On the Performance of Coded OTFS Modulation over High-Mobility Channels

In this paper, the error performance for coded orthogonal time frequency space (OTFS) modulation over high-mobility channels is investigated. We start from the study of conditional pairwise-error probability (PEP), based on which the performance upper bound of the coded OTFS system is derived. Based on the performance bound, we show that the coding improvement for OTFS systems depends on the squared Euclidean distance among codeword pairs and the number of independent resolvable paths of the channel. More importantly, we show that there is a fundamental trade-off between the coding gain and the diversity gain for OTFS systems. In particular, we prove that the diversity gain of OTFS systems improves with the number of resolvable paths, while the coding gain declines, for a given channel code. Furthermore, the rule-of-thumb code design criterion for the OTFS systems is presented to maximize the squared Euclidean distance according to the derived bounds. Our performance analysis and the proposed code design criterion are verified by simulation results, which also demonstrate the significant performance improvement of OTFS modulation over orthogonal frequency-division multiplexing (OFDM) modulation.