#### Abstract

Human is one kind of the most interesting targets in through-the-wall imaging. In high-resolution imaging applications, human is no longer a point target. Therefore, the previous signal models constructed by point target assumption cannot accurately describe real characteristics of EM propagation. We construct the signal models based on extended target theory in this paper. Compared with previous works, the main contributions are as follows. Firstly, human is considered as an extended target. The expressions of target scattering and wall reflections are derived. Secondly, target scattering is no longer isotropic in new model. A new kind of ghost problem which is caused by target obscuring in EM propagation is discovered and exploited. Thirdly, to improve image quality in moving target imaging, an efficient approach which adopts CFAR, clustering method, and spatial geometry relationship is proposed to remove the ghosts. The derived models are shown to agree with synthetic and experimental results. And the efficiency of proposed method is also validated, which illuminates that the ghosts are efficiently mitigated and the image quality is significantly improved.

#### 1. Introduction

Ultra-wideband (UWB) through-wall-imaging (TWI) approaches that can detect objects through obstacles, such as walls, doors, and other opaque materials, are considered as a powerful tool for a variety of civilian and military applications [1–5]. In real TWI application, human is one kind of the most interesting targets [6–10]. Studying human imaging, especially moving human imaging, is quite significant. Therefore, the corresponding moving target imaging (MTI) technique is widely researched in TWI application [11–15].

For exploiting the MTI, an accurate signal model is necessary and urgently required. Many efforts have been made to analyze the signal models to improve image quality. In [16, 17], an inverse scattering signal model is derived. Based on the model, tomography imaging method and change detection technique are adopted in MTI processing. Besides inverse scattering signal model, a back projection signal model is discussed in [18–20]. Electromagnetic synthetic experiments are given in this paper. In order to analyze the EM propagation in a building, ray multipath is computed with ATrace for a building structure, and all paths linking a transmitter-receiver are discovered in [21]. And in [22, 23], a multipath model for sensing through walls is proposed. To sum up, it is noted that all these models consider the target as point one and assume its scattering to be isotropic. Since the target is point one, effects of the target itself on EM propagation are not paid enough attention in these models.

However, in high-resolution imaging radar applications [24–27], most of the targets, such as human and furniture, are no longer point targets. For example, in a common high-resolution through-the-wall radar system, the frequency range is usually 1–3 GHz or even larger. If the frequency band is 2 GHz, the range resolution is 7.5 cm. However, the size of a common human is 1.8 m × 0.5 m × 0.35 m [28, 29]. In this case, the human will occupy several resolution units. Considering the relationship between human size and resolution, human must be considered as an extended target. So, in order to describe the echo and analyze its effects more accurately, the signal models need to be reconstructed by extended target theory.

In this paper, we construct the TWI signal models using the extended target theory in two typical applications: the MIMO through-the-wall mode and monostatic through-the-wall mode. Based on the models, a new kind of ghost is discovered and exploited. To improve the image quality, an efficient ghost mitigation approach is proposed. The paper is organized as follows. In Section 2, compared with the conventional point target signal models, two new signal models, for MIMO and monostatic modes, are constructed by extended target theory. Then moving target imaging for extended target is discussed in Section 3. The ghost caused by target obscuring is discovered and analyzed. In Section 4, to improve the imaging quality, a ghost mitigation method which applies CFAR, clustering method, and spatial geometry relationship is proposed. Simulations and experiments are given in Section 5. Conclusions end this paper.

#### 2. TWI Signal Model

After comparing with the conventional point target signal models, two new signal models for extended target, in MIMO and monostatic modes, are constructed in this section.

##### 2.1. Conventional Point Target Signal Model

In TWI applications, transmissivity coefficient and the reflectivity coefficient can be measured or computed by EM models. Besides, building walls, such as brick, adobe, and poured concrete walls, can be modeled by homogeneous dielectric slabs. Its transmission coefficient, , and the reflection coefficient, , are given in [30]. Their expressions are where is the thickness of the wall and and are the normal components of the propagation constants in the air and in the wall, respectively. Here is the th frequency point. is the velocity of EM in free space, and is the relative permittivity of the wall. and are the incident angle and refraction angle in the air-wall interface. is the ratio of to ; for horizontal polarization, and for vertical polarization. is the reciprocal of ; that is, . The expressions of variables and are

Using the Taylor series method, the expanded form of (2) is where denotes the reflection times when EM wave propagates inside the wall. The first term of (4) is the reflection coefficient of wall exterior. The second term corresponds to the reflection coefficient of the first reflection from the interior and multireflection inside the wall.

