Pulse Shaping Filter Design for Integrated Sensing & Communication with Zak-OTFS

Zak-OTFS is an emerging framework for integrated sensing & communication (ISAC) in high delay and Doppler spread environments. A critical enabler for ISAC with Zak-OTFS is the design of pulse shaping filters. For sensing, a localized pulse shaping filter enables ideal input-output (I/O) relation estimates close to the physical scattering channel. For communication, orthogonality of the pulse shape on the information lattice prevents inter-symbol interference, and no time and bandwidth expansion enables full spectral efficiency. A filter simultaneously meeting all three objectives is ideal for ISAC. Existing filter designs achieve two of the above objectives, but not all three simultaneously. For instance, the sinc filter is orthogonal and bandwidth/time-limited, but is not localized. The Gaussian filter is localized and bandwidth/time-limited, but not orthogonal. The RRC filter is localized and orthogonal, but not bandwidth/time-limited. A recently proposed hybrid Gaussian-sinc filter is more localized than the sinc filter and bandwidth/time-limited, but is not orthogonal. In this work, we design optimal pulse shaping filters meeting all three objectives via the Isotropic Orthogonal Transform Algorithm. The proposed pulse shaping filters offer improved data detection (communication) and I/O relation estimation (sensing) performance compared to existing filter choices in the literature.