TargettoClutter Ratio Enhancement of Images in ThroughtheWall Radar Using a Radiation PatternBased DelayedSum Algorithm
 Author: Lim Youngjoon, Nam Sangwook
 Organization: The School of Electrical Engineering and Computer Science, Institute of New Media and Communications, Seoul National University, Seoul, Korea.; The School of Electrical Engineering and Computer Science, Institute of New Media and Communications, Seoul National University, Seoul, Korea.
 Publish: Journal of electromagnetic engineering and science Volume 14, Issue4, p405~410, Dec 2014

ABSTRACT
In this paper, we compare the quality of images reconstructed by a conventional delayedsum (DS) algorithm and radiation patternbased DS algorithm. In order to evaluate the quality of images, we apply the targettoclutter ratio (TCR), which is commonly used in synthetic aperture radar (SAR) image assessment. The radiation patternbased DS algorithm enhances the TCR of the image by focusing the target signals and preventing contamination of the radar scene. We first consider synthetic data obtained through GprMax2D/3D, a finitedifference timedomain (FDTD) forward solver. Experimental data of a 2GHz bandwidth steppedfrequency signal are collected using a vector network analyzer (VNA) in an anechoic chamber setup. The radiation patternbased DS algorithm shows a 6.7dB higher TCR compared to the conventional DS algorithm.

KEYWORD
DelayedSum Algorithm , Synthetic Aperture Radar , TargettoClutter Ratio , ThroughtheWall Radar Imaging

