Full polarimetric beam-forming algorithm for through-the-wall radar imaging

Authors


Abstract

[1] Development of an imaging algorithm that accurately models the wave propagation physical process has become an important topic in through-the-wall radar imaging (TWRI). In this paper, a full polarimetric beam-forming algorithm for through-the-wall radar imaging for a general multilayer wall case is presented and applied to various 2D and 3D simulated and measured scenarios. Polarimetric TWRI not only enhances the target characterization but also mitigates the wall ringing effect in cross polarizations. The far field layered medium Green's function is incorporated in the proposed TWRI algorithm for the quad-polarization of the target returns, namely, VV, HV, VH and HH. Due to the incorporation of the layered medium Green's function, the imaging algorithm not only takes into account the wall reflection, bending, and delay effects but also accounts for the complex scattering mechanism due to the presence of the wall. Numerical and experimental results show that the proposed full polarimetric beam former can provide high quality focused images in various wall-target scenarios, in particular, when the technique is combined with a wall parameter estimation technique.

1. Introduction

[2] Through-the-wall radar imaging (TWRI) is a topic of current interest due to the wide range of public safety and defense applications. The TWRI technology is particularly useful in behind-the-wall target detection, surveillance, reconnaissance, law enforcement, and various earthquake and avalanche rescue missions [Chen et al., 2006; Baranoski, 2008; Amin and Sarabandi, 2009; Ahmad et al., 2005, 2008; Zhang and Hoorfar, 2011].

[3] Through-the-wall radar images the targets behind the wall by transmitting ultra-wideband electromagnetic (EM) waves and processing the reflected signal from the wall and targets. Previously, several effective TWRI algorithms that take into account the wall reflection, bending, and delay effects have been proposed, such as the delay-and-sum (DS) beam former, subspace based method and linear inverse scattering algorithm. The DS beam-forming algorithm incorporates the time delay, associated with the wave traveling through the wall, into the beam former [Ahmad et al., 2005, 2008]. However, it does not take into account multiple reflections within the wall, the complex scattering effects between the targets, and the interactions between the target and the wall. In order to build an accurate EM model, the Contrast Source Inversion (CSI) method is employed for TWRI [Song et al., 2005]. CSI is based on the full wave equation and does not make any assumption of the TWRI problem. Thus a very high resolution quantitative reconstruction (both electrical and geometrical parameters) of the targets can be achieved. However, CSI method is based on an optimization inversion scheme and needs to be solved iteratively, making it very time consuming. Linear inverse scattering algorithms based on the first order Born approximation are proposed by Soldovieri and Solimene [2007], Dehmollaian and Sarabandi [2008], Dehmollaian et al. [2009], and Li et al. [2009]. These algorithms show a good improvement over CSI in terms of computation speed and reach a good compromise between the imaging accuracy and efficiency. For multistatic radar systems, subspace method based on time reversal MUSIC (TR-MUSIC) was proposed to detect and localize targets behind the wall [Zhang et al., 2010]. Although successful imaging results could be obtained by using the aforementioned algorithms, one challenging problem in TWRI is the reflected signal from the wall itself [Dehmollaian and Sarabandi, 2008]. In many situations, the wall reflection is even stronger than the targets' reflections. In addition the multiple scattering from the front and back of the wall itself may lead to a ringing effect which can last for a long time duration and overlap with the return signal from the target, resulting in masking of the target's image. This problem is more pronounced when the target is in close proximity to the wall or the wall is hollow or made of composite materials.

