AI 中文总结
研究AFDM系统中联合线性调频参数选择与低复杂度MMSE接收机设计，利用有效信道矩阵结构特性，推导BER指标，开发FCDA算法选\(c_1\)，构建LC-BMMSE接收机，提出HS-JCPS算法，实现性能与复杂度权衡，减少搜索时间。
AI 中文摘要
仿射频分复用（AFDM）已成为高移动性通信场景下对抗双选信道的一种有前景的波形。AFDM中最优线性调频参数选择和降低复杂度的接收机设计对于以低计算复杂度实现令人满意的误码率（BER）性能至关重要。本文通过利用AFDM有效信道矩阵（ECM）的结构特性，研究线性调频参数选择和基于低复杂度最小均方误差（MMSE）的接收机设计的联合优化。首先，利用离散仿射傅里叶变换（DAFT）的对角和循环结构推导出简化的BER性能指标，在此基础上开发了快速循环对角聚合（FCDA）算法用于高效的\(c_1\)选择。然后，通过路径结构化稀疏化构建循环带状ECM来开发低复杂度带状MMSE（LC-BMMSE）接收机，采用带状Cholesky分解避免直接矩阵求逆。基于提出的BER指标和LC-BMMSE接收机，进一步提出基于分层搜索的联合线性调频参数和结构化稀疏化（HS-JCPS）算法，在给定复杂度约束下联合优化线性调频参数和稀疏化模式。仿真结果表明，与使用基于BER的准则相比，所提出的FCDA将最优\(c_1\)的搜索时间减少了一个数量级。此外，所提出的带有LC-BMMSE接收机的HS-JCPS算法可以识别接近最优的\(c_1\)，同时实现优异的性能-复杂度权衡。
英文摘要
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.
