Off-Grid Channel Estimation Using Grid Evolution for OTFS Systems

Orthogonal time frequency space (OTFS) as a newly proposed two-dimensional modulation scheme outperforms the orthogonal frequency division multiplexing in high-speed scenarios. Most recent studies focus on off-grid channel estimation with the ideal pulse which needs to satisfy the bi-orthogonality robustness condition but does not exist. In this paper, we consider an OTFS system with rectangular pulses and propose a grid evolution based off-grid sparse Bayesian inference (GESBI) by updating the virtual delay-Doppler grid to improve the accuracy of the channel estimation. In particular, different from the recently proposed off-grid channel estimation algorithms in OTFS where the virtual grid is fixed and uniform, the proposed channel estimation method consists of an external and internal iteration, where the grid evolution method performs in the external iteration to update the virtual grid to be non-uniform by utilizing the estimated on-grid and the off-grid information in the internal iteration. In addition, the grid evolution-based efficient sparse Bayesian inference with the student's T distribution prior (T-GEESBI) is proposed to reduce the channel estimation complexity while improving the channel estimation accuracy. Specifically, the matrix inversion is avoided by approximating the posterior distribution. Then the equal non-convex problem is handled by utilizing the block coordinate descent method in a majorization-minimization framework. Furthermore, the two types of genie bounds on the mean squared error of the estimated channel coefficients are derived. Finally, both theoretical and numerical analyses demonstrate low complexity, convergence, and the efficiency of the proposed channel estimation approach.