Faster-than-Nyquist Signaling is Good for Single-Carrier ISAC: An Analytical Study

TL;DR

This paper analytically demonstrates that faster-than-Nyquist signaling enhances spectral efficiency and sensing robustness in integrated sensing and communications systems by avoiding spectral aliasing and reducing ambiguity in velocity estimation.

Contribution

It provides the first analytical insights into how FTN signaling benefits ISAC, including bounds on spectral efficiency and improved sensing performance.

Findings

FTN signaling improves spectral efficiency over multipath channels.

FTN signals offer more robust ranging performance.

FTN reduces ambiguity peaks in velocity estimation.

Abstract

In this paper, we provide an analytical study of single-carrier faster-than-Nyquist (FTN) signaling for integrated sensing and communications (ISAC). Our derivations show that FTN is advantageous for ISAC, and reveal new insights that these advantages come from the fact that FTN signaling can effectively avoid the spectral aliasing due to the mismatch between the symbol rate and the bandwidth of the shaping pulse. Specifically, the communication spectral efficiency advantages of FTN signaling over time-invariant multipath channels are analytically shown, where both upper- and lower-bounds on the spectral efficiency are derived. We show that the gap between these two bounds corresponds to the potential signal-to-noise ratio (SNR) variation due to the presence of multipath delay and spectral aliasing, which diminishes as the symbol rate grows higher. Particularly, in the limiting case, this SNR variation disappears while the degree of freedom (DoF) of the system attain the maximum. Furthermore, the sensing advantages for FTN signals are verified in terms of the expected normalized squared ambiguity function. We show that FTN signals generally enjoy a more robust ranging performance. More importantly, we prove that FTN signaling can effectively avoid the undesired peaks in the considered ambiguity function along the Doppler dimension, thereby reducing the ambiguities in velocity estimation. All these conclusions are explicitly verified by numerical results.