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 ( γ), chirp rate ( α_c ), and phase coupling ( β_c ). On the sensing side, we derive closed-form Cramér–Rao lower bounds (CRLBs) that map ( (γ,α_c,β_c) ) to fundamental delay and Doppler precision. On the communications side, we show that ( α_c ) and ( β_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.

💡 Research Summary

The rapid evolution of 6G networks necessitates the integration of sensing and communication (ISAC) capabilities into a single waveform. However, a fundamental challenge arises in high-mobility scenarios, such as those involving high-speed trains or autonomous vehicles, where significant Doppler spread induces severe inter-carrier interference (ICI) in traditional OFDM-based systems. While the Delay-Doppler (DD) domain offers a robust alternative for handling such mobility, existing pulse-shaping designs are largely static or optimized solely for communication, failing to adapt to the dynamic requirements of non-stationary channels or the dual-purpose nature of ISAC.

This paper proposes a groundbreaking solution: the Tunable Gaussian Pulse (TGP). Unlike conventional fixed-shape pulses, the TGP is a DD-native waveform characterized by three analytically tunable parameters: the aspect ratio ($\gamma$), the chirp rate ($\alpha_c$), and the phase coupling ($\beta_c$). The core innovation lies in the ability to manipulate the interference structure of the signal without sacrificing signal energy.

On the sensing front, the authors derive closed-form Cramér-Rao Lower Bounds (CRLBs), providing a rigorous mathematical framework to map the TGP parameters directly to fundamental delay and Doppler estimation precision. This allows for a predictable and controllable sensing performance. On the communication front, the research demonstrates that by adjusting the chirp rate ($\alpha_c$) and phase coupling ($\beta_c$), the system can reshape the off-diagonal elements of the received covariance matrix. This effectively mitigates inter-symbol interference (ISI) by restructuring the interference pattern rather than simply reducing signal power, thereby isolating the impact on capacity to the interference structure itself.

The most significant contribution of this work is the demonstration of a “sweet spot” in the performance trade-off space. Traditional designs force a choice between the high-capacity but low-precision Sinc pulse and the high-precision but low-capacity Root Raised Cosine (RRC) pulse. The TGP, however, spans a flexible operational region that allows the system to achieve near-RRC sensing precision while retaining over 90% of the maximum capacity offered by the Sinc pulse. This ability to achieve a balanced operating region—previously unattainable with static designs—presents a transformative approach for designing adaptive, high-performance waveforms for future-generation ISAC networks.