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This paper proposes an off-grid channel estimation scheme for orthogonaltime-frequency space (OTFS) systems adopting the sparse Bayesian learning (SBL)framework. To avoid channel spreading caused by the fractional delay andDoppler shifts and to fully exploit the channel sparsity in the delay-Doppler(DD) domain, we estimate the original DD domain channel response rather thanthe effective DD domain channel response as commonly adopted in the literature.OTFS channel estimation is first formulated as a one-dimensional (1D) off-gridsparse signal recovery (SSR) problem based on a virtual sampling grid definedin the DD space, where the on-grid and off-grid components of the delay andDoppler shifts are separated for estimation. In particular, the on-gridcomponents of the delay and Doppler shifts are jointly determined by the entryindices with significant values in the recovered sparse vector. Then, thecorresponding off-grid components are modeled as hyper-parameters in theproposed SBL framework, which can be estimated via the expectation-maximizationmethod. To strike a balance between channel estimation performance andcomputational complexity, we further propose a two-dimensional (2D) off-gridSSR problem via decoupling the delay and Doppler shift estimations. In ourdeveloped 1D and 2D off-grid SBL-based channel estimation algorithms, thehyper-parameters are updated alternatively for computing the conditionalposterior distribution of channels, which can be exploited to reconstruct theeffective DD domain channel. Compared with the 1D method, the proposed 2Dmethod enjoys a much lower computational complexity while only suffers slightperformance degradation. Simulation results verify the superior performance ofthe proposed channel estimation schemes over state-of-the-art schemes.

Off-grid Channel Estimation with Sparse Bayesian Learning for OTFS Systems