High Resolution Radar Tomographic Imaging Using Single-Tone CW Signals

Hongbo Sun, Hongchuan Feng Temasek Laboratories

Nanyang Technological University Singapore 637553

{ehbsun, hcfeng}@ntu.edu.sg

Yilong Lu School of Electrical and Electronic Engineering

Nanyang Technological University Singapore 639798 eylu@ntu.edu.sg

Abstract—Radar tomographic imaging is a special radar imaging technique which can achieve very high spatial resolution (up to ¼ wavelength) but with very narrow signal bandwidth. Although the theory of radar tomography had been developed for more than 20 years, very few experimental results can be found in public literatures. In this paper, the radar tomographic imaging is investigated and some measurement results of radar tomographic imaging using single-tone CW signals are presented. The theoretical spatial resolution is achieved and good agreement is obtained between the measured and simulated results.

I. INTRODUCTION Normally the high resolution radar imaging is achieved

with large frequency diversity (wideband waveform up to hundreds of MHz) and small spatial diversity (small integration angle with respect to the target or the scene to be imaged). This is just the typical operating mode of synthetic aperture radar. Alternatively, high resolution imaging can also be achieved with very small frequency diversity (as low as a single-tone signal) but large spatial diversity (large integration angle up to 360 degrees). This special mode of imaging technique is called tomographic imaging, which has been successfully applied in medical applications (known as Computer Aided Tomography - CAT) since 1970s [1]. In 1980s, the concept of tomographic imaging was introduced into radar applications [2][3]. Different from the conventional radar imaging techniques, the tomographic imaging is quite unique as it can provide very high spatial resolution (about ¼ wavelength) with very narrow signal bandwidth (i.e., single-tone frequency). This is very attractive because potentially a high-resolution imaging system can be built with very simple hardware and at very low cost. It should be noted that the tomographic imaging using narrowband signal often requires large spatial diversity, i.e., large integration angle with respect to the target or the scene to be imaged. Thus, it is more suitable for some short-range surveillance applications [4].

The principle of radar tomographic imaging has been developed for more than 20 years. However, after the early

work of [5], there is not much experimental results can be found in public literatures. References [6] show some indoor measurement results where wideband signal is used. Reference [7] presented the results of both wideband and narrowband signal at X-band. The objective of this paper is to investigate the performance of radar tomographic imaging when using single-tone CW signals, which is organized as follows: Section II briefly summarizes the two different reconstruction techniques of radar tomographic imaging, i.e., direct Fourier reconstruction and matched filter reconstruction; Section III analyzes the point spread function (PSF) of tomographic imaging when using single-tone CW signals; Some measurement results in a microwave anechoic chamber are presented in Section IV; Finally, Section V concludes the whole paper.

II. TOMOGRAPHIC IMAGING TECHNIQUES

A. Direct Fourier Reconstruction [2][5] Direct Fourier reconstruction is based on the projection

slice theorem. Assume ),( yxg is the 2-D scattering coefficient to be imaged, )( jup

iθ is the projection of ),( yxg at angle iθ , and ),( YXG is the 2-D Fourier transform of

),( yxg . The scattering coefficient ),( yxg can be reconstructed from samples of its projections as follows: For each angle iθ , the samples of the Fourier transform )(Up

iθ

are computed from 1{ ( )}i

Nj jp uθ = via the fast Fourier transform

(FFT). From the projection-slice theorem, the samples of )(Up

iθ are samples of ),( YXG along a line at angle iθ . Thus, the series of 1-D FFT's for the various iθ provides samples of ),( YXG on the polar grid. Interpolating the polar samples of ),( YXG to a Cartesian grid allows the efficiency of the 2-D inverse FFT to be utilized to calculate the ),( yxg on a Cartesian grid (Note: recently the non-uniform FFT algorithm was applied in tomographic imaging, which can avoid the interpolation from polar to Cartesian grid [8]).

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B. Matched Filter Reconstruction [7] Matched filter reconstruction is an intuitive and

generalized radar signal processing technique, which can be applied in almost all applications. For the spatial domain image reconstruction, the matched filter simply attempts to compensate the signal’s expected delay for each pixel of the scene. For the pixel containing a target, all echoes from this pixel can be adapted to a constant phase with proper phase weights. Adding up these phase weighted echoes will produce an image of the target. This matched filter reconstruction technique is also extended to moving targets in [7].

C. Comparison Theoretically, both direct Fourier technique and matched

filter technique can achieve good image reconstruction performance. Benefiting from the efficiencies of the FFT operation, the computational load of direct Fourier technique is much lower than that of matched filter technique. Unfortunately, the application of direct Fourier technique is limited by the following constraints:

• Direct Fourier reconstruction is derived based on the assumption of plane wave propagation, that means the distance between target (or the scene to be imaged) and radar should satisfy the far-field condition, and the scene to be observed cannot be too large.

