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Doppler Invariant CNN for Signal Classification

Avi Bagchi, Dwight Hutchenson

TL;DR

The study tackles robust signal classification in Doppler-affected, contested environments by designing a Doppler-invariant CNN that operates in the frequency domain using complex-valued layers and adaptive polyphase sampling (APS) pooling. By proving invariance to Doppler-induced bin shifts and employing padding to handle fractional shifts, the approach achieves reliable performance without Doppler-based data augmentation, offering improved generalization and interpretability. Key findings show strong robustness to integer-bin Doppler shifts and near-invariance under fractional shifts when properly padded, albeit with some base-accuracy reductions for certain modulations and increased computational cost due to padding. This invariance-driven framework has practical implications for real-world spectrum monitoring where Doppler effects are common and training data may be limited.

Abstract

Radio spectrum monitoring in contested environments motivates the need for reliable automatic signal classification technology. Prior work highlights deep learning as a promising approach, but existing models depend on brute-force Doppler augmentation to achieve real-world generalization, which undermines both training efficiency and interpretability. In this paper, we propose a convolutional neural network (CNN) architecture with complex-valued layers that exploits convolutional shift equivariance in the frequency domain. To establish provable frequency bin shift invariance, we use adaptive polyphase sampling (APS) as pooling layers followed by a global average pooling layer at the end of the network. Using a synthetic dataset of common interference signals, experimental results demonstrate that unlike a vanilla CNN, our model maintains consistent classification accuracy with and without random Doppler shifts despite being trained on no Doppler-shifted examples. Overall, our method establishes an invariance-driven framework for signal classification that offers provable robustness against real-world effects.

Doppler Invariant CNN for Signal Classification

TL;DR

The study tackles robust signal classification in Doppler-affected, contested environments by designing a Doppler-invariant CNN that operates in the frequency domain using complex-valued layers and adaptive polyphase sampling (APS) pooling. By proving invariance to Doppler-induced bin shifts and employing padding to handle fractional shifts, the approach achieves reliable performance without Doppler-based data augmentation, offering improved generalization and interpretability. Key findings show strong robustness to integer-bin Doppler shifts and near-invariance under fractional shifts when properly padded, albeit with some base-accuracy reductions for certain modulations and increased computational cost due to padding. This invariance-driven framework has practical implications for real-world spectrum monitoring where Doppler effects are common and training data may be limited.

Abstract

Radio spectrum monitoring in contested environments motivates the need for reliable automatic signal classification technology. Prior work highlights deep learning as a promising approach, but existing models depend on brute-force Doppler augmentation to achieve real-world generalization, which undermines both training efficiency and interpretability. In this paper, we propose a convolutional neural network (CNN) architecture with complex-valued layers that exploits convolutional shift equivariance in the frequency domain. To establish provable frequency bin shift invariance, we use adaptive polyphase sampling (APS) as pooling layers followed by a global average pooling layer at the end of the network. Using a synthetic dataset of common interference signals, experimental results demonstrate that unlike a vanilla CNN, our model maintains consistent classification accuracy with and without random Doppler shifts despite being trained on no Doppler-shifted examples. Overall, our method establishes an invariance-driven framework for signal classification that offers provable robustness against real-world effects.

Paper Structure

This paper contains 7 sections, 2 theorems, 13 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Technique
  4. Numerical Results
  5. Conclusion
  6. Proof of Theorem \ref{['thm:1']}
  7. Additional Graphs

Key Result

Theorem 1

Let $N_i$ denote the signal length entering APS layer $i$. If $N_i \bmod s = 0$ for all APS layers, then $f_\theta$ is invariant with respect to a pure Doppler shift, i.e., where $T$ denotes a Doppler transformation corresponding to an integer bin shift $m \in \mathbb{Z}$.

Figures (9)

  • Figure 1: MaxPool (kernel=stride=3) vs APS (stride=2) for frequencies $a<b<c<d<e<f$. The MaxPool operation yields two distinct sets before and after a one bin shift while Algorithm \ref{['alg:complex_apspool']} yields the same set regardless of the shift.
  • Figure 2: Average Epoch Time (s) vs Padding
  • Figure 3: Absolute Accuracy Change (Chirp) vs Padding
  • Figure 4: Absolute Accuracy Change (Hopping Tone) vs Padding
  • Figure 5: Absolute Accuracy Change (Tone) vs Padding
  • ...and 4 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • proof
  • proof : Proof of Theorem \ref{['thm:1']}