Radar Pulse Signal Detection using Fourier Transform and FT-CNN

Course: Mathematics for Computing (22MAT122) / Elements of Computing Systems (22AIE113)
Institution: Amrita Vishwa Vidyapeetham, School of AI

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Detailed Project Overview

The Challenge

[cite_start]Radar pulse signal detection is a cornerstone of modern electronic warfare, spectrum monitoring, and aerospace communication systems[cite: 14]. Traditional detection techniques often rely on:

• Time-domain analysis: Analyzing the raw signal amplitude over time.
• Hand-crafted features: Manually selecting specific signal attributes.
• Threshold-based decisions: Simple cut-off points for signal classification.

[cite_start]These methods frequently fail in complex environments or when the Signal-to-Noise Ratio (SNR) is low, making it difficult to distinguish true radar pulses from background noise[cite: 15].

The Solution: Frequency Domain Learning

This project proposes a robust deep learning approach that shifts the analysis from the time domain to the frequency domain. [cite_start]By integrating Fourier Transform (FT) with a Convolutional Neural Network (CNN), we create a model (FT-CNN) capable of learning complex, periodic patterns that are invisible in raw time-series data[cite: 17, 286].

[cite_start]The core innovation lies in the FT-CNN architecture, which utilizes the Swish activation function to overcome gradient limitations found in traditional ReLU-based networks, resulting in superior detection reliability[cite: 287].

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Technical Architecture & Methodology

[cite_start]The system follows a strict four-stage pipeline to process signals and classify them as either "Good" (strong pulse) or "Bad" (weak/noisy) [cite: 352-367].

1. Data Preprocessing

• [cite_start]Dataset: We utilize the Ionosphere Dataset from the UCI Machine Learning Repository[cite: 20].
• [cite_start]Input Dimensions: 351 instances, each consisting of 34 continuous numerical features representing radar returns[cite: 22, 23].
• [cite_start]Normalization: Data is normalized to ensure all feature values fall within a consistent range, stabilizing the neural network training[cite: 45].
• [cite_start]Handling Missing Data: Any missing values are imputed using the mean of the respective feature column[cite: 46].

2. Feature Extraction (Fourier Transform)

[cite_start]Instead of feeding raw features into the network, we apply the Fast Fourier Transform (FFT)[cite: 48].

• [cite_start]Transformation: Converts the 34 time-domain features into the frequency domain[cite: 49].
• [cite_start]Magnitude Spectrum: We calculate the absolute value (magnitude) of the FFT output[cite: 51].
• [cite_start]Why this matters: This step isolates periodic signal components and patterns that are characteristic of high-quality radar returns, which are often obscured by noise in the time domain[cite: 50].

3. Deep Learning Model (FT-CNN)

[cite_start]The transformed frequency data is reshaped into a 1 x N x 1 format and passed through a Convolutional Neural Network designed with specific optimizations[cite: 56]:

• [cite_start]Convolutional Layers (Conv1D): These layers slide filters over the frequency data to detect local patterns and spectral features[cite: 58].
• Swish Activation Function: Unlike the standard ReLU (Rectified Linear Unit), we utilize Swish (f(x) = x * sigmoid(x)).
  • Theory: Swish is a smooth, non-monotonic function that allows a small amount of negative information to flow through. [cite_start]This solves the "Dying ReLU" problem where neurons become inactive and stop learning[cite: 287].
  • [cite_start]Result: Improved gradient flow and better learning of complex non-linear patterns[cite: 59].
• [cite_start]Max Pooling: Reduces the dimensionality of the feature maps, making the model computationally efficient and reducing the risk of overfitting[cite: 61, 62].

4. Classification

• [cite_start]Fully Connected Layers: Aggregates the local features learned by the CNN into global patterns[cite: 64].
• [cite_start]Softmax/Sigmoid Layer: Outputs the final probability, classifying the signal as either Class 1 (Good) or Class 2 (Bad)[cite: 65, 25].

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Performance & Model Comparison

We benchmarked the FT-CNN against two other frequency-domain neural networks to validate its superiority.

Model	Architecture Description	Accuracy Achieved
FT-CNN (Proposed)	Convolutional Neural Network with Swish activation. Learns spatial hierarchies in frequency data.	[cite_start]98.57% [cite: 282]
FT-BPNN	Back-Propagation Neural Network. A standard feedforward network that iteratively adjusts weights to minimize error.	[cite_start]90.00% [cite: 282]
FT-PNN	Probabilistic Neural Network. Uses Gaussian kernels and Bayesian decision theory to estimate class probability.	[cite_start]88.57% [cite: 282]

[cite_start]Conclusion: The FT-CNN significantly outperforms traditional architectures (PNN and BPNN) in the frequency domain, proving that learnable convolutional filters are the most effective method for decoding radar signatures[cite: 12, 288].

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🚀 How to Run the Project

This project uses Marimo, a reactive Python notebook format.

1. Install Dependencies:

   pip install marimo numpy pandas matplotlib seaborn scipy scikit-learn tensorflow

2. Run the Main FT-CNN Model:

   marimo run mfc_ft_cnn.py

3. Run Comparison Models:

   marimo run MFC_ft_pnn.py
   marimo run MFC_ft_bpnn.py

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📚 References

1. [cite_start]Dataset: Ionosphere Dataset, UCI Machine Learning Repository[cite: 20].
2. [cite_start]Primary Research: Fengyang Gu, et al., "Detection of Radar Pulse Signals Based on Deep Learning," IEEE[cite: 291].
3. [cite_start]Secondary Research: Vincent G. Sigillito, et al., "Classification of Radar Returns from the Ionosphere using Neural Networks," JHU APL Technical Digest[cite: 293].