Abstract
Affine frequency division multiplexing (AFDM) achieves full diversity in doubly selective channels. By exploiting its clear interference structure, decision feedback equalization (DFE) offers a robust, non-iterative receiver, yet suffers from severe error propagation. A permutation-driven DFE (P-DFE) framework is proposed to optimize both single-trajectory reliability and parallel structural diversity. For the single-branch P-DFE, permutation acts as an interference-shaping mechanism. Guided by derived statistical bounds, a low-complexity energy graph (EG) algorithm is developed to leverage the sparse AFDM channel for approximating optimal reliability sorting, reshaping the signal-to-interference-plus-noise ratio (SINR) profile to suppress initial errors. To decouple error propagation in high order constellations, permutation is elevated to a branch-generation tool for a parallel scheme. Specifically, a combination of cyclic shifts and time reversal is applied to the base order, generating a quality-preserving branch family. An optimal permutation-driven quad-branch DFE (P-QDFE) is configured by maximizing the harmonic mean of Kendall-Tau (KT) distances, minimizing inter-branch correlation. Simulations show P-QDFE effectively suppresses error floors in high-order modulations. At practical pre-decoding thresholds, this non-iterative scheme outperforms highly-iterated orthogonal approximate message passing (OAMP) under low-density parity-check (LDPC) coding, while integrating incomplete Cholesky factorization (ICHOL) ensures linear minimum mean square error (LMMSE)-level complexity.