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5
EXPERIMENTAL RESULTS
5.1 Experimental Scenario
In this chapter ISAR imaging with DVB – S/S2 signals is demonstrated by experiment. The experiment is a turntable experiment with a van as target: this geometry allows to have the maximum aspect angle variation, that leads to obtain images with a high quality in terms of scatterers recognition. Since the effective target rotation vector Ω𝑒𝑓𝑓(𝑡) (described in Section 3.1.1) is perpendicular to the turntable, because of its definition, and the Image Projection Plane (IPP) is the plane perpendicular to that vector, the IPP and the plane described by the platform coincide. For this reason, the images obtained during the tests will show the top part of the target.
5.1.1 Geometry
The (Fig. 5.1) explains the geometry of the tests:
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As shown in (Fig. 5.1), the exactly positions of each antennas were measured, using a GPS system, with respect to a Cartesian axes system centered in the target.
In this situation, the bistatic angle 𝛽(𝑡) is constant and it can be calculated using the Carnot Theorem, for a value of 𝛽 = 0.86233 𝑟𝑎𝑑.
As it will be explained in next sections, to attribute the bistatic system to a monostatic equivalent system, the angle 𝛼 between the surveillance antenna – target segment and the East direction must be calculated as well. Using the Scalar Product:
〈( 1 0 0 ) ( −17,8688 −48,0283 0,6493 )〉 (5.1)
between the East unit vector and the surveillance antenna vector (5.1), an angle of 𝛼 = 1,9270 𝑟𝑎𝑑. is obtained.
5.1.2 Target and Transponders
For the turntable tests, a Mercedes – Benz 416 CDI has been used as target (Fig. 5.2 – (a), (b)). It is 6.589 m. long and 1.988 m. wide.
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Fig. 5.2 – (b): Acquisition Test (Courtesy of Fraunhofer FHR)
Concerning the transponders used for the tests, two different cases have been taken under consideration:
1) Large gap between low and high band. In particular the two local oscillators have been set at 𝑓𝐿𝑂1 = 11626 𝑀𝐻𝑧 and 𝑓𝐿𝑂2 = 11817 𝑀𝐻𝑧, vertical polarization (Fig. 4.3), in order prevent high side lobes acting on the two bands. The frequencies correspond to the number 28 and number 70 of the Astra 1M transponders respectively (Fig. 4.2 – (c)).
2) Small gap between low and high band. In particular the two local oscillators have been set at 𝑓𝐿𝑂1 = 11641 𝑀𝐻𝑧 and 𝑓𝐿𝑂2 = 11720 𝑀𝐻𝑧 (Fig. 4.3), in order to try the Compressive Sensing technique (Section 5.3). The frequencies correspond to the number 29 and number 38 of the Astra 1M transponders respectively (Fig. 4.2 – (c)). The original choice was to take under consideration the horizontal polarization plan, but due to the fact that the files were not available during the processing tests, the vertical polarization has been used. At those frequencies, the vertical polarization plan has big frequency gaps (that contain noise) and any full transponder’s band is
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inside the 65 𝑀𝐻𝑧 bandwidth of the filter (Fig. 4.3). The latter is the reason why the performances will be limited with respect to the optimal achievable ones.
5.2 Range – Doppler Technique Results
As explained in (Section 3.1.2), the Range – Doppler technique is applied to the cases upper defined. The Range – Doppler technique is the easiest algorithm for the ISAR images formation. The main steps are:
Matched Filtering to the Received Signal,
Fourier Transform along the Fast Time (or Time Delay) 𝜏, Motion Compensation (unnecessary in turntable geometry),
Spatial Frequency Mapping,
2D – IFT.
The technique has two important limitations. It can be applied when:
- The total aspect – angle variation is small enough (≤ 5 − 6 degrees). In such a condition the domain 𝑊 can be approximated by means of a rectangle (Fig. 3.8),
- The grid is evenly spaced (Fig. 3.8). This is achieved when the rotation vector is constant (for short observation time, or in turntable geometry as well).
