Estimation of Electrical Characteristics of Complex Walls Using Deep Neural Networks

1. Problem Statement

Through-wall radar (TWR) systems suffer from significant signal distortions caused by the complex propagation of electromagnetic waves through inhomogeneous walls. These distortions include reflection, refraction, attenuation, ringing, and multipath effects, which create "ghost targets" and obscure real targets.

• Core Challenge: To deconvolve wall effects from target scattering signatures, the radar system must accurately estimate the wall's electrical characteristics (thickness, dielectric profile $\epsilon_r$, and conductivity profile $\sigma$).
• Limitations of Existing Methods:
  • Deterministic/Iterative Methods: Techniques like Born approximation, backpropagation, and iterative microwave imaging (e.g., DBIM) are computationally expensive, require high memory, and often fail with high dielectric constants or lossy materials. They are generally unsuitable for real-time reconstruction.
  • Traditional Machine Learning: Previous neural network approaches were limited to estimating simple parameters (e.g., width and permittivity) for homogeneous walls only.
• Objective: The authors propose using Deep Neural Networks (DNNs) to solve the highly non-linear Electromagnetic Inverse Scattering (EIS) problem to estimate both dielectric and conductivity profiles of complex, multi-layered, and lossy walls.

2. Methodology

The authors propose a data-driven approach where DNNs learn the mapping from scattered electric field data to wall property profiles.

A. Data Generation (Simulation)

• Technique: Finite Difference Time Domain (FDTD) simulations were used to generate training data.
• Setup: A 2D Cartesian space with a broadband vertically polarized source (Gaussian pulse, 2.4 GHz center, 2 GHz bandwidth).
• Wall Models: Three distinct wall types were simulated to represent real-world complexity:
  1. Type 1: Single-layer homogeneous lossy dielectric (varying $\epsilon_r$, $\sigma$, and thickness).
  2. Type 2: Single-layer dielectric with periodic lossy regions (inhomogeneous).
  3. Type 3: Multi-layered dielectric walls (e.g., insulation/facades) with periodic lossy regions.
• Dataset: 867 distinct wall cases. The input was the frequency-domain scattered electric field (real and imaginary parts) recorded at 10 receiver positions. The output was the vectorized 2D spatial profiles of $\epsilon_r$ and $\sigma$.

B. Neural Network Architectures

Three distinct DNN architectures were designed and compared:

1. Fully Connected Neural Network (FC-NN): A multi-layer perceptron with two hidden layers (256 and 512 nodes) and an output layer (1024 nodes).
2. Convolutional Neural Network (CNN): Incorporates 1D convolutional and pooling layers to capture spatial features, followed by dense layers.
3. Generative Adversarial Network (GAN): A game-theoretic framework consisting of:
   • Generator ($G_\theta$): Maps scattered electric fields to synthetic wall profiles.
   • Critic ($C_\phi$): Distinguishes between real (ground truth) and fake (generated) profiles.
   • Rationale: GANs are hypothesized to be more robust to smaller or less diverse datasets due to their adversarial training nature.

C. Training Strategy

• Loss Functions: Binary cross-entropy for FC-NN and CNN; a minimax value function for GAN.
• Optimization: Adam optimizer with varying learning rates ($2\times10^{-4}$ for FC-NN/CNN, $2\times10^{-4}$ for GAN).
• Validation: Models were tested on simulated test sets and, crucially, on real-world measured data to test generalization.

3. Key Contributions

1. Complex Wall Characterization: The study extends DNN applications beyond homogeneous walls to inhomogeneous, multi-layered, and lossy walls, estimating both dielectric and conductivity profiles simultaneously.
2. GAN for EIS: It demonstrates the efficacy of GANs in electromagnetic inverse scattering, showing they are superior to single-network approaches (FC-NN/CNN) when training data is limited.
3. Sim-to-Real Transfer: The paper validates that networks trained entirely on simulated FDTD data can successfully estimate the characteristics of real-world physical walls, bridging the simulation-to-reality gap.
4. Comprehensive Comparison: A rigorous quantitative and qualitative comparison of FC-NN, CNN, and GAN across different wall complexities and data volumes.

4. Results

A. Simulation Results

• Accuracy: The models achieved approximately 95% accuracy for wall thickness, 96% for dielectric profiles, and 90% for conductivity profiles.
• Performance Comparison:
  • Dielectric Profiles: All three methods performed well, with CNN and GAN showing slightly lower Normalized Mean Square Error (NMSE) than FC-NN.
  • Conductivity Profiles: Reconstruction was harder than dielectric profiles (higher NMSE). GAN and CNN outperformed FC-NN in capturing distinct lossy regions.
  • Data Scarcity: When training data volume was reduced (e.g., from 90% to 70% of the dataset), GAN maintained superior performance compared to FC-NN and CNN, confirming its robustness to limited data.
  • Complexity: GAN required significantly longer training times (120–150 mins) compared to FC-NN/CNN (30–45 mins) due to the dual-network architecture.

B. Experimental (Real-World) Results

• Setup: Measurements were taken on two exterior brick walls (30cm and 40cm thick) and a wooden door using a Vector Network Analyzer (VNA) and horn antennas.
• Thickness Estimation:
  • GAN: Estimated wall thickness with ~5% error.
  • FC-NN/CNN: Estimated thickness with 10–12% error.
• Profile Reconstruction: GAN successfully reconstructed the dielectric profiles of the complex brick/concrete walls, correctly identifying layer structures that FC-NN and CNN struggled with.
• Limitation: The models failed to reconstruct the profile of a 3.5cm wooden door. This was attributed to the door being largely transparent to the 1.4–2.4 GHz frequency range, resulting in negligible scattered energy for the network to analyze.

5. Significance and Conclusion

This paper establishes Deep Neural Networks as a viable, real-time alternative to traditional iterative methods for electromagnetic inverse scattering.

• Practical Impact: By accurately estimating wall properties, TWR systems can effectively "deconvolve" wall effects, significantly improving target detection and reducing false alarms in through-wall imaging scenarios.
• Robustness: The finding that GANs trained on simulation data can generalize to real-world measurements is a critical step toward deploying AI-driven radar systems in practical environments without needing exhaustive real-world calibration data.
• Trade-off: While GANs offer the highest accuracy and robustness to data scarcity, they come at the cost of higher computational training time. FC-NN and CNN remain viable for scenarios with abundant data and strict latency requirements.

In summary, the authors successfully demonstrated that deep learning, particularly GANs, can solve the highly non-linear problem of characterizing complex, inhomogeneous walls, paving the way for more advanced and accurate through-wall radar technologies.