To keep the system complexity at a reasonable level and conform to the propagation demands, MIMO arrays are usually sparse in through-the-wall applications, which results in corrupted and gapped data. The corresponding imaging results are seriously affected by the high-level sidelobes. To solve this problem, a new imaging model for ultra-wideband (UWB) MIMO arrays is constructed via spatial spectrum theory in this paper. Based on the model, the characteristics of the spatial spectrum for the MIMO array and its effects on imaging are discussed. To improve the imaging quality, a through-the-wall imaging enhancement method is proposed via spatial spectrum estimation. Synthetic and experimental results show that, unlike the conventional amplitude weighting methods and nonlinear techniques, the proposed method can efficiently suppress sidelobes in the imagery, especially for the sparse MIMO array, and consequently improve the target image quality without degrading the mainlobe resolution. The proposed method has been successfully used in our real through-the-wall radar system.

Ultra-wideband (UWB) through-the-wall imaging (TWI) approaches that can detect objects through obstacles, such as walls, doors, and other opaque materials, are considered powerful tools for a variety of civilian and military applications [

In TWI applications, the imaging component of the application is considered the most important because it is usually the first step for the subsequent processes, such as detection, identification, and wall parameters estimation [

By using the proper array design method, we can obtain an optimal array configuration. However, in certain real cases, the equipment complexity and the shape may be our first consideration. Therefore, we make the tradeoff between size and performance [

To suppress the sidelobes and improve the image quality, many imaging methods for through-the-wall imaging, including the back projection (BP) method [

To retain the main lobe resolution while reducing the sidelobes, several nonlinear signal processing methods are introduced into radar imaging. Typical methods include spatially variant apodization (SVA), super-SVA, and the CLEAN technique [

Based on the rigorous derivation of the UWB MIMO array and experimental validation via real TWI radar systems, we proposed in this paper a through-the-wall imaging enhancement method via spatial spectrum theory. Unlike the conventional amplitude weighting methods and nonlinear techniques, the proposed method can effectively suppress the sidelobes from imagery, especially for the UWB sparse MIMO array, and consequently enhance the target image quality without degrading the main lobe resolution.

This paper is organized as follows. In Section

We assume a MIMO array has M transmitters and N receivers, as shown in Figure

The geometry of the MIMO array imaging scene.

We consider a general bistatic radar scene with a target as shown in Figure

Then, (

The fixed value

We further define the virtual wavenumbers

If the wavenumbers are expressed in the form of vectors as

The relationship between the virtual element wavenumber, the transmitter wavenumber, and the receive wavenumber.

Therefore, by taking the inverse Fourier transform of the spatial spectrum of the target scattering, that is,

As a result, for the MIMO array constructed by M transmitters and N receivers, the spatial spectrum of the received signal is determined by the array structure. By using an ideal point target located at the origin, that is,

According to (

As we know, an imaging system can be fully characterized by the point spread function (PSF) defined as the response of the imaging system to an ideal point source. Equation (

For an imaging system, the ideal support area of the spatial spectrum is an evenly sampled rectangle, as shown in Figure

Geometric shapes of the spatial spectrum support area.

Rectangle

Isosceles trapezoid

Gapped rectangle

Three different support areas of the spatial spectrum and the corresponding target images: (a) rectangle, (b) isosceles trapezoid, (c) gapped rectangle, (d) target image for Figure

Unfortunately, the support area of a wideband wide beam imaging system is an annulus sector. In this situation, a trapezoid is used instead of a rectangle to approximate the actual spectral support area to increase the resolution [

For the isosceles trapezoid shown in Figure

For the gapped spatial spectrum shown in Figure

To analyze the effects of the gapped spatial spectrum on the imaging result, Figure

The PSF figures in the cross-range direction. In the figure, the blue lines denote the PSF for the ideal support area, that is, Figure

According to the derivation and figures, the PSF performance is determined by the spatial spectrum distribution. Furthermore, the distribution and levels of the sidelobes are determined by the shape and density of the spatial spectrum, respectively.

Three characteristics of the spatial spectrum for the UWB MIMO array can be determined. First, a large processing angle is needed in the low frequency band to obtain a satisfying azimuth resolution. However, in real practice, the processing angle is usually limited. Therefore, the support area is no longer nearly rectangular but is described by an annulus sector. In this situation, the trapezoid is usually used instead of the rectangle to approximate the actual spectral support area. Second, to keep the system complexity reasonable, the elements are usually sparse and the element spacing is significantly higher than

In order to explain the characteristics, here we take a spare array, for example. The configuration of the array is shown in Figure

Split transmit virtual aperture array and its virtual elements.

Split transmit aperture array

Virtual elements

The transmitted signal is a stepped frequency waveform, with a range from 0.5 GHz to 1 GHz. The increment frequency is 2 MHz. For a point target located at (0 m, 5 m), we obtain the spatial spectrum support area shown in Figure

Support area of the spatial spectrum for this array.

To analyze the effects of the gapped spatial spectrum on target imaging, the result and profile in the cross-range direction are presented in Figures

The target imaging result.

The profile in the cross-range direction of the target image.