• Before utilizing 2-D inverse FFT to reconstruct the image, the polar samples of spatial frequency domain data should be interpolated into a Cartesian grid. The final image quality depends on the interpolation accuracy.

• The processing of direct Fourier reconstruction involves the data transform between spatial domain and spatial frequency domain. Thus, the scene to be imaged (or targets distribution) must be limited within a certain unambiguous area. Outside this area the spatial ambiguity will occur.

The advantages and disadvantages of the two image reconstruction techniques are summarized in Table I. As the matched filter technique won’t suffer from these constrains, we only apply the matched filter technique to reconstruct the image in the following processing.

TABLE I. COMPARISON OF THE TWO IMAGE RECONSTRUCTION TECHNIQUES

Direct Fourier reconstruction

Matched filter reconstruction

Far-field constraint Yes No

Interpolation error Yes No

Spatial ambiguity Yes No*

Compurational load Low High * When using matched filter reconstruction, the scene to be imaged will

also be limited by the angular sampling interval, otherwise the high sidelobes of the scatterers at the scene periphery will appear in the scene. But this is different from the spatial ambiguity caused by direct Fourier reconstruction. More results can be found in Section IV.

III. POINT SPREAD FUNCTION ANALYSIS In this section, we will analyze the point spread function

(PSF) of tomographic imaging when using single-tone CW signals. All results are based on the observation of 360 degrees.

First, when only one single-tone frequency is used, the measurement samples in 2-D spatial frequency domain just form a circle around the origin with a radius λ2 , where λ is the signal wavelength. The corresponding PSF is the 2-D inverse Fourier transform of this circle, which is a zero-order Bessel function. Figure 1 illustrates the PSF when a 1GHz single-tone frequency is used. The spatial resolution is about

4λ and the first sidelobe is at about 8dB.

Figure 1. PSF when one single-tone frequency is used

When more than one single-tone frequencies are adopted, the sidelobe distribution of PSF will change. Figures 2(a)-(c) show some examples when two single-tone frequencies are used (with different frequency spacing).

(a) f1=1GHz, f2=1.2GHz

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(b) f1=1GHz, f2=1.5GHz

(c) f1=1GHz, f2=2GHz

Figure 2. PSF when two single-tone frequencies are used

Figure 3 shows the PSF when four single-tone frequencies are used (f =1GHz, 1.1GHz, 1.2GHz, and 1.3GHz). It can be seen that the sidelobes near mainlobe are very low, but the peripheral sidelobes are still high.

Figure 3. PSF when four single-tone frequencies are used (f =1GHz, 1.1GHz, 1.2GHz, and 1.3GHz)

Above simulation results show that high spatial resolution can be achieved by tomographic imaging even with only one single-tone frequency. But the high sidelobe level is an issue that should be taken into account in practical applications. When adopting two or more frequencies, the distribution of sidelobes changes significantly. It will be interesting to investigate how to combine a few single-tone frequencies to achieve low sidelobe level.

IV. EXPERIMENTAL RESULTS To verify and demonstrate the tomographic imaging

performance using single-tone CW signals, a series of

measurements are conducted in a microwave anechoic chamber. A vector network analyzer is employed as the radar transmitter/receiver to transmit/receive the single-tone CW signals and wideband stepped frequency signal (for comparison purpose). Some simple objects, such as thin metal rod (as point target) and metal box (as volume target), are fixed on top of a rotating platform as the target. For each target, data are collected for the whole round of 360 degrees with an angular sampling interval of 1 degree. The overall system setup is illustrated in Figure 4 and some photos of the measurements are shown in Figure 5.

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Figure 5. Photos of tomography imaging experimental system configuration

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Note that for this configuration, the effects of two types of signal need to be removed. The first one is direct path signal, i.e., the coupling signal directly from transmitting antenna to receiving antenna. Direct path signal will produce a false target located at the center of scene (rotation axis) when a single-tone frequency is adopted. When multiple frequencies are used, the direct path signal will form dispersed interference. The other signal that needs to be removed is the scattered signals from stationary objects in the scene (such as the base of rotator). These signals remain constant during the measurement, and will effectively form a false target at the center of scene when one frequency is used. The use of multiple frequencies can alleviate this effect, unless the distance of stationary scatterer is equal to that from radar to scene center. To remove the effects of these two types of signals, the technique of empty scene subtraction is applied. That means we conduct two separate measurements for the same scene with and without target, then subtract the result of empty scene from the image with target. The measurement results show that this technique is very successful and the effects of direct path signal and the scattered signals from stationary objects can be removed.

