AI 中文总结
该研究提出可解释可形变匹配滤波框架，结合Kolmogorov-Arnold Network，在光无线通信测试平台上使接收机性能提升18.1%，揭示了与经典匹配滤波最优性的结构化偏离。
AI 中文摘要
匹配滤波是通信理论的核心成果，当接收波形满足特定假设时，它能提供最优线性接收机。实际通信系统很少满足这些假设，而性能优于经典匹配滤波的学习型接收机，却难以揭示这些改进对基础理论局限性的体现。本文提出一种可解释可形变匹配滤波框架，其中机器学习被约束为学习经典匹配滤波的低维形变，而非替换它。由于每个学习到的修正都相对于理论匹配滤波解定义，该形变成为接收机失配的可测量表示，而非无约束优化。通信波形仍完全由匹配滤波处理，而Kolmogorov-Arnold Network仅从可物理解释的接收机状态描述符预测形变。使用包含10种信号格式、4类损伤和1600种条件的光无线通信测试平台，我们表明学习到的形变提升了接收机性能，实现了18.1%的中位数相对误差矢量幅度降低，同时揭示了与经典匹配滤波最优性的偏离。不同信号族占据不同形变区域，频谱分析确定了接收机失配的潜在物理机制，而潜在接收机状态组织表明这些偏离是结构化的，而非任意的。
英文摘要
Matched filtering is a central result of communication theory, providing the optimal linear receiver when the received waveform satisfies specific assumptions. Practical communication systems rarely satisfy these assumptions, yet learned receivers that outperform the classical matched filter provide little insight into what those improvements reveal about the limitations of the underlying theory. Here we introduce an explainable deformable matched-filter framework in which machine learning is constrained to learn a low-dimensional deformation of the classical matched filter rather than replacing it. Because every learned correction is defined relative to the theoretical matched-filter solution, the deformation becomes a measurable representation of receiver mismatch rather than an unconstrained optimisation. The communication waveform remains processed entirely by the matched filter, while a Kolmogorov-Arnold Network predicts only the deformation from physically interpretable receiver-state descriptors. Using an optical wireless communication testbed spanning ten signalling formats, four impairment classes and 1,600 conditions, we show that learned deformations improve receiver performance, yielding a median relative error-vector-magnitude reduction of 18.1%, while revealing departures from classical matched-filter optimality. Different signalling families occupy distinct deformation regimes, spectral analysis identifies the physical mechanisms underlying receiver mismatch, and latent receiver-state organisation demonstrates that these departures are structured rather than arbitrary.
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