Joint Chirp Parameter Selection and Low-Complexity MMSE Receiver Design for AFDM Systems

Ruiyuan Mao, Qu Luo, Jianguo Li, Fabien Héliot, Tianqi Mao, Pei Xiao, Hee Wook Kim, Kai Yang

Affine frequency division multiplexing (AFDM) has emerged as a promising waveform against doubly selective channels under high-mobility communication scenarios. Optimal chirp parameter selection and reduced-complexity receiver design in AFDM are essential for achieving satisfactory bit error rate (BER) performance with low computational complexity. In this paper, we investigate the joint optimization of chirp-parameter selection and low-complexity minimum mean square error (MMSE)-based receiver design by exploiting the structural characteristics of the AFDM effective channel matrix (ECM). First, a simplified BER performance metric is derived by leveraging the diagonal and circulant structure of the discrete affine Fourier transformation (DAFT), based on which a fast circulant-diagonal aggregation (FCDA) algorithm is developed for efficient $c_1$ selection. Then, a low-complexity banded MMSE (LC-BMMSE) receiver is developed by constructing a cyclic-banded ECM through path-wise structured sparsification, where banded Cholesky factorization is employed to avoid direct matrix inversion. Building upon the proposed BER metric and the LC-BMMSE receiver, a hierarchical-search-based joint chirp parameter and structured sparsification (HS-JCPS) algorithm is further proposed to jointly optimize the chirp parameter and sparsification pattern under a given complexity constraint. Simulation results demonstrate that the proposed FCDA reduces the search time for the optimal $c_1$ by an order of magnitude compared with using a BER-based criterion. Moreover, the proposed HS-JCPS algorithm with the LC-BMMSE receiver can identify a near-optimal $c_1$, while attaining a superior performance-complexity tradeoff.