Analytical characterization of ambiguity function sidelobes and peak sidelobe level for FSK-based JCR waveforms

Determine analytical characterizations of the ambiguity function sidelobe levels and the peak sidelobe level for M-ary frequency-shift keying (FSK) waveforms used in joint communications and radar, providing rigorous expressions or tight characterizations over the delay–Doppler plane that quantify sidelobe behavior as a function of waveform parameters.

Background

The work focuses on M-ary FSK waveforms for joint communications and radar because of their unit baseband PAPR and radar-sensing potential. While prior work analyzed time-bandwidth behavior, the ambiguity function sidelobe structure and peak sidelobe level lack analytical characterization.

The authors emphasize that, despite the appeal of FSK for high data rates and favorable hardware properties, the radar performance in terms of ambiguity function sidelobes and especially the peak sidelobe level has not been analytically established, motivating their partial treatment via grid-point analysis and approximations.

References

Nevertheless, the analysis of its AF SL and PSL remains an open problem.

— Can FSK Be Optimised for Integrated Sensing and Communications?  (2405.00945 - Han et al., 2024) in Section I-B (Motivation and Contributions)

This delay offset has been observed consistently across multiple experimental datasets acquired with SXM signals; however, its precise origin remains uncertain.

— Frame-Induced Doppler Self-Ambiguity in SiriusXM Satellite Signals for Passive Radar  (2609.09393 - El-Darymli et al., 8 Sep 2026) in Section 7, Discussion