Performance Analysis of OTFS with Imperfect Delay-Doppler Channel State Information

In this paper, we analyze the effect of imperfect delay-Doppler channel state information (CSI) on the bit error rate (BER) performance of orthogonal time frequency space (OTFS) modulation. We carry out the BER analysis when a mismatched maximum-likelihood (ML) detector is used, i.e., when an estimated channel matrix is used for detection in place of the true channel matrix. We derive an exact expression for the pairwise error probability (PEP) using the characteristic function of the decision statistic. Using the PEP expression, we obtain an upper bound on the BER. Our results show that the BER bound is tight at high SNRs. We also obtain the decision rule for the true ML detector with imperfect CSI, which takes into account the delay-Doppler channel estimation error statistics. We quantify the performance gap between the true ML detector and the mismatched ML detector through simulations.