I. INTRODUCTION
Throughthewall radar imaging (TWRI) is an emerging area of research and development dealing with ‘seeing’ the target behind the wall. There have been many studies on TWRI. Some have focused on TWRI system architecture [1], while others have investigated signal processing issues related to TWRI [2–4]. To make the system more complete, however, suitable reconstruction of the radar scene is indispensable. Various reconstruction algorithms have been developed to process TWR measurement data. Several of these are based on beamforming or beamspace multiple signal classification (MUSIC) [5], while others cast the TWRI problem as an inverse scattering problem [6,7]. Among the reconstruction algorithms, a delayedsum (DS) algorithm is widely used because of its algorithmic simplicity and robustness [8]. The conventional DS algorithm uses only the range information of measured data, although the TWR antenna has its own radiation pattern.
In this paper, the synthetic and experimental results of TWRI are presented using a radiation patternbased DS algorithm. We assume that wall clutter is adequately removed using the subspace projection method. Images are evaluated using the targettoclutter ratio (TCR), which is widely used in synthetic aperture radar (SAR). This paper shows that a radiation patternbased DS algorithm shows higher TCR compared to the conventional DS algorithm.
This paper is organized as follows: in Section II, we present the basic theory of TWRI. Then, Sections III and IV deal with the simulation and experiment results. Finally, a conclusion is presented in Section V.
II. THEORY
1. Signal Modeling
We apply SAR signal modeling for TWRI, as depicted in Fig. 1. The second layer is a wall with thickness represented by d_{w} and permittivity by ԑ_{w}. The first and third layers are free space. We assume a monostatic radar case, and
N antennas are uniformly spaced parallel to the wall. ForP point targets, due to the targets only, the signal received at then th antenna is given by [8],where
s (t ) is the transmitted signal convolved with the twoway transfer function of the wall,σ _{p} is the reflection coefficient of thep th target, andτ _{n,p} is the twoway traveling time between then th antenna and thep th target.2. Wall Clutter Mitigation
In TWRI, strong reflections from the wall often cause the target signal to become obscured. There are various methods of mitigating such wall clutter [2–4]. In this paper, we adopt the subspace projection method. This is based on the fact that the most significant terms of signal spectrum are dominated by the wall clutter. A received signal matrix,
Z , can be factorized using singular value decomposition (SVD) as:U = [u _{0},u _{1}, ... ,u _{N1}] andV = [v _{0},v _{1}, ... ,v _{M1} ] are unitary matrices containing the left and right singular vectors, andΛ is an [M, N] diagonal matrix containing singular values in decreasing order.H denotes Hermitian. If wall clutter is spanned by the firstp singular vectors, the clutter can be removed by projecting the signal matrix on the remaining singular vectors, i.e.,with
where
e_{target} andI is the wall clutter removed from the data matrix and identity matrix, respectively [2].3. The Conventional DS Algorithm
A DS algorithm is a simple and robust image reconstruction algorithm for TWRI. The
ij th pixel value in the DS image is [8]:where
τ _{n,(i,j)} is the twoway traveling time, through the air and the wall, between the nth antenna and theij th pixel location.4. The Radiation PatternBased DS Algorithm
The conventional DS algorithm considers only a range of targets. This makes the radar scene contaminated. In order to obtain a clean radar scene and crossrange resolution that is independent of slantrange, the aperture segment length has to be directly proportional to the slantrange [9]. This is equivalent to keeping the integration angle at a fixed value. By using a radiation pattern window, a similar effect can be achieved simply. The DS algorithm can be rewritten as follows:
where
w (n ,(i,j )) is the radiation pattern window. The window matches the antenna's location and theij th pixel to the radiation pattern. This formula makes the algorithm more close to real experimental scenario.5. The TargettoClutter Ratio
TCR is commonly used to evaluate the quality of a SAR image. TCR is calculated as [8]:
where
A_{t} is the target area,A_{c} is the clutter area, andN_{c} is the number of pixels in the clutter area.III . SIMULATION
In order to verify the theory, we first consider the simulated data obtained through a finitedifference timedomain (FDTD) forward solver [10]. Elementary current sources located at a standoff distance of
h_{w} = 1.25 m from the front face of the wall are employed and the field data are collected atN = 41 positions uniformly taken over the measurement line Ω = [0 2] m. The wall consists of a homogeneous dielectric layer of thicknessd_{w} = 0.1 m, relative dielectric permittivity ԑ_{w} = 6.0, and conductivityσ = 0.02 (S/m) for the modeling of the concrete wall. A Ricker waveform with a center frequencyf _{0} = 2.5 GHz is used. As a simulation example, two circular metallic scatterers with a radius equal to 0.05 m are considered. The two circular scatterers’ centers are located ath_{t} = 0.3 m from the wall and separated with 0.2 m from the center of the Ω (See Fig. 2). Fig. 3 shows DS images of the scene reconstructed by two different DS algorithms. We assumed that the radiation pattern has cos^{10}θ variation. The DS image is normalized to the maximum value of the image. The targetlike signature and curvatures being shown along the horizontal line is the effect of interaction (multiple reflection) between the two targets. To remove them, additional signal processing techniques are needed. For quantitative evaluation of the quality of the images, Table 1 shows the TCR results of each DS algorithm.Basically, the elementary current source has an isotropic radiation pattern so the patternbased DS algorithm is not practical. However, using a directional radiation pattern window, we can reconstruct a more focused target image. In addition, assuming a directional pattern can make the wall clutter area cleaner. This makes the TCR superior to the conventional DS algorithm.
IV. EXPERIMENT
To validate the theory, an experiment is carried out. The experimental setup is implemented with dualridged horn antennas (DRH020180) [11] having radiation pattern of Fig. 4 and a vector network analyzer (VNA; Agilent E5071B). A linear array of 2.0 m and 0.1 m spacing between antenna locations is synthesized. The VNA generates a 2GHz bandwidth steppedfrequency signal covering 4–6 GHz with a 40 MHz frequency step. Using an inverse Fourier transform (IFT),
S _{21} can be transformed from frequency domain data to time domain data [12]. The wall is placed at 1.0 m from the antenna and consists of a homogeneous plywood layer of thickness 0.02 m. The target is placed at 0.7 m from the wall and 0.1 m from the center of the measurement line (see Fig. 5).Fig. 6 and Table 2 show the DS images and TCR results, respectively. To describe the radiation pattern more simply, we assumed that the radiation pattern has a cos^{10}θ variation. This assumption fits well in a certain angle in which most of the energy exists. The TCR of the image reconstructed by the radiation patternbased DS algorithm is improved 6.7 dB compared to the conventional DS algorithm. Some remaining clutter near the target in Fig. 6(c) is presumed to be the nonideal measurement effect. To mitigate that kind of error, more precise experiments are needed.
V. CONCLUSION
In this paper, the performance of the conventional and radiation patternbased DS algorithms was presented. Synthetic and experimental data were used to evaluate the TCR. As a result, the TCR of the radiation patternbased DS algorithm showed a remarkable improvement over the conventional DS algorithm.
There are two main reasons for this improvement. First, the radiation patternbased DS algorithm prevents contamination of the radar scene with the same distance from the antenna to the target. Second, it concentrates the target signal more closely. In the simulation result, the target is imaged at a slightly longer distance from the antenna because we did not consider the wave delay in the dielectric medium. Future work could be directed toward the study of the effect of wall parameters in TWRI, wall clutter mitigation, TWRI in inhomogeneous wall cases, and so on.

11.

[]

[Fig. 1.] The throughthewall radar imaging (TWRI) scenario.

[]

[]

[]

[]

[]

[]

[]

[Fig. 2.] Simulation scenario.

[Fig. 3.] Reconstructed images with synthetic data. (a) Raw data image, (b) DS image (without wall clutter mitigation), (c) DS image (with wall clutter mitigation, conventional DS), and (d) DS image (with wall clutter mitigation, radiation patternbased DS). DS = delayedsum.

[Table 1.] TCR measurement results (for Fig. 3)

[Fig. 4.] Gain of antenna: (a) Eplane, (b) Hplane.

[Fig. 5.] Experimental setup.

[Fig. 6.] Reconstructed images with experimental data. (a) Raw data image, (b) DS image (without wall clutter mitigation), (c) DS image (with wall sclutter mitigation, conventional DS), and (d) DS image (with wall clutter mitigation, radiation patternbased DS). DS = delayedsum.

[Table 2.] TCR measurement results (for Fig. 6)