Multistart projected gradient descent optimization with Armijo backtracking-based pre-chirp tuning for PAPR reduction in AFDM

Abstract

The coalescence of sensing and communication is one of the major requirements of 6 G wireless communication. Affine Frequency Division Multiplexing (AFDM) is propitious in the attainment of Integrated Sensing and Communication (ISAC). The signal processing technique in AFDM offers adaptable chirp parameters pivoting on channel conditions. The major concern in AFDM is the high Peak-to-Average-Power ratio (PAPR). The pliability of pre-chirp parameter expedites the PAPR reduction strategy in AFDM. In this paper, optimizing a single scalar pre-chirp parameter for PAPR reduction is considered a one-dimensional nonlinear nonconvex problem. The Projected Gradient Descent using Finite Difference method with Armijo Backtracking (PGA) minimizes the non-smooth, non-convex PAPR objective function. To further explore the global optimum, a multi-start strategy is adopted, which solves the optimization problem from several initial points and selects the best solution with the minimum PAPR. To facilitate robust AFDM-ISAC sensing parameter estimation, a bounded constraint is instilled on the pre-chirp parameter such that the superposition of complex exponentials at the receiver is negligible. Simulation results show that the proposed algorithm achieves a 51.75% reduction in PAPR without compromising BER. Additionally, the computational time and the distribution of the optimal pre-chirp parameter of the proposed algorithm are compared with those of other traditional algorithms.