Estimation of Electrical Characteristics of Complex Walls Using Deep Neural Networks

Electromagnetic wave propagation through complex inhomogeneous walls introduces significant distortions to through-wall radar signatures. Estimation of wall thickness, dielectric, and conductivity profiles may enable wall effects to be deconvolved from target scattering. We propose to use deep neural networks (DNNs) to estimate wall characteristics from broadband scattered electric fields on the same side of the wall as the transmitter. We demonstrate that both single deep artificial and convolutional neural networks and dual networks involving generative adversarial networks are capable of performing the highly nonlinear regression operation of electromagnetic inverse scattering for wall characterization. These networks are trained with simulation data generated from full wave solvers and validated on both simulated and real wall data with approximately 95% accuracy.

💡 Research Summary

The paper addresses the challenging electromagnetic inverse scattering problem of estimating the electrical characteristics of complex walls—specifically thickness, relative permittivity (εr) and conductivity (σ)—using only the scattered electric field measured on the same side of the wall as the transmitter. Traditional deterministic approaches such as the Born approximation, distorted Born iterative methods, and other iterative microwave imaging techniques suffer from low accuracy for high‑dielectric or lossy materials and are computationally intensive, making them unsuitable for real‑time applications. Recent advances in deep learning have shown promise for highly nonlinear and ill‑posed electromagnetic problems, but most prior work has been limited to homogeneous or lossless wall models and to estimating only a few parameters.

To overcome these limitations, the authors generate a large synthetic dataset using two‑dimensional finite‑difference time‑domain (FDTD) simulations. The simulation domain spans 2.5 m × 2.5 m, with a line‑source transmitter placed at (0 m, 0.5 m) emitting a Gaussian pulse centered at 2.4 GHz with a 2 GHz bandwidth. Ten receiver positions are placed 0.2 m behind the wall front face, and the complex frequency‑domain scattered field is recorded from 1.4 GHz to 3.4 GHz at 46.5 MHz intervals. Three wall families are considered: (1) homogeneous lossy dielectric (εr = 4–8, σ = 10⁻⁴–10⁻² S/m, thickness = 10–50 cm), (2) single‑layer dielectric with periodic lossy inclusions, and (3) three‑layer inhomogeneous walls with a higher‑εr inner layer containing periodic loss regions. In total, 867 distinct wall configurations are simulated, providing a rich variety of thicknesses, permittivities, and conductivities.

The input to the neural networks is a concatenated vector of the real and imaginary parts of the scattered field across all frequencies and receiver positions, yielding an 880‑dimensional feature vector. The desired output is a 32 × 32 pixel map (1024 values) of εr and a separate 32 × 32 map of σ, representing the region of interest behind the wall.

Three deep learning architectures are investigated:

1. Fully Connected Neural Network (FC‑NN) – Two hidden layers with 256 and 512 neurons, ReLU activation, sigmoid output, learning rate 2 × 10⁻⁴, Adam optimizer, 100 epochs, batch size 32, binary cross‑entropy loss.

2. Convolutional Neural Network (CNN) – Two 1‑D convolutional layers (64 filters, kernel size 3) followed by a dense layer of 512 neurons and a 1024‑neuron output layer. ReLU in hidden layers, sigmoid in output, learning rate 1 × 10⁻⁴, otherwise same training regime as FC‑NN.

3. Generative Adversarial Network (GAN) – A generator mirroring the CNN architecture (ReLU hidden, tanh output) and a critic consisting of two 1‑D convolutional layers (64 filters each, ReLU) ending with a sigmoid output. The generator receives the scattered‑field vector and produces synthetic εr/σ maps; the critic evaluates whether a map is real or generated. Training uses a learning rate of 2 × 10⁻⁴, Adam optimizer, 500 epochs, batch size 32, binary cross‑entropy for both generator and critic.

Training curves show convergence without over‑fitting for all three models. Performance is evaluated on both unseen simulated cases and on real‑world measurements obtained with a through‑wall radar testbed operating in the same frequency band. Results indicate that the FC‑NN and CNN achieve thickness estimation accuracy of about 95 %, permittivity accuracy of 96 %, and conductivity accuracy of 90 % on simulated data. The GAN, while slightly lower on permittivity, demonstrates superior robustness when the training set is reduced, confirming its advantage in data‑scarce regimes. Crucially, models trained exclusively on simulated data generalize well to measured data, achieving comparable accuracy, which suggests that the domain gap between FDTD‑generated fields and real measurements is modest for the considered setup.

The authors highlight several contributions: (i) a systematic framework that maps broadband scattered fields directly to high‑resolution wall property maps using deep learning, (ii) demonstration that a single‑network approach (FC‑NN or CNN) can achieve near‑real‑time inference, (iii) evidence that adversarial training (GAN) improves resilience to limited training data, and (iv) validation that simulation‑only training can be transferred to real‑world scenarios without additional fine‑tuning.

Limitations are acknowledged. The study is confined to a 2‑D transverse‑magnetic configuration, which may not capture three‑dimensional effects such as edge diffraction or out‑of‑plane scattering. The input field is sampled at only ten receiver locations and a relatively narrow frequency band; richer measurement configurations could further improve resolution and robustness. The output resolution (32 × 32) is deliberately coarse to keep network size tractable, potentially limiting the detection of fine‑scale material variations. Future work is suggested to extend the methodology to full 3‑D modeling, incorporate more diverse antenna arrays, explore higher‑resolution output representations, and investigate transfer‑learning techniques to adapt models across different radar hardware or environmental conditions.

In summary, the paper presents a compelling case for using deep neural networks—particularly fully connected, convolutional, and generative adversarial architectures—to solve the electromagnetic inverse scattering problem for complex, lossy walls. By leveraging extensive FDTD‑generated training data, the authors achieve high‑accuracy, real‑time estimation of wall thickness, permittivity, and conductivity, and demonstrate successful transfer to real measurements, opening pathways for practical through‑wall radar applications such as target de‑cluttering, material inspection, and security screening.