As shown in the analysis above, the serious sidelobes problem in the STVA system is caused by the missing spatial spectrum. To suppress the sidelobes, conventional methods are applied using a weighting function, such as the Hanning, Hamming, or Blackman functions. However, these weighting methods suppress the sidelobes at the expense of the main lobe resolution. A through-the-wall imaging enhancement method via a spatial spectrum estimation for suppressing the sidelobes without degrading the main lobe resolution is presented in this section.

The principle of our method is to extrapolate the missing support area using the existing spatial spectrum. Then, according to the filled support area, the sidelobes-suppressed image can be obtained by applying the two-dimensional inverse Fourier transform.

The common method for obtaining the support area of the spatial spectrum for the target image is the Stolt interpolation, which is widely used in far-field-based imaging. However, in TWI MIMO radar applications, the distribution of the spatial spectrum is so complicated that the interpolation processing is inaccurate. According to the derived relationship between the image and the spatial spectrum, in our method, the support area is obtained by taking the 2D Fourier transform of the image. Thus, the steps of our method are as follows.

The missing sample data of the spatial spectrum can be estimated by the existing data. (a) The target is in the middle line of the array. (b) The target is not in the middle line of the array. In this situation, a transfer matrix is needed.

When the target is not in the middle line of the array, the spatial spectrum will not be symmetrical along

Additionally, in TWI MIMO radar applications, different targets have different incident angles and received angles. Therefore, the spatial spectrums of the targets will be located at different places. To minimize the effects of the overlapped spectrum, the whole image area can be divided into several small subregions. Then, the extrapolation can be applied in each subregion.

The simulation and experiments used to validate the proposed method are described in this section. In the simulation, the abovementioned array, which is shown in Figure

Using the back projection (BP) imaging method, the original image is given in Figure

The original imaging result by the back projection imaging method.

The processed result by the proposed method.

The sidelobes are suppressed by the proposed method. The PSLR for each target decreased from −10.0 dB to −15.9 dB, −17.1 dB, and −15.9 dB, respectively. The main lobes in this figure are all unchanged.

Because the spatial spectrums of the targets overlap (see Figure

The spatial spectrums for the three targets overlap largely when we take the 2D Fourier transform of the whole image area.

By dividing the imaging area into several subregions, the spatial spectrum for each target is obtained. (a–c) The gapped spatial spectrum for three targets, namely, P1, P2, and P3, respectively. (e-f) The extrapolated spatial spectrum for each target, that is, P1, P2, and P3.

To validate the performance of the proposed method, the through-the-wall imaging experiments are processed in a real environment. In this experiment, a sparse STVA array, which has two transmitters and six receivers, is used. The length of the array is 4.1 m, and two transmitters are placed at the two ends of the array. The height of the array is 1.5 m and the interelement space of the receivers is 0.25 m. The antennas used in the system are Archimedes antennas. A transreceiver module is designed to transmit and receive the EM wave. The waveform used in the system is stepped frequency signal. Its frequency range is from 1 GHz to 2 GHz, with the increment step of 2 MHz. The principle of the radar system is given in Figure

The principle diagram of through-the-wall radar system.

Imaging data were collected by the radar system. Radar system is placed at the left side of a cinderblock building at a distance of 23.7 m. The antennas are parallel to the side wall. As shown in Figure

Imaging of a person inside a building: (a) the geometry of the imaging and (b) a man stands behind the left-side cinderblock wall.

A standard differential back projection (BP) imaging algorithm is adopted to process the acquired data. It is noted that the wall parameters are estimated and compensated by using the image-domain method (see [

The original imaging result by the standard differential BP imaging algorithm.

The processing result by the method proposed in this paper.

To validate the algorithm performance for the static target behind the wall, another experiment is processed. In the experiment, we use a 30 cm trihedral as the target. The trihedral is placed in the abovementioned building, with 2 m behind the side cinderblock wall (see Figure

In the static target experiment, a trihedral is used as the target and placed 2 m behind the wall.

By using the BP imaging method and background subtract technique, the original imaging result is obtained (see Figure

The original imaging result of the trihedral. In the figure, target has strong sidelobes.

By using the proposed method, the sidelobes are suppressed.

In this paper, we construct an imaging model for an UWB MIMO radar via the spatial spectrum. The rigorous derivation of the model shows that the more spatial spectrum is used, the better imaging performance will be obtained. Therefore, when designing a MIMO array, the best solution is to make full use of the spatial spectrum. Unfortunately, to keep the system complexity at a reasonable level and conform to the propagation demands, MIMO arrays are usually sparse in through-the-wall applications, which results in corrupted and gapped data. The corresponding imaging results are seriously affected by the high-level sidelobes.

Aiming at this problem, we proposed a spatial spectrum-based imaging enhancement method in this paper. By estimating the missing spatial spectrum, the effects of the gapped virtual elements can be significantly minimized. The processing results of the synthetic and experimental data show that the proposed method can efficiently improve the imaging quality for both the moving target and static target in through-the-wall applications. Unlike the conventional amplitude weighting methods and nonlinear techniques, the proposed method does not degrade the main lobe resolution when suppressing the sidelobes. At present, the proposed method has been successfully applied to our real through-the-wall radar system.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China under Grants 61372161 and 61271441.