[4] In this paper the polarimetric TWRI problem is studied from the EM perspective. Full polarimetric radar measures the targets' return signals with quad-polarizations: horizontal transmitting and receiving (HH), horizontal transmitting and vertical receiving (HV), vertical transmitting and horizontal receiving (VH), and vertical transmitting and vertical receiving (VV) [Yamaguchi et al., 1995; Shlivinski and Heyman, 2008]. Polarimetric imaging benefits TWRI in two aspects. First, polarized signal carries more useful information of the target thus enhancing the accuracy and detail of target detection and feature extraction. Second, for cross polarized signal the reflection from a homogeneous wall is mitigated and an enhanced image of the targets can be obtained. Some previous work has been carried out on polarimetric TWRI [Ahmad and Amin, 2008; Yemelyanov et al., 2005, 2009; McVay et al., 2007]. Yemelyanov et al. [2005, 2009] and McVay et al. [2007] applied the Polarization-Difference Imaging (PDI) algorithm and its adaptive version (APDI) for the detection and identification of changes behind the wall. PDI is a bio-inspired technique where the “polarization sum” and “polarization difference” signals are obtained by summing and differencing the two signals from orthogonal polarization channels to enhance target detection and feature extraction [Rowe et al., 1995; Tyo et al., 1998; Yemelyanov et al., 2003]. The basic ideal behind the adaptive Polarization-Difference Imaging algorithm (APDI) for TWRI is that the imaging system can be “adapted” to the observation scene in the absence of the target by utilizing the polarization statistics of the scene in the previous look, i.e., on the polarization information from the background (i.e., “nontarget”) scene [Yemelyanov et al., 2005, 2009; McVay et al., 2007]. This adaptation makes the changes in the scene, e.g., appearance/disappearance of objects and/or changes in the mutual orientation of the objects behind the wall, more pronounced and noticeable to the adapted imaging system. Ahmad and Amin [2008] applied the DS beam former to experimental data for TWRI, wherein only the propagation delays were taken into account for the processing of the co- and cross- polarized return signals and the EM characteristics of the polarimetric signals were not considered. The EM waves traveling through the building walls, however, generally undergo several processes such as reflection, transmission, attenuation, multiple scattering, distortion and depolarization. The development of an imaging technique that well models the physical process of wave propagation is, therefore, an emergent and important topic for TWRI.

[5] In this paper, a full polarimetric beam-forming algorithm for through-the-wall radar imaging for a general multilayer wall case is presented and applied to various 2D and 3D simulated and measured scenarios. The proposed polarimetric TWRI algorithm not only takes into account the conventional wall reflection, bending, and delay effects but also compensates for the complex EM scattering mechanism due to the presence of a multilayer wall by incorporating the multilayered medium Green's functions for the quad-polarizations (VV, HV, VH and HH) into the beam former.

[6] The organization of the remainder of the paper is as follows. In section 2, the full polarimetric beam-forming algorithm which incorporates the far-field Green's functions for the TWRI is presented. Some numerical and experimental results are provided in section 3 to validate effectiveness of the proposed beam-forming algorithm. In addition, for the single-layer wall, the technique is combined with a wall parameter estimation technique to enhance the polarimetric imaging of unknown walls. Finally, some conclusions are drawn in section 4.

2. Full Polarimetric Beam Former for TWRI

[7] Figure 1 shows a simple scenario for TWRI. The transmitter and receiver moves along a scan line parallel to the x axis at Nt locations from Lmin to Lmax with either horizontal or vertical polarization. The distance between the transmitter and receiver is dant. The operating frequency of the through-wall radar ranges from fmin to fmax with Nf frequency points. The locations of the m-th transmitter and receiver are denoted as rtm and rrm, respectively. The targets are located in an inaccessible region denoted as Dinv behind the wall. The dielectric constant, conductivity and thickness of the wall are ɛb, σb and d, respectively. The ejωt time convention is assumed and suppressed throughout this paper.

Figure 1.

Measurement configuration of polarimetric TWRI.

2.1. Polarimetric TWRI

[8] Radar imaging problem is essentially an EM inverse scattering problem which involves the process of inferring the properties of unknown objects in a region of interest from the measured field outside that region. For freespace synthetic aperture radar imaging, the image of the targets can be reconstructed by applying the matched filter or adjoint operation of the forward scattering operator to the measured scattered field at each image pixel [Ulander et al., 2003; Ding and Munson, 2002]:

equation image
equation image

where I(r) is the reconstructed image pixel at position r, Es(rrm, rtm, kn) is the received scattered field at the m-th receiver location due to the illumination of the m-th transmitter, rtm, rrm, and r are the position vectors of the transmitter, receiver and target, respectively, i.e., rtm = equation imagextm + equation imageytm + equation imageztm, rrm = equation imagexrm + equation imageyrm + equation imagezrm, and r = equation imagex + equation imagey + equation imagez; kn is the freespace wave number of the n-th transmitting frequency, c is the speed of light in freespace, Rtm and Rrm are the distances from the m-th transmitter and receiver to the target, i.e., Rtm = |rtmr|, Rrm = |rrmr|.

[9] Equations (1a) and (1b) are also referred to as the frequency domain standard backprojection (SBP) algorithm. The term (Rtm+Rrm)/c in (1a) and (1b) is essentially the wave propagation time from the transmitter to target then from the target to the receiver. Equation (1a) backprojects the measured signal to the position when it is excited and the coherent summation of the backprojected signal forms the image. Equation (1a) can also be written in the equivalent form in (1b). From electromagnetic perspective, the physical meaning of the beam former in (1b) is straightforward: the integral kernel is essentially the scattered field dividing by the free-space Green's functions G(r, rtm, kn) and G(rrm, r, kn) which relate the wave propagation process from the transmitter to the target and the target to the receiver, where

equation image

The division of the Green's function is a compensation of the wave propagation process [Jofre et al., 2009]. Due to the reason that in radar remote sensing applications the distance from the transmitter and receiver is too far away from the target, Rtm, Rrm become approximately constant thus the total constant coefficient 16π2RrmRtm is omitted in (1b).

