  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.
