An Ambiguity-Function-Assisted Newtonized Channel Estimation Method for Pulse-Shaped AFDM Under Fractional Delay and Doppler

Abstract

Accurate channel estimation for pulse-shaped AFDM systems over doubly selective channels with fractional normalized delay and Doppler remains challenging. This paper proposes a low-complexity ambiguity-function-assisted newtonized channel (AFNC) estimation method. Specifically, we first present a closed-form input-output relation for pulse-shaped affine frequency division multiplexing (AFDM) under fractional normalized delay and Doppler. As a further step, we demonstrate that the input-output relation admits a low-complexity representation by offline precomputing and storing the discretized ambiguity function of the shaping pulse, followed by tailored cyclic-shift and stacking operations. Building on this representation, AFNC performs fractional delay-Doppler channel estimation through Newtonized refinement, where the required Jacobian and Hessian updates are computed efficiently using the low-complexity input-output representation. Simulation results confirm the effectiveness of the proposed approach.