Fractional Delay and Doppler Estimation for OTFS Based ISAC Systems

In this paper, we consider an orthogonal time frequency space (OTFS) modulation based single input single output (SISO) radar for integrated sensing and communication (ISAC) where the transmitter sends OTFS frames and the radar receiver co-located with the transmitter leverages the transmit frame along with the reflected signal for the estimation of the target range and velocity. We present a novel radar channel model that is capable of capturing both integer as well as fractional delays and Doppler shifts accounted for by the targets in the channel. A two-step modified orthogonal matching pursuit with fractional refinement (OMPFR) algorithm is also proposed to estimate the delays and Doppler shifts that can be non-integer multiples of the system delay and Doppler resolutions respectively. We show that our algorithm has much lower complexity than the traditional orthogonal matching pursuit (OMP) algorithm if used in estimating the fractional delays and Dopplers, as the latter requires a colossal dictionary matrix. Target profiles and the root mean square error (RMSE) plots for range and velocity estimates validate the effectiveness of the proposed OMPFR algorithm.