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

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