Improving Channel Estimation Performance for Uplink OTFS Transmissions: Pilot Design based on A Posteriori Cramer-Rao Bound

Orthogonal time frequency space (OTFS) has been widely acknowledged as a promising wireless technology for challenging transmission scenarios, including high-mobility channels. In this paper, we investigate the pilot design for the multi-user OTFS system based on the a priori statistical channel state information (CSI), where the practical threshold-based estimation scheme is adopted. Specifically, we first derive the a posteriori Cramer-Rao bound (PCRB) based on a priori channel information for each user. According to our derivation, the PCRB only relates to the user's pilot signal-to-noise ratio (SNR) and the range of delay and Doppler shifts under the practical power-delay and power-Doppler profiles. Then, a pilot scheme is proposed to minimize the average PCRB of different users, where a closed-form global optimal pilot power allocation is derived. Our numerical results verify the multi-user PCRB analysis. Also, we demonstrate an around 3 dB improvement in the average normalized-mean-square error (NMSE) by using the proposed pilot design in comparison to the conventional embedded pilot design under the same total pilot power.