In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive channels encountered in high-mobility environments become time-invariant. OTFS outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios, making it an ideal waveform candidate for 6G. Generally, OTFS is considered a pre- and postprocessing step for OFDM. However, the so-called Zak transform provides the fundamental relation between the DD and time domain. In this work, we propose an OTFS system based on the discrete Zak transform (DZT). To this end, we discuss the DZT and establish the input-output relation for time-frequency (TF) dispersive channels solely by the properties of the DZT. The presented formulation simplifies the derivation and analysis of the input-output relation of the TF dispersive channel in the DD domain. Based on the presented formulation, we show that operating in the DD incurs no loss in capacity.
Keywords: 6G; delay-Doppler channel; discrete Zak transform; orthogonal time frequency space modulation; time-frequency dispersive channel.