Sparse Bayesian Learning Approach for OTFS Channel Estimation with Fractional Doppler

This paper addresses the channel estimation problem for Orthogonal time frequency space (OTFS) systems in the presence of fractional Doppler. Channel estimation with fractional Doppler can be considered as an off-grid sparse signal recovery problem, where the virtual sampling grid is introduced in the delay-Doppler domain. First-order linear approximation as a conventional approach to estimate fractional Doppler and sparse signal in OTFS systems. However, linear approximation approach may incur considerable modeling errors, since the finite sampling grid may be insufficiently refined in the OTFS systems. Furthermore, this error will deteriorate recovery performance. To solve this problem, we propose an efficient sparse Bayesian learning (SBL) method to jointly estimate the fractional Doppler and sparse channel vectors. Specifically, we reformulate the input-output relationship for fractional Doppler, and further present an off-grid channel estimation model. Then, an in-exact block majorization-minimization (MM) algorithm is adopted to iteratively update the associated parameters under the SBL framework. Fractional Doppler can be iteratively refined to eliminate the off-grid gap using the gradient descent method. The proposed scheme presents an exact channel estimation model that avoids any approximation operation, so that it effectively alleviates the model error. Simulation results show that the proposed channel estimation method significantly outperforms state-of-the-art methods