Based on the aforementioned experimental setup, many measurements are conducted and the phenomenons in different scenarios are analyzed. Some examples of the measurement results are as follows:

A. Images of two point targets (metal rods) To verify the resolution performance of the tomography

imaging, two metal rods are installed on top of the rotating platform as point-like targets, as shown in Figure 6. The spacing between the two metal rods is 10cm. Figure 7(a) shows the measured image of the two rods when one single-tone CW frequency 2.5GHz is used. For comparison, Figure 7(b) depicts the simulated image. It can be seen that the two rods can be clearly separated and the measured image is quite close to the simulated result. Although the two rods can be easily separated in the image, the effect of high sidelobe level is also very prominent. To reduce the sidelobe level, we also tested the performance of tomographic imaging when using stepped frequency waveform. The network analyzer was configured to transmit/receive stepped frequencies from 2.5GHz to 3.5GHz with 5MHz step. The measured and simulated image of two rods are shown in Figure 8(a)(b). The sidelobe level is significantly reduced and the two rods are detected more prominently.

Figure 6. Metal rods for point target measurement

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Figure 7. Measured and simulated images of two metal rods (one single-tone frequency 2.5GHz)

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Figure 8. Measured and simulated images of two metal rods (stepped frequency 2.5~3.5GHz)

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B. Images of metal box (volume target) A metal box (dimension 45×43.5×12.5 cm) is selected as

an example of volume target for tomographic imaging, as shown in Figure 9. Note that the scatterers on the surface of volume target can only be illuminated for a certain sector, and thus cannot be ideally focused when only one single-tone frequency is used (this phenomenon will be discussed separately in another paper). Figure 10 shows the measured image when one single-tone CW frequency 2.5GHz is used. As expected, the sidelobes are very high and the shape of the metal box cannot be identified. Figure 11 shows the measured result when stepped frequency 2.5~3.5GHz is used. The shape of metal box can be seen and the sidelobe level is also significantly reduced. Another interesting phenomenon is that some prominent scatterers are formed “inside” the box due to the interaction of the sidelobes from the box surfaces.

Figure 9. Metal box for volumn target measurement

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Figure 10. Measured image of metal box (one single-tone frequency 2.5GHz)

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Figure 11. Measured image of metal box (stepped frequency 2.5~3.5GHz)

C. Effects of angular sampling interval The data in tomographic imaging are sampled at discrete

angular intervals. This angular sampling interval determines the sampling interval in spatial frequency domain, and further determines the size of unambiguous observation area in spatial domain. It can be easily proven that the maximum radius of unambiguous area is )2( θλ Δ≤r , where θΔ is the angular sampling interval. For any scatterer (which is not necessarily at scene centre), its ambiguities will occur at the rings whose radius is integral multiple times of r. Moreover, outside the radius r with respect to a scatterer, the Nyquist sampling theorem is not satisfied and the normal sidelobes cannot be formed.

To verify this effect, measurements are conducted for a metal rod, where the distance between the rod and rotation axis is 20cm (as shown in Figure 12). First, the angular sampling interval is 1 degrees and one single-tone frequency 2.5GHz is used. The measured image is plotted in Figure 13. For this case, we can easily calculate that the radius of unambiguous area is 3.44m. So we cannot see any ambiguity in Figure 13. Figure 14 shows the measured result when the angular sampling interval is changed to 3 degrees. The theoretical radius of unambiguous area is 1.14m. Accordingly, we can clearly find the ring of high sidelobes with the radius 1.14m in Figure 14. Figure 15 shows the result when the frequency is changed to 3.5GHz, and the angular sampling interval is still 3 degrees. Because the wavelength is smaller, the maximum radius of unambiguous area is also reduced to be 0.82m. It should be noted that such ambiguity of high sidelobe won’t be removed by adopting stepped frequency signal. As shown in Figure 16, the ambiguity is still there, although the image quality is significantly improved.

Figure 12. Metal rod for point target measurement

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Figure 13. Measured image of a metal rod (1 degrees angular sampling interval, single-tone frequency 2.5GHz)

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Figure 14. Measured image of a metal rod (3 degrees angular sampling interval, single-tone frequency 2.5GHz)

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Figure 15. Measured image of a metal rod (3 degrees angular sampling interval, single-tone frequency 3.5GHz)

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Figure 16. Measured image of a metal rod (3 degrees angular sampling interval, stepped frequency 2.5~3.5GHz)

CONCLUSION AND FUTURE WORK The concept of high resolution tomographic imaging using

single-tone CW signals is experimentally demonstrated in this paper. It is shown that the spatial resolution can be as high as ¼ wavelength, even with only one single-tone frequency is used. This is very attractive for some short range surveillance applications. However, the high sidelobe level is a big problem to be solved. The simulation results show that when two or more frequencies are adopted, the distribution of sidelobes will change significantly. More research work needs to be done to investigate how to combine a few single-tone frequencies to achieve low sidelobe level in tomographic imaging.

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