[10] For TWRI the transmitting wave generally undergoes the process of reflection, transmission, attenuation, multiple scattering, distortion and depolarization when traveling through the walls. Similar phenomenon occurs for the scattered field when it travels from the targets to the receiver. For TWRI, the free-space assumption no longer holds and the scattering mechanism when wave travels through the wall should be taken into account. TWRI with the SBP beam-forming algorithm in (1a) and (1b) will cause image distortion, smearing and displacement of the targets [Dehmollaian and Sarabandi, 2008; Dehmollaian et al., 2009]. For TWRI, the propagation process of the wave traveling through the wall should be well modeled in the imaging algorithm. Inspired by the compensation of the wave propagation process with the freespace Green's function in 1(b), the through-the-wall image can be reconstructed by employing the layered medium Green's function which well characterizes the wave propagation process as it travels through the wall. Through the proper compensation of the wave propagation effect with the background medium Green's function, the TWRI formula can be written as

equation image

where G(r, rtm, kn) and G(rrm, r, kn) are the layered medium Green's functions which relate the wave propagation process from the transmitter to the target and the target to the receiver in the presence of the wall. In the above TWRI formula, in order to compute the image an efficient evaluation of the layered medium Green's function is required. However, an exact evaluation of the layered medium Green's function is complicated and time consuming as it generally involves the process of numerical or semi-analytical evaluation of the corresponding Sommerfield integrals [Hoorfar et al., 1992]. This results in a long computation time in the imaging process and is therefore not well suited for real time TWRI applications; in particular, if the imaging takes too long time, the target may have moved so much that the solution is no longer valid – the target is not in the old place anymore.

[11] In order to compromise between the computation time and the computation accuracy, assuming that the target is located in the far field of the antenna, the far field Green's functions can be approximately written as [Dehmollaian and Sarabandi, 2008]

equation image

where Tt and Tr are the wall transmission coefficients from the transmitter to target and the target to receiver, respectively, and will be given in section 2.2.

[12] By substituting (4) into (3) the TWRI formula can be written as

equation image

Because the transmitter and receiver are far away from the target when the targets are within the far field region of the radar, Rtm and Rrm become approximately constant. Thus the total constant coefficient 16π2RrmRtm has been omitted in equation (5).

[13] In TWRI scenarios, many of the targets of interest are polarimetric scatterers, such as furniture, human and weapons. Polarimetric scattered fields may be helpful not only for target characterization and feature extraction, but also for mitigating the wall effects. For co-polarized field, the ringing signal caused by multiple scattering from the front and back boundary of the wall may cause the masking of the targets in the image. However, for cross-polarized field, there should be no reflections from homogeneous walls such as brick or poured concrete wall, and relatively small reflections from hollow concrete wall. This effect for cross-polarized signal in TWRI is very helpful in the wall reflection mitigation and target enhancement [Dogaru and Le, 2009], provided of course that the target-generated cross-polarized field intensities are within the radar system's dynamic range. We also note that full consideration of various polarization status of the scattered field is essential in imaging of targets behind an anisotropic wall.

[14] For full polarimetric TWRI, the quad-polarized (VV, HV, VH and HH) images can be computed by modifying (5) as

equation image

where

equation image
equation image
equation image

The superscripts h, v stand for H and V polarization and the subscripts t, r represent the transmitter and receiver. In radar imaging the most important factor to achieve a focused imaging result is to compensate the phase term properly. In the above polarimetric TWRI algorithm we compensate the wave propagation phase delay through the far field layered medium Green's function for different polarizations. We did not, however, accurately compensate the amplitude because it is a real-valued slowly varying function, which will generally not affect the imaging result.

2.2. Transmission Through Multilayered Walls

[16] By incorporating the far field approximation of the layered medium Green's function, the imaging algorithm can easily be generalized for the polarimetric imaging of targets behind multilayered homogeneous and composite walls or a large room with inner walls. For the planar multilayered homogeneous medium shown in Figure 2, the permeability and permittivity in the i-th region are denoted as μn and ɛn, and ki is the wave number in the i-th layer.

