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

TL;DR

The paper addresses designing pulse shaping filters for Zak-OTFS ISAC that simultaneously achieve localization in the delay-Doppler domain, orthogonality on the DD lattice, and no time/bandwidth expansion. It introduces an Isotropic Orthogonal Transform Algorithm (IOTA) to orthogonalize maximally localized prototypes (Gaussian and PSWF) in the DD domain, producing DD pulses that meet all three criteria. Numerical results on a Vehicular-A channel show improved input-output relation estimation and data detection with the IOTA-based pulses, with PSWF-based IOTA offering the strongest localization and BER/NMSE benefits while preserving spectral efficiency. The work demonstrates practical ISAC gains without bandwidth/time expansion and points to hardware implementations and information-theoretic trade-offs as avenues for future study.

Abstract

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.

Figures (3)

• Figure 1: Pulse shaping filter variation and energy concentration. (a)-(b): The proposed IOTA pulse shapes have a sharper main lobe and lower sidelobes compared to the Gaussian-sinc filter Chockalingam2025_gs. Moreover, the IOTA PSWF pulse has smaller main lobe and sidelobes compared to the IOTA Gaussian filter. (c)-(d): The IOTA pulse shapes have flat energy spectral density within $f \in [-B/2,B/2]$ and $t \in [-T/2,T/2]$ and a roll-off similar to their prototype pulses (Gaussian or PSWF). All pulse shapes have $99.99\%$ energy concentration within $f \in [-B/2,B/2]$ and $t \in [-T/2,T/2]$.
• Figure 2: Uncoded $4$-QAM data detection performance with perfect I/O relation knowledge at the receiver. The proposed IOTA pulses achieve ideal performance due to their orthogonality.
• Figure 3: Uncoded $4$-QAM data detection performance with I/O relation estimation using a separate pilot frame with pilot SNR equal to data SNR. The simultaneous localization and orthogonality of the proposed IOTA pulses results in improved BER and I/O relation NMSE compared to the Gaussian-sinc filter Chockalingam2025_gs, with no time or bandwidth expansion (unlike the RRC filter).