Sensing-Compatible AFDM Channel Estimation in Time-Scaled Wideband Doubly-Dispersive Channels

Abstract

Affine frequency division multiplexing (AFDM) is a promising chirp-based waveform for high-mobility and underwater acoustic communications. However, underwater acoustic channels are inherently wideband and characterized by timescaling effects, where Doppler distortion cannot be accurately modeled as a simple frequency shift. Instead, Doppler time scaling effect spreads an embedded pilot over a delay- and scale-dependent support region in the discrete affine Fourier (DAF) domain, making conventional narrowband pilot-guard designs insufficient. This paper proposes a sensing-compatible embedded-pilot AFDM frame structure for wideband time-scaled channel estimation. Specifically, the guard region is constructed by using the principle of stationary phase (POSP) to predict the receive-side support of the wideband pilot response across admissible channel delay and Doppler scale. Based on the proposed frame structure, we develop a POSP-guided energy projection (POSP-EP) method along with an orthogonal matching pursuit (OMP)-based scheme specifically developed for the wideband channel estimation. Simulation results demonstrate that the proposed frame structure achieves effective pilot-response coverage with reduced leakage into the data region. Moreover, the proposed scheme improves both normalized mean square error (NMSE) performance and bit error rate (BER), while preserving the desired properties of wideband ambiguity function under random data transmission conditions.