5.2.1 Single Bands
The (Fig. 5.3 – (a), (b)) show the HRR (High Range Resolution) profile and the RD (Range – Doppler) map of the target respectively, using the low band signal.
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Fig. 5.3 – (a): High Range Resolution Profile
Fig. 5.3 – (b): Range – Doppler map of the target
The (Fig. 5.4 – (a), (b)) show the HRR (High Range Resolution) profile and the RD (Range – Doppler) map of the target respectively, using the high band signal.
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Fig. 5.4 – (a): High Range Resolution Profile
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As explained in (Section 3.3.3), with a bandwidth of 𝐵 = 65 𝑀𝐻𝑧, a range resolution of Δ𝑅 =
𝑐
2𝐵= 2.4 𝑚. is obtained for both the RD images. The observation time is 𝑇𝑜𝑏𝑠 = 1 𝑠., thus a cross – range
resolution of Δ𝑅𝑐𝑟 = 𝑐
2𝑓0|Ω⃗⃗ 𝑒𝑓𝑓|𝑇𝑜𝑏𝑠 ≅ 12.32 𝑐𝑚. is obtained.
5.2.2 Double Band
Since the radar developed by the institute (Fig. 4.3) has two receiving branches, one for the low band and one for the high band, it is interesting to see the effect when both the signals are used for the imaging processing. Using the Complex Sampling Theorem, and reconstructing the signal (the high band part is brought by the receiver between 0 and 65 𝑀𝐻𝑧, so it must be modulated again to have the signal in the original position with respect to the low band signal), we have a total bandwidth of 𝐵 = 137 𝑀𝐻𝑧. The (Fig. 5.5 – (a), (b), (c)) show the HRR (High Range Resolution) profile, the RD (Range – Doppler) map of the target and the spectrum of the image respectively.
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Fig. 5.5 – (b): Range – Doppler map of the target
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As explained in (Section 3.3.3), with a bandwidth of 𝐵 = 137 𝑀𝐻𝑧, a range resolution of Δ𝑅 =
𝑐
2𝐵= 1.1 𝑚. is obtained. In (Fig. 5.5 – (c)) the gap of 7 𝑀𝐻𝑧 can be appreciated.
The gap between the two parts of the spectrum creates unwanted degradations on the image, such as it do not allow to reach the theoretical value of the range resolution given a bandwidth of 137 𝑀𝐻𝑧, and creates high grating lobes along the range axis. The grating lobs may be interpreted as false scatterers, inducing errors during the image interpretation and target classification.
5.3 COMPRESSIVE SENSING RESULTS
As seen in previous sections, one of the main limitations of the passive ISAR is the range resolution. Since the range resolution depends on the bandwidth of the signal used for the ISAR processing, we cannot control directly the performances.
To obtain high quality ISAR images, a great spatial resolutions should be reached. Television broadcast sources, since they are not thought for radar application, offer a really low range resolution, as the bandwidths used are smaller with respect to those normally used in dedicated ISAR systems. To reach the desired range resolution, multiple DVB – S/S2 transponders can be coherently adjoined in order to create a wideband signal.
5.3.1 Basic Theory
With Compressive Sensing we refer to the techniques able to reconstruct a sparse or compressible signal from a limited number of measurements by solving an optimization problem. The Compressive Sensing can be applied when real data present missing samples (frequency and slow – time both) due to some system malfunctioning, data compression or frequency gaps. In these cases, the RD image obtained is distorted or has a coarse resolution, because of the signal deficiency.
The important thing for the CS application is that the signal must be sparse, that is, it can be represented by some non – zero samples in a suitable orthonormal basis: at high frequencies, as on our case (Section 4.1), a radar signal is sparse in the image domain, since it can be approximated by the superimposition of few prominent scatterer responses [15]. In other words, images are composed of a limited number of strong point – like scatterers with respect to the number of pixels.
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As previously mentioned, and explained in (Section 3.3.3), for passive ISAR with DVB – S/S2 signals, a higher range resolution can be achieved by adjoining multiple adjacent channels. When such a multichannel signal is used for ISAR imaging, grating lobes appear in the ISAR image [16].
