An image focusing method based on a realistic model for a wall is proposed for throughthewall radar imaging using a multipleinput multipleoutput array. A technique to estimate the wall parameters (i.e., position, thickness, and permittivity) from the radar returns is developed and tested. The estimated wall properties are used in the developed penetrating image formation to form images. The penetrating image formation developed is computationally efficient to realize realtime imaging, which does not depend on refraction points. The throughthewall imaging method is validated on simulated and real data. It is shown that the proposed method provides high localization accuracy of targets concealed behind walls.
Throughthewall imaging (TWI) and, in general, imaging of buildings internal structure have received much interest in recent years [
In order to obtain a good focusing quality of behindthewall targets, the effect of wall should be compensated during the imaging procedure, where the wall parameters need to be known or estimated. Fortunately, radar receives backscattered signals from targets of interest and their surroundings, that is, the wall, which potentially allows extracting the surrounding information from the received echo.
In TWI, the wall parameters, such as width and permittivity, are required for good quality imaging. There are some methods to estimate the wall parameters, such as using different array structures or multiple standoff distances [
In this paper, we propose a novel throughthewall image formation for virtual aperture radar (VAR). Compared with synthetic aperture radar (SAR), which obtains the imaging aperture by the platform movement, a VAR system forms the imaging aperture by a multipleinput multipleoutput (MIMO) array. For a MIMO array with
In a typical scenario for throughthewall radar (TWR), a wall separates radar and targets. Figure
Imaging geometry of TWR with MIMO array.
The wall and behindthewall targets will both cause backscattered signals, where the propagation path of EM wave with respect to the
Developed realistic model of TWR.
For the echo from the wall, the transmitted signal will be reflected at the front and rear surfaces, which is denoted as the 1st and 2nd reflections, respectively. The echo phase history of the 1st and 2nd reflections can be defined by the electrical length of the twoway path traveled by a spherical wave from the transmitting antenna to the reflection point and back to the receiving antenna.
Given the
The propagation medium of the 2nd reflection is airwall, which refracts at
When the transmitting signal refracts at the point
Substituting (
The realistic model is characterized by three wall parameters: position, width, and permittivity, which should be estimated from the received echo in practice. For the MIMO array, the time delay between the 1st reflection and the 2nd reflection with respect to the
The range resolution
Based on (
The estimations of the width and the relative permittivity are obtained accordingly as
According to the equivalent twolayer model [
Equivalent twolayer propagation model.
According to the geometry relationship depicted in Figure
Substituting (
In the simulation, the finitedifference timedomain (FDTD) method is used to simulate the echo. The transmitting signal is the first derivative Gaussian impulse with the lowest and highest frequencies of the transmitted signal being 0.5 GHz and 2 GHz, respectively. The antenna array is composed of 1 transmitting antenna and 21 receiving antennas. The receiving antennas form a linear receiving array of 2 m length. The transmitting antenna is placed at the center of the receiving array with its coordinates (0, 0). The array is parallel to the wall with the distance to the front surface of 1.2 m. The thickness of the wall is 0.2 m and its relative permittivity is 6.25. One target, with its coordinates of (0, 1.7), is behind the wall.
The envelope amplitude image of the BP imaging result is depicted in Figure
Imaging result using traditional imaging method.
Imaging result of proposed method with SNR = 10 dB.
The additive white Gaussian noise (AWGN) with zeromean is added to the above FDTD simulated data to evaluate the performance of proposed estimation method under different signaltonoise ratios (SNRs). The SNR is defined as the power of transmitted signal over the variance of AWGN. The estimated wall parameters under different SNRs are shown in Table
Mean value of the estimated wall parameters in different SNRs.
SNR (dB) 




5  1.19  0.220  5.355 
10  1.20  0.211  6.623 
15  1.20  0.205  6.368 
20  1.20  0.203  6.291 
The imaging result of proposed method in SNR = 10 dB is depicted in Figure
We use the real data, collected by our built throughthewall VAR system (Figure
Photograph of the throughthewall VAR system.
The experimental scene is depicted in Figure
Estimation of wall parameters for real data.


 

Estimated value  8.51 m  0.27 m  5.86 
True value  8.50 m  0.28 m  5.56 
Data collection scenario.
The imaging results of the BP algorithm and the method proposed are compared in Figure
Comparison of imaging results of real data with 20 dB dynamic range: (a) BP algorithm; (b) proposed method.
In this paper, the realistic model based TWI method is proposed. The way to estimate the wall parameters (i.e., position, width, and permittivity) from the radar return is suggested. A RPF penetrating image formation algorithm is proposed to focus behindthewall targets based on the estimated wall parameters, which is computationally efficient to realize the realtime imaging. The imaging results of simulated and real data have shown that the proposed method provides high localization accuracy of behindthewall targets.
The realistic model with a realvalued permittivity is assumed in this paper. Although the focusing quality can be further improved when considering a more complex realistic model with a frequencydependent and/or complexvalued permittivity with sacrifice of the computational time, it is not necessary for TWR application in practice. When TWRs are used for detection of behindthewall persons, a radar video is more useful than a single radar image in detection, where a computationally efficient imaging method is preferred to increase the framerate rather than to obtain the perfect focusing quality. For some walls, their dispersive effect will change the shape of signal and make it hard to discern the 1st and 2nd reflections from the wall. In such cases, the higher downrange resolution is required. An alternative approach without increasing the hardware burden is to correct the dispersive effect with data processing methods, that is, deconvolution methods. Nevertheless, further research is required.
The proposed realistic model is possible to be extended to describe a multilayered homogenous wall or multiple homogenous walls, whose derivation is analogous to that of the equivalent twolayer model, but more restriction requirement on the downrange resolution is needed. For an inhomogeneous wall, the more complex realistic model is required to characterize the scattering of the wall and its effects on behindthewall targets. Fortunately, inhomogeneous walls in practice usually have the periodic structure, such as reinforced concrete walls and cinder block walls, which might simplify the modeling work based on their approximate scattering solutions [
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grants 61271441 and 61372161 and the research project of NUDT under Grant CJ120402.