Figure 2.

Transmission through multilayered medium.

[17] It is well-known that by applying the boundary condition at the interface of each layer, the generalized reflection coefficient for horizontal and vertical polarizations can be derived as [Chew, 1997]

equation image

where equation imagei,i+1 is the total reflection coefficient from the i + 1-th layer to the i-th layer, kiz is the normal components of the propagation constant in the i-th layer, Ri,i+1 is the reflection coefficient from the i + 1 th layer to the i-th layer, i.e.,

equation image

Similarly, the generalized transmission coefficient from the first layer to the N-th layer can be derived as [Chew, 1997]

equation image

where

equation image

and equation imagep,p+1 can be calculated from (10).

[18] In most TWRI scenarios, wall are purely dielectric, thus μi = 1, i = 1, 2,··· N; also the radar and targets are located in the first and N-th region, which is free-space, i.e., ɛ1 = ɛN = 1. For a single layer homogeneous wall the total transmission and reflection coefficients in (9) and (11) reduce to

equation image
equation image

3. Numerical and Experimental Results

[19] Some numerical results for different wall-target scenarios and experimental result for a simple canonical target behind a homogeneous wall are presented in this section to show the effectiveness of the proposed full polarimetric TWRI algorithm. In order to show the validity and efficiency of the algorithm, however, we first present some co-polarized imaging results for different wall-target scenarios and compare with existing imaging algorithm.

3.1. Imaging of Three Targets Behind Different Walls

[20] To demonstrate the effectiveness of the proposed TWRI algorithm and validate its accuracy in resolving multiple targets, we first investigate imaging of targets behind a single layer homogenous wall. The targets used in this example are a collection of rectangular, cylindrical, and square PEC objects. The scattered field was generated using a two-dimensional (2D) Finite difference Time Domain (FDTD) code (A. Giannopoulos, GprMax 2D/3D, User's Manual 2002, available at http://www.gprmax.org), where the transmitter is modeled as a point source. The radar scans along a line parallel to the front wall to synthesize a 4 m aperture with a step of 0.05 m at a standoff distance 0.3 m. The dielectric constant, conductivity and thickness of the wall are ɛr = 7.66, σ = 0.01 S/m and d = 0.2 m, respectively, corresponding to a typical concrete wall. The radar operating frequency ranges from 1 to 3 GHz with a step of 25 MHz.

[21] In TWRI an accurate estimation of the wall parameters, such as the thickness and permittivity, is essential to the precise detection and localization of the targets. The incorrect estimation of the wall parameters will lead to the degradation of image, such as the shift of the target position, and the smearing and blurring of the image [Wang and Amin, 2006; Ahmad et al., 2008]. In this single layer wall example the wall parameter is estimated with the time domain reflectometry method [Aftanas et al., 2009], which mainly consists of two steps: (1) measure the wall response in time domain w(t) and (2) measure the PEC plate response in time domain at the same standoff distance p(t). For a single layer homogenous wall, the reflection coefficient of the first surface of the wall can be determined from the peak values of the measured wall and PEC plate response:

equation image

[22] Then the permittivity and the thickness of the wall are given by

equation image
equation image

where c is the speed of light in the freespace, Δt is the propagation time from the front wall to the back wall. Then the conductivity of the wall can be estimated as

equation image

where

equation image
equation image

Figure 3 gives the FDTD simulated time domain responses of a PEC plate and the dielectric wall. By using the time domain reflectometry method the wall parameters were estimated and are given in Table 1. From the comparison of the estimated and the actual wall parameters we find that the estimations of the wall parameters are less than 3%.

Figure 3.

Time domain responses from the PEC plate and dielectric wall.

Table 1. Actual and Estimated Wall Parameters
 ɛrσ (S/m)d (m)
Actual7.660.010.2
Estimated7.780.00720.198

[23] Figure 4a is the imaging result of the targets using the beam-forming algorithm in (5) with the estimated wall parameters in Table 1, where the three layered medium transmission coefficient in (15) is used in the beam former. For comparison, the imaging result using the DS beam former [Ahmad et al., 2005] with the same estimated wall parameters is provided in Figure 4b. The correct locations of the three targets are indicated with white a dashed rectangle, square and circle in Figure 4. It is clear from the two figures that focused image of the targets can be achieved using the two imaging algorithms. From the comparison of Figures 4a and 4b one can observe that a bit less cluttered and cleaner image is obtained using the beam former in this paper due to the better modeling of the wave propagation phenomenon through the incorporation of the wall's Green's function. In particular, the DS beam former which does not account for the effects of multiple reflections within the wall results in ghost images seen in the upper portion of Figure 3b. The computation times to generate these images, on a four-core P4 2.66G CPU, 16G memory computer, were 28.32 and 36.67 s for the proposed beam former in this paper and the DS beam former, respectively.

