Uplink Multi-User OTFS: Transmitter Design Based on Statistical Channel Information

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 uplink multi-user OTFS transmission designs based on statistical channel information. Specifically, we investigate the pilot power allocation based on the a priori statistical channel state information (CSI) only, where performance on channel estimation is considered. We first derive the a posteriori Cram<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\acute {\text {e}}$ </tex-math></inline-formula>r-Rao bound (PCRB) based on the a priori channel information of each user. We unveil that the PCRB only relates to the user’s pilot signal-to-noise ratio (SNR) and the maximum of delay and Doppler shifts under the practical power-delay and power-Doppler profiles. Furthermore, a pilot power allocation scheme is proposed to minimize the average PCRB of different users, whose closed-form optimal allocation solution is derived. Moreover, we study the impact of statistical CSI on transmission rates, where a tight approximation of the sum-rate is derived. Particularly, the approximated sum-rate only relates to the user’s symbol SNR and the maximum of delay and Doppler shifts. More importantly, we propose a power allocation for different users based only on the statistical CSI to maximize the achievable sum-rate while ensuring user fairness. The optimal power allocation solution is obtained by a fractional programming approach. Our numerical results verify the derived PCRB and the sum-rate analysis, where a roughly 3 dB improvement in terms of channel estimation accuracy and a significant rate improvement can be obtained.