AFDM-ISAC With Fractional Delay-Doppler Coupling

2026-08-12

AI Summary

This work addresses the challenges in AFDM-ISAC systems arising from energy leakage, peak shift, and misaligned matching score surfaces caused by representing continuous delay–Doppler parameters on discrete grids, as well as the inherent delay–Doppler coupling. To overcome these issues, the paper proposes a transform-domain sparse-aware model based on fractional DAFT-domain responses and develops a Coupled-Coordinate Newtonized Orthogonal Matching Pursuit (CC-NOMP) algorithm. By parameterizing local ridge structures via coupled coordinates and integrating Newton refinement, safe updates, coupled-aligned delay optimization, and cyclic multi-target refinement, the method enables joint high-accuracy estimation of angle and delay–Doppler parameters. Simulations demonstrate that CC-NOMP substantially reduces delay and Doppler estimation errors for off-grid targets, closely approaching the Cramér–Rao bound while maintaining angle estimation accuracy comparable to existing approaches.

Abstract

Affine frequency division multiplexing (AFDM) is a promising chirp-based multicarrier waveform for high-mobility integrated sensing and communication (ISAC). Accurate angle, delay, and Doppler estimation is essential for AFDM sensing. Since target delays and Doppler shifts are generally continuous-valued, representing them on a discrete delay--Doppler grid causes energy leakage and peak displacement in the discrete affine Fourier transform (DAFT) domain. The AFDM chirp also induces delay--Doppler coupling in the DAFT-domain response. The resulting DAFT-domain matching-score surface exhibits a local ridge that is not aligned with the normalized-delay and normalized-Doppler axes. To address these issues, this paper investigates joint estimation of angle and continuous-valued delay--Doppler parameters for a colocated AFDM-ISAC sensing architecture. A transform-domain sparse sensing model is formulated from the fractional DAFT-domain response. Based on this model, a coupled-coordinate Newtonized orthogonal matching pursuit (CC-NOMP) estimator is developed. CC-NOMP uses the AFDM-induced coupling coordinate to parameterize the dominant local ridge. It combines coupled-coordinate Newton refinement with safeguarded updates, coupling-aligned delay refinement, and cyclic multi-target refinement to estimate angle, continuous normalized delay, and normalized Doppler. A deterministic Cramér--Rao bound and a dominant-order complexity analysis are also derived. Simulation results with continuous-valued off-grid target parameters show that CC-NOMP achieves lower delay and Doppler error floors than the considered baselines while maintaining comparable angle-estimation accuracy.

Problem

• AFDM-ISAC
• delay-Doppler coupling
• continuous parameter estimation
• off-grid sensing
• angle-delay-Doppler estimation

Innovation

• AFDM-ISAC
• fractional DAFT
• delay-Doppler coupling
• CC-NOMP
• off-grid estimation