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[7] W. Kang, S. Lee, and K. Kim, “Investigation of radiation patterns of longitudinally oriented slot antenna array for imaging radar applications,” Microw. Opt. Tech. Lett, vol. 54, pp. 2408–2412, 2012. [8] W. Kang, D. W. Yang, and K. Kim, “Design of shared-arm dipole array for imaging radar applications,” Electron. Lett, vol. 48, pp. 951–953, 2012. [9] J. G. Maloney and G. S. Smith, “A Study of Transient Radiation from the Wu-King Resistive Monopole—FDTD Analysis and Experimental Measurements,” IEEE Trans. Antennas Propag., vol. 41, pp. 668–676, 1993. [10] EM software and Systems FEKO [Online]. Available: http://www. feko.info [11] T. P. Montoya and G. S. Smith, “Vee dipoles with resistive loading for short-pulse ground penetrating radar,” Microw. Opt. Tech. Lett, vol. 13, pp. 132–137, 1996. [12] K. Kim and W. R. Scott, Jr., “Design of a resistively loaded Vee dipole for ultrawide-band ground-penetrating radar applications,” IEEE Trans. Antennas Propag., vol. 53, pp. 2525–2532, 2005. [13] T. T. Wu and R. W. P. King, “The cylindrical antenna with nonreflecting resistive loading,” IEEE Trans. Antennas Propag., vol. 13, pp. 369–373, May 1965. [14] D. M. Pozar, Microwave Engineering. New York, NY, USA: Wiley, 2004. [15] Agilent Technologies, E8362B PNA Microwave Network Analyzers Data Sheet [Online]. Available: http://www.agilent.com [16] T. T. Wu and R. W. P. King, “The cylindrical antenna with nonreflecting resistive loading,” IEEE Trans. Antennas Propag., p. 998, Nov. 1965.
Three-Dimensional Synthetic Aperture Radar Imaging Through Multilayered Walls Wenji Zhang and Ahmad Hoorfar
Abstract—Most of existing through-the-wall radar imaging (TWRI) algorithms deal with a single layer homogeneous wall in two-dimensional scenario. In this communication we present a generalized three-dimensional (3-D) beamforming algorithm for the focused imaging of targets behind multilayered building walls. The far field layered medium Green’s function is incorporated in the 3-D beamformer for the compensation of the wall effect. 3-D polarimetric imaging is exploited in TWRI for enhanced target identification and feature extraction as well as wall effect mitigation. Numerical results show that the proposed 3-D beamformer provides high quality focused images in various wall-target scenarios. Index Terms—3-D imaging, multilayered wall, polarization, wall mitigation.
I. INTRODUCTION The high-resolution and noninvasive imaging of targets through visually opaque obstacles, such as walls and doors has sparked a growing Manuscript received March 07, 2013; revised August 18, 2013; accepted September 30, 2013. Date of publication October 24, 2013; date of current version December 31, 2013. W. Zhang was with the Antenna Research Laboratory, Villanova University, Villanova, PA 19085. He is now with the Department of Electrical and Computer Engineering at Duke University, NC 27708 USA (e-mail: wenjizhang@gmail. com). A. Hoorfar is with the Antenna Research Laboratory, Department of Electrical and Computer Engineering, Villanova University, Villanova, PA 19085 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2013.2287274
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interest in through-the-wall radar imaging (TWRI) in both military and commercial applications, such as homeland security, urban counter-terrorism, search and rescue missions [1]–[8]. To make intelligent decisions about the contents of a room or building, one needs not only to know if there is a target behind the walls but also as detailed as possible information about the target, such as its location, shape, height, width, etc. During the past decade, linear inverse scattering methods based on the Born approximation or the point target model [3], [5], [6], [8], [13] and nonlinear inverse scattering method based on the strict electric field integral equation have been developed for TWRI [7]. Although successful imaging results can be obtained using these algorithms, they mainly deal with two-dimensional (2-D) scenarios, which only reconstruct the cross sections of the targets. Moreover, most of these algorithms deal with only a single layer homogeneous wall. In urban sensing applications, we often encounter situations to detect and identify targets behind more realistic walls consist of multilayered composite materials or inside a building with multiple inner walls or walls separated by a hallway [1], [2], [4], [18], [22]. This is a challenging problem in TWRI and is beyond the capability of the aforementioned imaging algorithms. In [15], the time reversal imaging is applied to the 2-D imaging of targets behind multilayered walls. The scattering and imaging of buried targets under multilayered subsurface are investigated in [16], [17]. In this communication we presented a generalized 3-D beamforming algorithm for urban sensing of building interior target behind multilayered walls. In addition to the down range, 3-D TWRI provides valuable information about the target extent in length, height, and width [5]. This additional information is critical for enhanced target identification, such as the identification of a sitting or standing person behind the walls. In [8] a strategy based on the super- position and interpolation of 2-D imaging results at different