  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.