When EM wave propagates in the wall, the energy of multireflections is rather weak because of amplitude attenuation. Therefore, wall echo is mainly composed of the first reflections from the exterior and interior. For convenience hereinafter, the multi-reflections are neglected in the following derivation. After considering the penetration losses in the wall, the reflections coefficients for the exterior and interior can be obtained from (5). One has

Here, the variable denote EM penetration losses of the interior reflection.

*(A) MIMO Through-the-Wall Mode.* Figure 1(a) is the conventional point target signal model in the MIMO mode. In the figure, we take an antenna array with two transmitters and seven receivers as an example. EM illuminated by is marked with red lines and that transmitted by is marked with blue lines.

**(a)**

**(b)**

Therefore, taking stepped frequency signal, for example, the wall echo received by antenna is the sum of the returns corresponding to all the transmitters. One has

where denotes the wall echo received by receiver . is the total factor involving EM wave propagation attenuation and the influence of the antenna footprint. is the wave number with . is the inverse Fourier transform operator with respect to . is the spectrum of the signal transmitted by antenna . and are the positions of transmitter and receiver , with and , respectively. The variables and are signal distance of the exterior reflection and interior reflection, respectively. Taking in Figure 1(a), for example, the expressions of and are

In (7a), is a reflection position on air-wall interface. In (7b), and are refraction positions on air-wall interface and wall-air interface, respectively. is the reflection position on wall-air interface of the wall. The operation denotes the Descartes range.

Based on the model, returns of the point target scattering are where is the target echo received by antenna . is the factor involving target scattering amplitude, EM wave propagation attenuation, and the influence of the antenna footprint. is the signal distance of target scattering. Taking in Figure 1(a), for example, the expression of is where and are refraction positions on air-wall interface and wall-air interface of the exterior, respectively, and and are refraction positions on wall-air interface and air-wall interface of the interior, respectively.

*(B) Monostatic Through-the-Wall Mode.* Figure 1(b) shows the conventional point target signal model for monostatic through-wall-imaging applications. In this mode, signal is emitted and received by the same antenna. The antennas work alternately. Based on the signal model, wall reflection is computed by
Here, the signal distances of the wall exterior and interior, that is, and , are

where is the distance from the antenna to the wall.

Anonymously, the point target scattering is

where the signal distance of target scattering is

##### 2.2. TWI Signal Model for Extended Target

As mentioned above, target is considered as an isotropic point target in conventional models. However, in real TWI applications, most of the targets, such as the human and furniture, are extended targets rather than point targets. And these scatterings are no longer isotropic. Therefore, the signal models for TWI applications need to be reconstructed.

In the new models, we assume a simple scene where a human is placed in a four-wall room (Figure 2). The human is located at . Considering amplitude attenuation, reflections from the interior on the back wall and the multipath components are neglected in the derivation.

**(a)**

**(b)**

*(A) MIMO Through-the-Wall Mode.* In the new signal model, reflection from the front wall is the same as that in point target signal model, that is, (6). But the target scattering is changed. As an extended one, the target scattering is consequently the sum of the returns from its scattering points. Therefore, the extended target returns received by antenna can be expressed as
where denotes the th scattering point of the target. is the count of scatter points. is the factor of each scattering point.

Because the target is an extended one, it will partially obscure the EM waves. In Figure 2, and ′ denote the left end and right ends of the target. When EM propagates through the front wall, the waves get partially reflected by the back wall and partially obscured by the target (shown in Figure 2(a)). Now, we analyze the range of the obscured area on the back wall.