Figure 4.

Single layer wall imaging result: (a) beam former in this paper; (b) DS.

[24] As discussed in section 2, the imaging formula is derived based on the assumption that the targets are within the far field of the antennas. Distortion and smearing will appear when the targets are in the close proximity to the wall. Figure 5a is the imaging result of three targets which are within 0.3 m behind the wall using the beam former in this paper. Although the targets could still be identified in the image, more smearing and distortion were observed compared with the imaging result of far field target in Figure 4a. Figure 5b is the imaging result of the same targets near to the wall using the DS beam former. Although we assumed far field approximation in the beam former in (5), from the comparison of the two images we find that heuristically the beam former in (5) could still image the targets and gives a slightly better imaging result than the DS beam former. In the above simulations a 2D point source was used, which is equivalent to a 3D line source directed in the y direction (as shown in Figure 1). Therefore, the vertical transmitting and vertical receiving (VV) polarizations were used in the above examples.

Figure 5.

Imaging of three targets near to the wall: (a) beam former in this paper; (b) DS.

[25] Another advantage of the proposed method is the easy generalization to the imaging of targets behind multilayered walls, especially for composite wall, hollow concrete wall or wall separated by an inner hallway, which is beyond the capability of the DS beam former. In order to demonstrate this capability of the proposed beam former, the imaging of targets behind a hollow concrete wall and an inner hallway was investigated using FDTD simulated data. The estimation of wall parameters associated with a multilayered building wall has been extensively studied in the past decade within the framework of one-dimensional inverse scattering problem. We would refer the authors to Thajudeen and Hoorfar [2010], Thajudeen et al. [2011], Zhang et al. [2001], Nakhkash et al. [1999], and Emad Eldin et al. [2009] for the estimation of wall parameters associated with multilayered building walls. The radar operating condition and electrical parameters (permittivity and conductivity) of the wall are the same as in previous example. Figures 6a and 7a show the considered scene layouts and also provide the thickness of the various walls. Figures 6b and 7b provide the corresponding imaging results of the three target scenes behind the hollow concrete wall and walls separated by a hallway. The correct locations of the targets are indicated with white dashed rectangle, square and circle. It is clear from the two images that, due to the proper compensation of the wall effects with the layered medium Green's function, high quality focused images of the targets can be achieved using the proposed beam former. In the above imaging result due to the employment of the point target model, which ignores the multiple interactions, only qualitative imaging results can be achieved. In order to get a perfect reconstruction of the target shape and permittivity distribution a nonlinear iterative inversion schemes has to be employed [Song et al., 2005], which is very time consuming and CPU intensive.

Figure 6.

Hollow wall: (a) simulation geometry; (b) imaging result.

Figure 7.

Two walls separated by a hallway: (a) simulation geometry; (b) imaging result.

3.2. Imaging of a Human Behind a Single Layer Wall

[26] To demonstrate the mitigation of the wall ringing effect for cross polarizations and the effectiveness of the full polarimetric beam former for more realistic TWRI scenario, some numerical results are presented in this and next section. In the first numerical example the imaging of a human behind a homogeneous concrete wall is presented. The measurement configuration for the TWRI is shown in Figure 8 (left), where the radar measures the scattered field at a standoff distance 0.3 m along a line parallel to the front wall in y direction. The synthetic aperture length is 2 m with a step of 0.05 m. The scattered field data were generated using XFDTD®, a commercial full wave electromagnetic simulator based on Finite difference Time domain method (FDTD) from Remcom Inc. The dimension of the HiFi male human model is 0.57 m × 0.324 m × 1.88 m, which is made up of 2.9 mm cubical FDTD mesh cells, incorporating 23 different tissue types with realistic dielectric and conductivity parameters. The front and side view of the human is shown in Figure 8 (right). The dielectric constant, conductivity and thickness of the wall are ɛr = 6, σ = 0.01 S/m and d = 0.2 m. The working frequency ranges from 1 to 3 GHz with a step of 36 MHz.

Figure 8.

Simulation geometry of a human behind the wall.

