A Novel Off-Grid Channel Estimation with Fast BCS Using LSM Prior for OTFS Modulation

Orthogonal time-frequency space (OTFS) is a two-dimensional (2D) modulation technology for processing high mobility communication signals. The integer delay and Doppler shifts can lead to significant modeling error in the delay-Doppler (DD) domain. To obtain accurate estimation of fractional DD domain channel, we propose a novel two-step off-grid channel estimation using Bayesian compressive sensing (BCS) for OTFS systems. First, we analyze the vectorized form of fractional DD domain input-output relationship and derive a simplified expression form to adapt compressive sensing model. Then, to tackle the problem of fractional parameters estimation, we build an off-grid compressive model in light of high-order Taylor expansion. The channel parameters can be obtained by our proposed off-grid BCS (OG-BCS) algorithm, where we edge out the noise parameters and adopt a hierarchical Laplacian scale mixture (LSM) prior for OTFS signal. At the same time, based on likelihood maximization we derive the off-grid update expressions and incorporate it into our optimized BCS framework. To further reduce the computational complexity, we propose a fast BCS (FBCS) algorithm via LSM prior. In our proposed FBCS algorithm, the hyper-parameters modeling the sparse signal are separated for calculation, and only a single hyper-parameter is considered for updating in each iteration. Specially, we analyze the condition of maximization for obtaining the solution of hyper-parameters and derive its update expressions. Simulation results illustrate that our proposed algorithm has better computational efficiency and precise channel estimation performance.