Taking antenna , for example, when EM is illuminated by transmitter , there are two cases about obscuring (shown in Figure 2(a)). One occurs before the reflection from the back wall (marked in red lines); the other occurs after the reflection from the back wall (marked in black lines). In the first case, the obscured area, , on the back wall conforms to (15a), (15b), and (15c). Here, variable denotes the length of the target along the cross range axis,

In the second case, the obscured area, , on the back wall conforms to (16a), (16b), and (16c). The derivations about (15a), (15b), and (15c) and (16a), (16b), and (16c) are given in the Appendix. One has

Anonymously, when EM is illuminated by transmitter , there are also two cases about obscuring. In the first case, the obscured area, , on the back wall conforms toIn the second case, the obscured area, , on the back wall conforms to

Using set to denote the total obscured area, as in the above analysis, set is

It is noted that set is a function of transmitter positions and target position. Besides, signal distance in the first case is smaller than that in the second case. Furthermore, reflections from the obscured area in and will be scattered by the target and then received by other antennas. So in real application, EM is mainly obscured by the target in the first case, that is, and .

Therefore, reflection from the back wall is where is reflections from the back wall received by antenna . is the reflection position on the back wall. denotes signal distance of the back wall reflections. Taking in Figure 2(a), for example, the expression of is where and are refraction positions on air-wall interface and wall-air interface of the front wall after signal transmitted by antenna , respectively. and are refraction positions on air-wall interface and wall-air interface of the front wall before signal received by the receiver, respectively.

*(B) Monostatic Through-the-Wall Mode.* Figure 2(b) demonstrates the signal model for monostatic through-the-wall mode when an extended target is in a four-wall room. In this mode, reflection from the front wall is the same as (10). According to the extended target theory, the extended target scattering is

As shown in the figure, the obscured area is different from that in MIMO mode. Obscured area on the back wall conforms to

Therefore, the back wall reflection is where the signal distance of back wall reflection is

##### 2.3. TWI Signal Model for Moving Extended Target

We assume that an extended target moves with constant speed . At time , the target is located at , with . At time , the target moves to a new position, namely, . For convenience in the following derivation, we define and as the velocity components along the cross range axis and the range axis, respectively:

*(A) MIMO Through-the-Wall Mode.* When the extended target moves in MIMO mode, target scattering is computed as
where variable is the position of the th scattering point of the extended target at time .

When target moves in this room, reflection from the first wall is the same as (6). However, the back wall reflection is different because the obscured area varies with target movement. In this model, the obscured area on the back wall at time is

Therefore, reflection from the back wall can be derived:

So, when an extended target moves in a four-wall room, the total echo received by antenna at time is

*(B) Monostatic Through-the-Wall Mode.* When the extended target moves in monostatic mode, target scattering is computed as

Target movement does not affect the reflection from the first wall, which is denoted by (10). However, the obscured area varies with time . So reflections from the back wall are

As a result, in monostatic through-the-wall mode, the total echo received by antenna at time is

#### 3. Moving Target Imaging and Ghost Analysis

Compared with the conventional point target signal models, new characteristics can be concluded when the target is an extended one. (i) The extended target, such as human, obscures the EM propagation. As a result, reflection from the back wall changes. (ii) The obscured area varies with target movement. Therefore, the moving target imaging results will be affected. In this section, we will analyze the effect of target obscuring on moving target imaging and propose a method to remove or minimize these effects.

In moving target imaging, change detection method is the first step because of its efficiency in removing the strong clutter and noise. The change detection operation is where is the subtraction result after change detection.

Then we make imaging processing for the subtract result, . Here we adopt the back projection (BP) imaging method [18–20]. In the imaging operation, the region of interest is divided into a finite number of pixels in range and cross range directions. The complex amplitude image value for the pixel located at is obtained by applying frequency-dependent phase and weights to all the received data: where is the weighting function to shape the beam. is the compensation signal distance for the pixel . It is computed as

According to change detection and BP method, moving target imaging for extended target in MIMO and monostatic modes can be computed.

