Gradient-Based Fractional Doppler Estimation for OTFS Systems via Convex Correlation and Residual Functions

Orthogonal Time Frequency Space (OTFS) modulation has recently emerged as a promising technique for high-mobility communication scenarios, owing to its ability to represent time-varying channels more effectively in the delay-Doppler (DD) domain. However, accurate estimation of fractional Doppler shifts in the DD domain remains challenging. Existing methods often suffer from high computational complexity and limited accuracy. To address these issues, we refine the correlation- and residual-based optimization functions of the channel response. Benefiting from the convexity of these optimization functions in the integer interval, the proposed methods can accurately estimate fractional Doppler values through gradient ascent/descent with relatively low computational complexity. In addition, we derive a closedform expression of the single-path Cramér-Rao lower bound (CRLB) for OTFS systems to validate the estimator efficiency. Simulation results demonstrate that the two proposed gradientbased algorithms are effective estimators for both fractional Doppler and channel response in the exclusive pilot case. Moreover, in embedded pilot scenarios, the residual-based optimization function outperforms existing algorithms.