height is presented for 3-D TWRI. The delay-and-sum (DS) beamformer is extended to 3-D imaging in [5]. In [13] a 3-D diffraction tomographic algorithm implemented with fast Fourier transform (FFT) is presented for the fast imaging of targets behind a single layer homogeneous wall. In this communication, the polarimetric TWRI is also investigated using the proposed 3-D through-the-wall beamformer. In TWRI, the multiple scattering from the front and back boundaries of the wall 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 [6], [19], [20]. This problem is more pronounced in the presence of multilayered walls. Polarimetric imaging maybe used to reduce the adverse effects of the wall’s reflection since the cross-polarized return signal from an isotropic wall is negligible thus return signals from the targets become dominant. Moreover, the cross-polarized return signal carries additional information of the target which enhances the details of target feature extraction. The organization of the remainder of this communication is as follows. In Section II, the generalized 3-D beamformer incorporating the far-field Green’s functions for the compensation of the wall effect is presented. Some numerical results are provided in Section III for various wall-target scenarios. Finally, some conclusions are drawn in Section IV. II. PROBLEM FORMULATION Fig. 1 shows a typical scenario of 3-D imaging of targets behind multilayered building walls using synthetic aperture radar (SAR). The transceiver transmits a wideband electromagnetic (EM) wave and collects the return signal over a rectangular planar aperture within . The return signal at the receiver is then coherently processed using the TWRI algorithms to form a
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Fig. 1. Configuration of 3-D SAR imaging through multilayered building walls. Fig. 2. Transmission through multilayered building walls.
focused image of the targets. The operating frequency ranges from to with a frequency step . Under the point target model, which ignores the multiple scattering effects, the received signal can be written as
Substituting (3) into (2), the 3-D TWRI formula can be written as:
(1) where is the received scattered field at the -th receiver location due to the illumination of the -th transmitter, is , and are the position vectors of the reflectivity of the target, , the -th transmitter, receiver and target, i.e., , , is the freespace wavenumber and 3 are of the -th operating frequency, the layered medium Green’s functions which relate the wave propagation process from the transmitter to the target and from the target to the receiver in the presence of the walls. Then the through-the-wall image can be reconstructed through the adjoint operation
(2) where the subscript represent complex conjugation. From the concept of time reversal imaging, the complex conjugation in the frequency domain is equivalent to the time reversal in the time domain. The backpropagation of the time reversed field will focus on the target. In the above equation the inner two integrands corresponds to the beamforming over the cross range and the outer integrand is the coherent summation over all the operating frequencies. In the above imaging formula, an efficient evaluation of the layered medium Green’s function is critical to the imaging. However, the exact calculation of the layered medium Green’s function requires the evaluation of the Sommerfeld integrals [14], which is generally complicated and computational expensive, especially for 3-D problem. To compromise between the computation efficiency and the accuracy, assume that the targets are within the far field of the antenna, the far field Green’s function of the walls can be approximated as [6]:
(4) where the superscripts represent the polarization direction, . In the above equation, the real-valued term 16 is omitted. In (4) the wall effect is efficiently taken into account and well compensated through the layered medium Green’s function. Due to the incorporation of the layered medium Green’s function, the imaging algorithm can easily be generalized for the imaging of targets behind multilayered building walls. For planar multilayered homogeneous medium shown in Fig. 2, the permeability and permittivity in the -th region are denoted as and , is the wavenumber in the -th region. Apply the boundary condition at the interface of each layer, or use an equivalent multi-section cascaded transmission line formulation, the reflection coefficient for the horizontal and vertical polarizations can be derived as [9]: (5)
is the total reflection coefficient from the layer to where layer, is the normal components of the propagation constant the layer, is the reflection coefficient from the layer in the layer, i.e., to the
(6) Similarly, the transmission coefficient from the first layer to the layer can be derived as [9]:
-th
(7) (3) where , , and are the wall where transmission coefficients from the transmitter to target and the target to receiver, respectively.
(8)
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Fig. 3. 3-D imaging of targets behind a hollow concrete wall (a) target dimension; (b) VV polarization before background subtraction; (c) VV polarization after background subtraction; (d) HV polarization without back ground subtraction.