*(A) MIMO Through-the-Wall Mode.* By using (30), the subtract result, , after change detection is

where the first term in (37) is the subtraction result for target scattering. The second and the third terms denote the subtraction result for the back wall reflection when and work, respectively. Two sets, and , denote the obscured areas corresponding to transmitter and transmitter , respectively. Referring to (15a), (15b), (15c), (16a), (16b), (16c), (17a), (17b), (17c), (18a), (18b), and (18c), expressions of the two sets are

After BP imaging, there are two types of targets in the result; namely,

where denotes the true target image. and are the ghosts corresponding to transmitter and transmitter . It is noted that target obscuring is more severe in the first case than in the second case, so and are mainly contributed by target obscuring in the first case in real application.

*(B) Monostatic Through-the-Wall Mode.* By using change detection method, the subtract result in monostatic through-the-wall mode is

Then the imaging result for an extended moving target is

where is the ghost in monostatic through-the-wall mode.

It is mentioned that when EM wave propagates through the wall, the velocity will be slow; that is, , which is determined by the electromagnetic parameters of the wall. In the processing by (41), the velocity is assumed to be propagating in free space; that is, . Therefore, in the original imaging results, the target will be imaged behind its true position and the ghost will also be imaged behind the obscured area. The shift distance equals in range direction. In this paper, all the following processing is applied based on the original imaging results.

#### 4. Ghost Mitigation in Through-the-Wall Moving Target Imaging

According to the proposed signal models, some conclusions can be obtained. For one thing, ghosts have a spatial relationship with the targets and transmitters in the original imaging results. In MIMO mode, as shown in Figure 3, when ghost occurs in the first case, transmitters, target, and ghost are approximately on a line in the imaging result. When it occurs in the second case, mirror transmitter, ghost, and target are approximately on a line. In monostatic mode, as shown in Figure 4, the line of the target and ghost is approximately perpendicular to the antennas array. For another, ghosts are in essence the imaging residue of the back wall. So the values in range direction of their positions are constants.

**(a)**

**(b)**

Here an approach is proposed to remove the ghosts. Firstly, adopt CFAR algorithm to obtain the detected imaging result. Then extract spatial positions of all the targets via clustering method. Finally judge the ghosts and remove them according to the spatial geometric relationship.

*(**1) CFAR Detection.* To detect targets and suppress the clutter, a Gauss distribution based CFAR method is adopted firstly. When CFAR detection is finished, a new image, , is obtained, with . Here, and are the number of pixels in range axis and cross range axis, respectively.

*(**2) Extract Spatial Positions via Clustering Method.* By using the clustering method, spatial positions of all the targets can be extracted. During clustering processing, clustering centers are updated by iterative operation. They are computed by

where and are the position of the th clustering center before and after the updating operation, respectively. denotes grey value of the pixel located at . is the maximum grey value of all the pixels in the image. and denote the number of the th cluster before and after the updating operation, respectively.

*(**3) Ghosts Judgment and Mitigation.* Steps for removing the ghost are as follows (taking the th imaging result, for example).

*Step 1. *Detect the back wall in the th imaging result. Then calculate the symmetric positions of transmitters from the back wall. Transmitters and corresponding mirror transmitters are denoted by and , respectively, where is the index, with . Here is the number of the transmitters.

Using the change detection, CFAR, and clustering methods, extract spatial positions of all the targets and define them as , with , where denotes the number of the targets in the image.

*Step 2. *Read one of the targets in the image and define it as , with . Then read another target behind , denoted by , with .(a) If it is in the MIMO through-the-wall mode, then judge whether one of transmitters (or mirror transmitters) exists conforming to
where the variable is a threshold for judging whether the target, ghost, and transmitters (or mirror transmitter) are approximately on a line. If the transmitter or mirror transmitter can be found, then go to Step 3, or update variable .(b) If it is in the monostatic through-the-wall mode, judge whether the line of and is perpendicular to the antennas array
where the variable is the judgment threshold. If the line of and is perpendicular to the antennas array, then go to Step 3, or update variable .

*Step 3. *Judge whether the position value in range direction of is unchanged according to
where the variable is a threshold. denotes the position value in range direction of in the th imaging result. is the number of imaging results.

*Step 4. *If