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].
 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 , Dehmollaian and Sarabandi , Dehmollaian et al. , and Li et al. . 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.
 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.  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  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.
 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.
 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.