Source-linked AI summary
Explainable deformable matched filtering reveals measurable departures from classical receiver theory in optical wireless communications
Paul Anthony Haigh
TL;DR
Existing learned receivers can improve on classical matched filtering but provide limited insight into why practical systems depart from its assumptions. This paper learns interpretable deformations of the matched filter and finds an 18.1% median relative EVM reduction across 1,600 conditions, with structured, signalling-dependent mismatches.
Problem
Existing adaptive and neural receivers optimise detection performance but provide limited insight into the origin and structure of departures from matched-filter theory.
Method
The framework constrains machine learning to predict low-dimensional, interpretable deformations of the theoretical matched filter from compact receiver-state descriptors.
Results
18.1% median relative EVM reduction occurred across 1,600 format-impairment-attenuation-session conditions, with improvements spanning signalling formats and receiver conditions.
Takeaways & Limitations
Matched-filter departures are measurable, structured and signalling-dependent, with spectral and structural forms that vary across channel conditions and signalling families.
Takeaways & Limitations
The selected receiver-state features are one physically motivated parameterisation rather than a unique or optimal description.
Abstract
from arXiv · showhide
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.
Training and evaluation · Supplementary Information
The supplementary methods define the training protocol, matched-filter comparison procedures, latent-state analysis, and deformation metrics used to quantify receiver mismatch. Data and code are publicly available, while statistical summaries rely on session-level observations and correlation analyses.
- Training and evaluation: Training used experimentally acquired waveform datasets split into 70% training, 15% validation, and 15% test subsets with random seed 1234.The network was optimised for 50 epochs using AdamW with learning rate 1×10-3, weight decay 1×10-4, and batch size 32.
- Training and evaluation: The objective combined receiver EVM with smoothness, curvature, coefficient-magnitude, and stability terms weighted 10−3, 10−4, 10−5, and 10−4, respectively.
- Training and evaluation: CMF and DMF used identical matched-filtering, symbol-rate sampling, and timing-alignment procedures, isolating the effect of filter deformation.
- Training and evaluation: The 64-dimensional latent receiver state was extracted from the second KAN hidden layer, with up to 2,000 examples per condition yielding 819,200 latent vectors.A global mean-centred PCA explained 27.15%, 9.44%, and 8.25% of variance in its first three components.
- Training and evaluation: Condition-level summaries were arithmetic means over independent sessions, with 95% confidence intervals computed across session-level observations.Deformation–performance relationships used Pearson, Spearman rank, and partial correlations controlling for neutral-density attenuation; no hypothesis test defined DMF benefit.
- Training and evaluation: Deformation energy quantifies overall departure from the nominal matched filter, while relative deformation energy provides a scale-independent measure of receiver mismatch.Coefficient energy quantifies the magnitude of the latent deformation required to generate the observed filter modification.
- Training and evaluation: These deformation metrics compare receiver mismatch across signalling formats, impairment classes, and optical attenuation levels, directly measuring departures from matched-filter optimality.
- Supplementary Information: The study provides both its data and code through the public repository github.com/qmul-optocomms/kan-dmf-public-data.