Tunable Gaussian Pulse for Delay-Doppler ISAC

Integrated sensing and communication (ISAC) for next-generation networks targets robust operation under high mobility and high Doppler spread, leading to severe inter-carrier interference (ICI) in systems based on orthogonal frequency-division multiplexing (OFDM) waveforms. Delay--Doppler (DD)-domain ISAC offers a more robust foundation under high mobility, but it requires a suitable DD-domain pulse-shaping filter. The prevailing DD pulse designs are either communication-centric or static, which limits adaptation to non-stationary channels and diverse application demands. To address this limitation, this paper introduces the tunable Gaussian pulse (TGP), a DD-native, analytically tunable pulse shape parameterized by its aspect ratio $\gamma$, chirp rate $\alpha_c$, and phase coupling $\beta_c$. On the sensing side, we derive closed-form Cram\'er--Rao lower bounds (CRLBs) that map $(\gamma,\alpha_c,\beta_c)$ to fundamental delay and Doppler precision. On the communications side, we show that $\alpha_c$ and $\beta_c$ reshape off-diagonal covariance, and thus inter-symbol interference (ISI), without changing received power, isolating capacity effects to interference structure rather than power loss. A comprehensive trade-off analysis demonstrates that the TGP spans a flexible operational region from the high capacity of the Sinc pulse to the high precision of the root raised cosine (RRC) pulse. Notably, TGP attains near-RRC sensing precision while retaining over $90\%$ of Sinc's maximum capacity, achieving a balanced operating region that is not attainable by conventional static pulse designs.