[27] Figure 9 is the imaging result of a human behind a single layer homogeneous wall for the quad-polarizations (VV, HV, VH and HH) using the proposed full polarimetric beam-forming algorithm. From the co-polarization (VV, HH) results we could see that that target is not well identified and masked by the strong parallel lines in the image. The multiple lines are the images of the ringing signal due to the multiple scattering between the front and back boundary of the wall. In many situations, the ringing signal can be even stronger than the return from the targets. Due to the multiple scattering effect, the ringing signal may last for a long duration of time and overlap with the return signal from the target, resulting in masking of the total or partial detailed feature of the target. However, in the cross polarization images in Figures 9b and 9c we could see that the ringing signal of the wall disappears and the target is clearly identified in the image at its true location. In cross polarizations there are no or negligible reflections from the wall thus the target return is predominant. For through-the-wall radar system the received signal is mainly composed of the reflection from the wall and the return from the target. For co-polarizations (HH, VV), background subtraction can be performed to mitigate the wall effect and enhance the target characterization [Dehmollaian and Sarabandi, 2008]. Figure 10 is the full polarimetric imaging result of the human after background subtraction. That is, two measurements are employed: one with the presence of the target and one without the target. By subtracting the received data, the effect of reflection from the wall is removed [Dehmollaian and Sarabandi, 2008]. From the comparison of the co-polarized image in Figures 9 and 10, it is confirmed that part of the detailed feature of the human is masked by the ringing signal of the wall. For the cross-polarized images, however, there are no observable differences in the image quality whether one performs background subtraction or not. The wall effect is mitigated in cross polarizations which are particularly important in situations where it is difficult or impossible to perform background subtraction. It takes about 24.63 s to generate each image in Figure 9. Due to the 1D nature of the receiving array in this example, the images in Figure 8 basically correspond to the human's chest area. It is noticed that some artifacts show up in Figures 10a and 10d. This is due to the fact that the male human model in the simulation is composed of realistic dielectric tissues. The ghost images in Figure 10 are caused by the multiple scattered fields inside the dielectric human chest. The imaging algorithm only compensates for the phase delay when passing through the wall but does not take into account the wave propagation effect when it penetrates into the dielectric human body.

Figure 9.

Imaging of a human behind a single layer wall using the proposed polarimetric beam former before background subtraction: (a) VV, (b) HV, (c) VH, (d) HH.

Figure 10.

Imaging of a human behind a single layer wall using the proposed polarimetric beam former after background subtraction: (a) VV, (b) HV, (c) VH, (d) HH.

3.3. Imaging of a Human Behind a Hollow Concrete Wall

[28] In this section we investigate the imaging of a human behind a hollow concrete wall. The measurement configuration is shown in Figure 11. The radar operating condition and the targets are the same as in the previous example. The hollow wall is modeled as three-layer geometry. The dielectric and conductivity of the first and third layer are ɛb = 6, σb = 0.01S/m. The thickness of the air gap and two concrete layers are assigned to be the same with d = 0.1 m, resulting in 0.3 m total thickness of the wall. The working frequency ranges from 1 to 3 GHz with a step of 36 MHz. The polarimetric through-wall images are formed by employing the five layered medium transmission coefficient in the beam former in (5) for all polarizations. Figure 12 is the imaging result for the quad-polarizations through proper compensation of the wall effect with the far field Green's functions after background subtraction. In Figure 12, we can see that target is clearly identified and well located at its true position. It is clear that focused images can be achieved using the proposed technique. Similar focused imaging results can also be obtained under other multilayered wall scenarios, i.e., multilayer composite material decorated wall or large rooms with multiple inner walls, which may be beyond the DS beam-forming algorithm based on ray tracing technique.

Figure 11.

Simulation geometry of a human behind a hollow concrete wall.

Figure 12.

Imaging of a human behind two layer composite material wall after background subtraction: (a) VV, (b) HV, (c) VH, (d) HH.

3.4. Imaging of a Tilted PEC Plate Behind an Anisotropic Wall

[29] In the above simulations we have demonstrated that high quality focused imaging result can be achieved through the proper compensation of the wall effect using full polarmetric Green's functions based algorithm. However, in many situations the wall is anisotropic which exhibits different dielectric parameters in the horizontal and vertical polarizations, such as the reinforcement concrete wall and cinder block wall. In this section a simple example for the imaging of a tilted PEC plate behind a uniaxially anisotropic wall is presented to show the capability of the proposed beam former for the imaging of targets behind anisotropic walls. The geometry of the TWRI scene is shown in Figure 13. The radar operating condition is the same as the simulation in section 3.3. The permittivity tensor of the wall is assumed to be

