On the Bit Error Performance of OTFS Modulation using Discrete Zak Transform

In orthogonal time frequency space (OTFS) modulation, Zak transform approach is a natural approach for converting information symbols multiplexed in the DD domain directly to time domain for transmission, and vice versa at the receiver. Past research on OTFS has primarily considered a two-step approach where DD domain symbols are first converted to time-frequency domain which are then converted to time domain for transmission, and vice versa at the receiver. The Zak transform approach can offer performance and complexity benefits compared to the two-step approach. This paper presents an early investigation on the bit error performance of OTFS realized using discrete Zak transform (DZT). We develop a compact DD domain input-output relation for DZT-OTFS using matrix decomposition that is valid for both integer and fractional delay-Dopplers. We analyze the bit error performance of DZT-OTFS using pairwise error probability analysis and simulations. Simulation results show that 1) both DZT-OTFS and two-step OTFS perform better than OFDM, and 2) DZT-OTFS achieves better performance compared to two-step OTFS over a wide range of Doppler spreads.