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.

翻译：在正交时频空(OTFS)调制中，Zak变换方法是一种将复用延迟-多普勒(DD)域的信息符号直接转换为时域信号进行传输的自然方法，且在接收端实现逆变换。以往对OTFS的研究主要采用两步法：先将DD域符号转换至时频域，再转换为时域传输，接收端则进行逆过程。与两步法相比，Zak变换方法在性能和复杂度方面具有优势。本文初步研究了基于离散Zak变换(DZT)实现OTFS的误码性能。我们通过矩阵分解建立了DZT-OTFS紧凑的DD域输入输出关系，该关系适用于整数和分数延迟-多普勒。利用成对错误概率分析与仿真，我们研究了DZT-OTFS的误码性能。仿真结果表明：1) DZT-OTFS和两步法OTFS均优于OFDM；2) 在较宽的多普勒扩展范围内，DZT-OTFS的性能优于两步法OTFS。