equation image

The thickness of the wall is 0.2 m and the dimension of the tilted PEC plate is shown in Figure 13. For comparison, we first present in Figure 14 the VV and HV polarization result of the tilted PEC plate behind a single layer isotropic wall with ɛb = 4, d = 0.2 m. The dielectric constant and thickness of the single layer homogeneous wall are ɛb = 4, d = 0.2 m. Figure 15 shows the VV and HV imaging results of the same tilted plate behind a uniaxially anisotropic wall. For the defined coordinate system in Figure 13, ɛxx is used for the calculation of Th and ɛzz is used for the calculation of Tv in (8). From the comparison of Figures 14 and 15, we find that through the proper compensation of the wall effects using the corresponding dielectric parameters for horizontal and vertical polarizations, similar focused result to the homogeneous wall can be achieved for the anisotropic wall. However, if the anisotropic wall is processed as homogeneous and the same wall parameters are used for both horizontal and vertical polarizations, the target will be shifted in the downrange and widened in the cross range. Figures 16 and 17 provide the result when the anisotropic wall is processed as homogeneous using the same parameters for all polarizations for ɛb = 4, d = 0.2 m and ɛb = 8, d = 0.2 m, respectively. From the comparison of Figures 16 and 17 with Figure 15, it is observed that due to the different wall parameters in the horizontal and vertical polarizations for anisotropic wall, imaging under the assumption of homogeneous parameters for all polarizations results in an unfocused image, which involves smearing of the image, shifting of the targets in the downrange, widening in the cross range and appearance of ghost images. It is noteworthy that in the VV image, in Figure 15, one can identify the width of the PEC plate, whereas the HV image roughly shows the edge diffractions from the edges of the tilted plate. Finally, we note that the Green's function formulation in section 2 can be extended in future to incorporate the case of a wall with a full permittivity anisotropy tensor. We note that certain type of walls like hollow concrete (cinder-block) and reinforced concrete walls are generally anisotropic. From the examples in this subsection we demonstrated the applicability of the algorithm to an anisotropic wall, provided, of course, if the anisotropy is known (or measured) in advance.

Figure 13.

Simulation geometry of a tilted PEC plate behind a diagonally anisotropic wall.

Figure 14.

Imaging of a tilted PEC plate behind a single layer homogeneous wall: (a) VV, (b) HV.

Figure 15.

Imaging of a tilted PEC plate behind a diagonally anisotropic wall: (a) VV, (b) HV.

Figure 16.

Imaging of a tilted PEC plate behind a diagonally anisotropic wall using homogeneous parameter ɛb = 4, d = 0.2 m for all polarizations: (a) VV, (b) HV.

Figure 17.

Imaging of a tilted metallic plate behind a diagonally anisotropic wall using homogeneous parameter ɛb = 8, d = 0.2 m for all polarizations: (a) VV, (b) HV.

3.5. Experimental Results

[30] Finally, we present some experimental results for imaging of a dihedral and metallic sphere behind a single layer wall. An ultra-wideband synthetic aperture through-the-wall polarimetric radar system was set up in the Radar Imaging Lab at Villanova University. A stepped-frequency continuous wave (CW) signal, consisting of 801 frequency steps of size 3 MHz, covering the 0.7–3.1 GHz band was chosen for imaging. An Agilent vector network analyzer (VNA), model ENA 5071B which has a typical dynamic range of greater than 90 dB over the frequency band of interest, was used for signal transmission and data collection.

[31] A dual-polarized horn antenna, model ETS-Lindgren 3164-04, with an operational bandwidth from 0.7 to 6 GHz, was used as the transceiver and mounted on a field probe scanner to synthesize a 57-element linear array with an inter-element spacing of 2.2 cm on a square grid. The dual-polarized antenna has a gain of 3 dBi to 12 dBi over the operating range with a cross polarization isolation of greater than 20 dB. The array was positioned 1.05 m in downrange from a 0.143 m thick solid concrete block wall. Ports 1 and 2 of the network analyzer were connected to the V- and H-feeds of the antenna and full-polarization measurements were conducted under monostatic measurement configuration. That is, the set of 801 CW frequencies is transmitted from a single array element and the returns are received at the same array location only. This process was then repeated for the next array location until all 57 array locations are exhausted. All 801 frequency points at all 57 locations were collected in approximately 2 min.

[32] The scene, shown in Figure 18, consists of a dihedral (each face is 15.5 inches high and 11 inches wide) whose center is located 2 m behind the wall at a cross range of 0.285 m. Both the array and the center of the target were at the same height. An empty scene full-polarization measurement was also made and was coherently subtracted from the target scene. The resulting data sets were used for generating the images.

Figure 18.

Scene being imaged.

