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Complex-Valued Convolutional Neural Network With Learnable Activation Function for Frequency-Domain Radar Signal Processing
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DOI：10.1109/TAES.2025.3646567.png)
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Abstract
En 中文
Recent advancements in deep learning and the availability of open-source datasets have enabled real-valued convolutional neural networks (CNNs) and vision transformers to achieve high performance in synthetic aperture radar (SAR) target recognition, SAR-based land use and land cover classification, radar micro-Doppler signature-based human activity recognition (HAR), and small unmanned aerial vehicle (SUAV) target recognition. However, their high computational cost and resource requirements limit deployment in resource-constrained environments. Frequency-domain complex-valued CNNs have recently emerged as a promising alternative, leveraging the convolution theorem to perform efficient spectral convolutions, reducing computational complexity while preserving both amplitude and phase characteristics of SAR and continuous-wave radar signals. Despite their potential, adoption remains constrained by the need for frequency-adaptive complex-valued layers, robust spectral complex-valued activation functions, and efficient parameter initialization methods. Traditional frequency-domain CVNNs often require frequent Fourier transform transitions (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(n \log n)$</tex-math></inline-formula> complexity) for spatial-domain pooling and activations, increasing computational overhead. In addition, many existing complex-valued CNNs employ real-valued activation functions on complex tensors in a split-type manner, which might destroy phase–magnitude relationships and reduce effectiveness for phase-sensitive tasks. Moreover, architectures that use complex-valued weights but rely on real-valued activation functions suffer from phase distortion, limited expressiveness, and mathematical inconsistency. Considering these limitations, we propose a frequency-adaptive complex-valued CNN with a complex-valued learnable activation function designed for SAR-based analysis, SUAV detection, and HAR. Our model operates entirely in the frequency domain and processes only complex-valued data. Extensive experiments on MSTAR-10, EuroSAT all bands, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{DIAT-}\mu \text{RadHAR}$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{DIAT-}\mu \text{SAT}$</tex-math></inline-formula> datasets exhibit performance comparable to existing real and complex-valued CNNs. In addition, we show that our learnable activation function preserves phase–magnitude relationships and mitigates phase distortion, thereby enhancing accuracy compared to the complex-valued rectified linear unit (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {C}\text{ReLU}$</tex-math></inline-formula>) activation function.
Keywords:
Deep learning
frequency-domain complex-valued convolutional neural networks (CNNs)
frequency-domain complex-valued learnable activation function
radar signal processing
synthetic aperture radar (SAR)
Journal
IF:
5.7
Papers:
676
Citations:
2.4W