSBL) based channel estimation framework is proposed in this paper. Specifically, we address the inherent coupling between delay and Doppler dimensions in ODDM by developing a partially-decoupled 2D sparse signal recovery (SSR) formulation on a virtual sampling grid defined in the delay-Doppler (DD) domain. With the help of the partially-decoupled formulation, the proposed 2D HSBL framework first performs low-complexity coarse on-grid 2D sparse Bayesian learning (SBL) estimation to identify potential channel paths. Then, high-resolution fine grids are constructed around these regions, where an off-grid 2D SBL estimation is applied to achieve accurate channel estimation. Simulation results demonstrate that the proposed framework achieves performance superior to conventional off-grid 2D SBL with significantly reduced computational complexity.