[33] In order to show the effectiveness of the introduction of far field layered medium Green's functions for the compensation of wall effect in the beam former, a conventional radar imaging results using (1a) and (1b) are first provided in Figure 19 where the true region of the dihedral is indicated with a white rectangle in the image. From the freespace beam formed imaging we can find that the target is not only shifted in the downrange (about 0.25 m) but also a bit widened and blurred in the cross range. This is due to the fact that the EM propagation process is not considered and compensated in the conventional backprojection beam-forming algorithm. This phenomenon will be more pronounced in the presence of wall with high dielectric or large thickness.

Figure 19.

Imaging of a dihedral behind the wall using freespace beam former: (a) VV, (b) HV, (c) VH, (d) HH.

[34] Before the applying of the TWRI beam former, the time domain reflectometry was employed to retrieve the parameters of the wall. Figure 20 is the measured time domain responses from a PEC plate and the wall shown in Figure 18. By using the time domain reflectometry the wall parameters were efficiently estimated as ɛr = 6.84 σ = 0.0384 S/m, d = 0.1417 m. The error between the estimated wall thickness and the exact thickness (0.143 m) is less than 1%. Figure 21 is the imaging result of the dihedral for the quad-polarizations using the polarimetric beam former in (5) employing the far field Green's function for the compensation of the wall effect with the estimated wall parameters. For the single layer homogeneous wall in the experiment, the three layered medium transmission coefficient in (15) is used. It is clear from Figure 21 that the full polarimetric beam former was successful in imaging of the target without distortion or displacement.

Figure 20.

Measured time domain responses from the PEC plate and the wall.

Figure 21.

Imaging of a dihedral behind the wall using the proposed full polarimetric beam former: (a) VV, (b) HV, (c) VH, (d) HH.

[35] In the second experimental example we present the imaging result of a PEC sphere behind the wall. The radius of the sphere is 15cm. We first present the numerical simulated result of the same scenario as the experiment using a 3D FDTD generated data. Figure 22a is the imaging result of the sphere behind the wall using the FDTD simulated data. Figure 22b provides the experimental imaging result of the sphere. In both the experimental and numerical results we find that the target is correctly localized and well identified in the image. Also from Figure 22b we find that the experimental result is similar to the numerical simulation.

Figure 22.

VV polarized imaging result of a sphere behind the wall (a) simulated result, (b) experimental result.

[36] In the above experimental results, 2D images of the targets are obtained using the proposed beam former. Finally we present a 3D imaging result of the dihedral used in Figure 21. In addition to the downrange, 3D TWRI provides valuable information about the target extent in length, height, and width. This additional feature is instrumental to effective target classification/identification. Figure 23 is the 3D imaging result of the dihedral. From Figure 23 we can clearly see that the imaging result not only localized the target correctly in the downrange but also provided the information of the target's dimension in the horizontal and vertical directions. This information is important for TWRI applications where the distinction between the targets like adults and children or between a person standing or sitting is of considerable interest.

Figure 23.

Three-dimensional experimental imaging result of the dihedral behind the wall.

4. Conclusion

[37] Polarimetric TWRI is useful in mitigating the wall ringing effects, enhancing target characterization as well as in imaging scenarios involving anisotropic walls. In this paper a novel full polarimetric beam-forming algorithm for the imaging of hidden targets behind different wall-target scenarios is presented. Due to the incorporation of the far field layered medium Green's function, the proposed imaging algorithm not only enhances the target characterization by taking into account the wall reflection, bending, delay and multiple scattering effects for all polarization states of the radar returns but also mitigates the wall ringing effects in the cross polarizations. As it was shown, the algorithm can also be easily generalized to multilayered walls by incorporating the transmission coefficients of multilayered medium into the beam former. Numerical and experimental results were presented to show that through the proper compensation of the wall effects, the full polarimetric beam former is able to generate high quality 2D and 3D focused images under different wall-target scenarios for both isotropic and uniaxially anisotropic walls. An extension of the proposed technique for near field polarimetric TWRI through an efficient evaluation of the layered medium Green's function is presently under investigation and will be presented in a future work. In addition, as shown through simulated and measured results, the imaging technique presented here may also be supplemented by a wall parameters estimation technique [Thajudeen and Hoorfar, 2010], where the radar returns can be first used to estimate the walls' thickness, dielectric constant and loss-tangent before implementation of the proposed polarimetric imaging technique.

Acknowledgments

[38] This work was supported in parts by DARPA under contract HR0011-07-1-0001 and by NSF under award 0958908. The content of the information does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.

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