The generalized transmission coefficient in (7) is used in the imaging , formulation in (4) to compensate for the wall effect. For TWRI , the radar and targets are located in the freespace, thus . III. NUMERICAL RESULTS In this section we present some numerical results for different walltarget scenarios to demonstrate the capability of the 3-D beamformer for the focused imaging of targets behind multilayered building walls. In the following simulations we assume that the wall parameters are known and are used in the imaging. The estimation of wall parameters associated with single or multilayered building walls has been extensively studied in the past decade within the framework of one-dimensional inverse scattering problem. We refer the readers to [10], [11], [21]–[23] for the estimation of parameters for single or multilayered walls. As the first example we investigate the 3-D imaging of targets behind a hollow concrete wall. The scattering signal from the wall and the targets was simulated using a time domain 3-D full wave EM solver based on finite difference time domain method (FDTD). In the simulation a composite target consisting of a sphere on top of a square cylinder is investigated. The dimensions of the sphere and bottom square cylinder and are shown in Fig. 3(a). The target is placed at a distance of 1.3 m behind the hollow concrete wall, which is modeled as a three-layered geometry. The dielectric constant and conductivity of the first and third layers (walls) are , . The thicknesses of two walls and the air gap between the walls are 0.1 m each. The 3-D FDTD simulation was performed with data collected at 40 40 monostatic measurement locations over a planar square aperture parallel to the wall at a standoff distance of 0.1 m. The transmitting signal covers the frequency range from 0.8 GHz to 2.6 GHz with a frequency step of 25 MHz. Fig. 3(b) shows the 3-D VV polarized imaging result of the target. We can see the target in the image, however, part of the features are masked by the multiple parallel planes with stronger intensity in the image. The stronger multiple parallel planes in the image are due to the multiple scattering signals between the front and back boundaries of the wall. For the co-polarized signal, the background subtraction
Fig. 4. 3-D imaging of a titled cylinder behind external and interior walls separated by a hallway (a) top view of the exterior and inner walls; (b) target dimension; (c) VV polarization before background subtraction; (d) VV polarization after background subtraction; (e) HV polarization without back ground subtraction.
can be performed to remove the wall effect and enhance the target’s image [6]. In scenarios where background measurement may not be available, wall mitigation techniques can be used to remove the wall effect [19]–[21]. Fig. 3(c) shows the 3-D VV polarized imaging result of the target after background subtraction. From this figure we find that the top sphere and bottom square cylinder can be clearly identified in the image at their correct locations. Fig. 3(d) shows the cross polarization image without the background subtraction. As can be seen, the clutter due to the wall ringing in Fig. 3(b) disappears and the target can be clearly observed in the image. In the cross polarization the reflection from the homogeneous wall is mitigated and the target return becomes dominant. We note that, unlike the co-polarized image, in the cross-polarized image, there are no observable differences in the image quality whether one performs background subtraction or not. The mitigation of the wall effect in the cross polarization is particularly useful in situations where it is difficult or impossible to perform background subtraction. In urban sensing applications, we often encounter situations where we are interested in imaging of targets behind multiple walls inside a building. In the second example, we present the imaging of target behind external and interior walls separated by a hallway (shown in Fig. 4(a)), which is a representative scenario in urban sensing of building interior targets [1], [2], [18] and is beyond the capability of the existing through-the-wall DS beamformer based on ray tracing technique [5]. The permittivity, conductivity and thickness of the exterior and interior walls are , , and . The width of the hallway between the exterior and interior walls is 1 m. The target under investigation is a tilted cylinder 2.25 m away from
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the exterior wall in the down range ( direction). The tilted angles with respect to the x and y axis are 45 degrees, as shown in Fig. 4(b). The radar operating conditions are the same as previous example. Fig. 4(c) shows the 3-D VV polarized imaging result of the target. From this image we can hardly see the target since it is significantly blurred and masked by the strong ringing effects due the multiple scattering signals inside the exterior and interior walls. Fig. 4(d) is the imaging result of the target after background subtraction. From this figure we can clearly see a focused image of the tilted cylinder, which not only correctly localizes the target in the down range but also provides information about the width, length and tilted angle of the target. These additional information of the target in width and height are important in TWRI applications for enhanced target identification and classification. Fig. 4(e) shows the HV polarized imaging result of the target without background subtraction. From the HV polarized image, one can clearly identify the tilted cylinder without background subtraction. The cross-polarized image not only mitigates the wall effect but, in conjunction with the co-polarized image, may also provide more detailed information of the target. From the co- and cross-polarized images in Fig. 4 it is clear that by incorporating the far field approximation of the layered medium Green’s function, the multilayered wall effect has been properly compensated and focused imaging result of the targets can be achieved. IV. CONCLUSION In this communication, a generalized 3-D through-the-wall beamformer for the imaging of hidden targets behind multilayered building walls is presented. Due to the incorporation of the far field layered medium Green’s function, the wall effect is efficiently compensated and focused imaging result of the targets can be achieved. Using the proposed beamformer, the 3-D polarimetric TWRI is investigated for enhanced target characterization and wall effect mitigation. Numerical results show that the 3-D beamformer provides high quality focused images under different wall-target scenarios.
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