The (Fig. 5.5 – (c)) represent the spectrum of the (Fig. 5.5 – (b)): it shows a gap of 7 𝑀𝐻𝑧, that can be filled by the utilization of the CS, since the gap is due by the configuration of the two bands at radio frequency.
5.3.2 Results
The (Fig. 5.6 – (a), (b)) show the processed spectrum and the respective RD image after the Compressive Sensing application respectively.
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Fig. 5.5 – (b): Range – Doppler map of the target
In the RD image, a reduction of the grating and side lobes can be appreciated, as the filled gap in the image spectrum. Unfortunately, as explained in the (Section 5.1.2), the quality of the image is altered due to the noise inside the gaps at those frequencies for the vertical polarization plan. Being uncorrelated between the surveillance and reference channel, the noise does not allow to obtain an high scattered signal from the target, reducing the general quality of the image.
5.4 BACK – PROJECTION RESULTS
In order to prove the validity of the experiments, another type of image formation algorithm has been applied. The intention is to obtain another ISAR image where the dimensions of the spot matches quiet well with the dimensions of the spot in the Range – Doppler image, and the real dimensions of the target.
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In this section the Back – Projection algorithm is proposed. This algorithm is the most basic image formation algorithm with the fewest assumptions: no far – field assumption, no assumption on the form of the target motion. Furthermore, it is also suitable for the bistatic geometry [17].
5.4.1 Basic Theory
The algorithm assumes that the signal return in the frequency domain of a single scatterer at a bistatic distance 𝑑𝑒 and with reflectivity 𝐴𝑒 is
𝑆𝑒(𝑓, 𝑛) = 𝐴𝑒𝑒−𝑗2𝜋𝑓 𝑑𝑒(𝑛)
𝑐 (5.2)
and the complete signal is composed as the superimposition of all the observed scatterers from the target
𝑆(𝑓, 𝑛) = ∑ 𝑆𝑒
𝑒
(𝑓, 𝑛) (5.3)
Depending on this signal model, after matched filtering with the signal caught by the reference channel 𝑆𝑟𝑒𝑓(𝑓, 𝑛) (for the SNR maximization), the reflectivity 𝐴̂ of a point (𝑥′, 𝑦′) (at a given 𝑧′) is
estimated by using the estimated complex phase term from (5.2) to compensate the phase displacement:
𝐴̂(𝑥′, 𝑦′) = ∑ ∑ 𝑆(𝑓, 𝑛)𝑆 𝑟𝑒𝑓∗ (𝑓, 𝑛)𝑒𝑗2𝜋𝑓 𝑑̂(𝑥′,𝑦′,𝑛) 𝑐 𝑓 𝑛 (5.4)
The coordinates (𝑥′, 𝑦′, 𝑧′) relate to a coordinate system that is embedded on the target.
5.4.2 Results
In order to compare the Range – Doppler and the Back – Projection images, it is necessary to have both in a coordinate system defined by range and cross – range. This is simply done by applying an axes rotation so that the angular bisector between transmitter and receiver coincides with the y – axis (equivalent monostatic geometry) (Section 5.1.1).
The (Fig. 5.7) and (Fig. 5.8) show the resulting image after the Back – Projection application and a comparison between the two images obtained with the two different algorithms:
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Fig. 5.7: Back – Projection image of the target
(a) (b)
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As significant result, we can observe that the two spots have about the same dimensions and are comparable with the dimensions of the real target (Section 5.1.2). Of course, the exact dimensions of the two spots depend on the angular position of the target (angular shift of the front-back bumber segment with respect to the line of sight of the surveillance channel) over the turntable during each recording time (e.g. the segment could be aligned with the LOS of the surveillance channel, or it could be perpendicular to the LOS).
In particular, in cross – range direction the dimensions of the spots and the target width match quite well; in range direction it is more complicated to judge because the resolution in poorer with respect to the cross – range: the bandwidth of the signal is not enough wide to obtain a range resolution able to discriminate small close scatterers (Section 3.3). Nevertheless, within the larger boundaries given by the range resolution, the dimensions are compatible with reality.
