Achieving Secure and Low-PAPR AFDM Transmission with Pre-Chirp Signal Design

This paper proposes a pre-chirp shift keying-aided affine frequency division multiplexing (PCSK-AFDM) scheme for secure and low peak-to-average power ratio (PAPR) high-mobility communications. Motivated by the fact that existing secure AFDM designs mainly rely on modifying pre-chirp parameters, we exploit legitimate channel state information to construct a secure permutation between information indices and cyclic shifts of the pre-chirp matrix, thereby conveying additional information without altering the conventional chirp-parameter configuration. To reduce PAPR while introducing additional waveform uncertainty at the eavesdropper (Eve), we further incorporate affine Fourier-domain phase rotations and develop an efficient gradient-screened refinement-aided quantized projected gradient descent (GSR-QPGD) algorithm. We derive the bit error ratio (BER) performance of both the legitimate receiver (Bob) and Eve, along with their mutual information and secrecy mutual information. For scalable detection, a candidate-screened orthogonal approximate message passing (CS-OAMP) detector is proposed. Simulation results show that Eve's BER approaches 0.5, GSR-QPGD effectively reduces PAPR while mitigating nonlinear power amplifier (PA) distortion and increasing Eve's information entropy, and CS-OAMP achieves improved BER performance with a favorable complexity trade-off.