Diversity and BER Performance of Zak-OTFS Modulation

Zak-OTFS is a promising modulation scheme for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{6 G}$</tex> and beyond due to its enhanced resilience to high Dopplers and its structured input-output relation through twisted convolution operation. In this paper, we analyze the diversity performance of Zak-OTFS under maximum-likelihood (ML) detection and perfect delay-Doppler (DD) domain channel state information (CSI). Our analysis provides a condition in the design of pulse shaping filters to achieve full DD domain diversity. Our results show that sinc and Gaussian filters achieve full DD diversity in Zak-OTFS. This is in contrast with the widely investigated multicarrier (MC) version of OTFS (MC-OTFS), whose diversity order is one and requires phase rotation operation on the transmit vector to achieve full DD diversity. Further, we analyze the bit error performance of Zak-OTFS under imperfect CSI. We carry out the analysis for 1) the mismatched ML detector, where the channel matrix in the conventional ML decision rule is replaced with the estimated channel matrix, and 2) the true ML detector which takes into account the CSI error statistics in the ML decision rule, and quantify the performance gap between the two detectors.