Explainable deformable matched filtering reveals measurable departures from classical receiver theory in optical wireless communications

Abstract

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.