Multi-Chirp AFDM for Rydberg Atomic Quantum Receivers: Waveform and Algorithm Design

Abstract

We propose a multi-chirp affine frequency division multiplexing (MC-AFDM) scheme for joint delay-Doppler estimation with Rydberg atomic quantum receivers (RAQRs). The work is motivated by the fact that RAQRs, while offering superior sensitivity and advantageous sensing capabilities, suffer from an optical ambiguity due to Doppler shifts in doubly-dispersive (DD) channel caused by target mobility, which precludes the reliable estimation of delay-Doppler parameters. To resolve this optical ambiguity and unleash the potential of RAQRs in DD channel, the proposed MC-AFDM employs multiple distinct AFDM post-chirp signals to overcome the rank-deficiency problem of the classical single-chirp AFDM (SC-AFDM), thereby enabling accurate delay-Doppler estimation of multiple targets. Our analysis reveals that the edge distribution of the multiple post-chirp parameters can further improve estimation accuracy by minimizing the condition number. Building on the proposed MC-AFDM waveform, we design a sequential signal processing algorithm based on orthogonal matching pursuit (OMP) and least squares (LS), and we derive the theoretical lower bounds for delay and Doppler estimation. Numerical results show that the proposed MC-AFDM improves range and velocity estimation accuracy by up to two orders of magnitude compared to the classical SC-AFDM, and approaches its theoretical bounds through post-chirp optimization, validating the quantum-induced advantage of RAQRs for high-resolution quantum wireless sensing.