A Unified Framework for Ambiguity Function Shaping and PAPR Control in AFDM Systems

Affine frequency division multiplexing (AFDM) has emerged as a promising integrated sensing and communication (ISAC) waveform due to its intrinsic chirp signalling nature. Nevertheless, practical AFDM-based ISAC still faces two key obstacles, namely, high ambiguity function (AF) sidelobes and high peak-to-average power ratio (PAPR). By leveraging the reserved chirp-subcarrier (RCS) symbols, we develop a unified AFDM waveform design framework for AF shaping and/or PAPR control. The proposed framework supports three modes: AF shaping via weighted integrated sidelobe level (ISL) minimization, PAPR minimization, and joint AF shaping and PAPR control under a prescribed PAPR constraint. To solve the formulated nonconvex problem and to accommodate the discrete-phase constraints on the optionally optimized pre-chirp parameters, a joint ISL-PAPR-discrete-phase majorization-minimization (JIPD-MM) algorithm is developed. Simulation results verify the effectiveness of the proposed framework under all three design modes. The joint mode further demonstrates that the prescribed PAPR constraint can be effectively satisfied while still achieving meaningful ISL reduction. These gains are also reflected in improved weak-target detectability under multitarget scenarios and lower bit error rate (BER) under power-amplifier (PA) nonlinearity.