IMPLANTACION DE PROYECTO SBAS 1. Situación Actual si estuviera el proyecto

In the previous subsection it was shown that some target information can be extracted from the 1D target signal. In this section true 2D target imaging will be discussed, as a means for improving the generated target images. Here a 2D target image means that

the expected result is an image in x- and y-axis, rather than an outline of the profile, as shown above.

Two dimensional signatures of the FS target are produced by the simulation models, discussed in section 4.4, for an array receiving the target signal, as shown in Fig. 5.9. An example of a target signature and the corresponding image can be seen in Fig. 5.10, below. It shows very good resemblance with the target shadow, with a further accuracy analysis of the 2D images done in chapter7. For 2D target imaging the accuracy analysis is done only in the form of resolution analysis, as such configurations are impractical. In the discussion below it can be seen that the vertical array required will be of the order of a few target heights.

Figure 5.9: Simple schematic of a 2D FSR configuration with a vertical Rx array.

The TSRP algorithm was applied to the modelled two-dimensional target signatures of a Range Rover Sport (RR) target. Simulated signals and profile reconstructions for a RR target are seen in Fig. 5.10, 5.11 and 5.12 for three different frequencies - 100 MHz, 1 GHz and 2 GHz.

(a) (b)

(c)

(d)

Figure 5.10: Two-dimensional FSR imaging for a Range Rover Sport target of size 4.6 x 1.8 m at 1 GHz incident frequency. Real part (a) and imaginary part (b) of the complex signal are shown. Also, the target shadow - (c) and the reconstructed image - (d). Receive array dimension is equivalent to the dimension of the vertical axis in (a) and (b) - 60 m

(a) (b)

(c)

Figure 5.11: Two-dimensional FSR imaging for a RR target of size 4.6 x 1.8 m at 100 MHz incident frequency. Real part (a) and imaginary part (b) of the complex signal are shown. Also, the reconstructed image - (c). Receive array dimension is equivalent to the dimension of the vertical axis in (a) and (b) - 100 m

(a) (b)

(c)

Figure 5.12: Two-dimensional FSR imaging for a RR target of size 4.6 x 1.8 m at 2 GHz incident frequency. Real part (a) and imaginary part (b) of the complex signal are shown. Also, the reconstructed image - (c). Receive array dimension is equivalent to the dimension of the vertical axis in (a) and (b) - 40 m

As it can be seen from Fig. 5.11, the resolution of TSPR 2D images is acceptable even at 100 MHz (λ = 3m). The resolution of the target images will be discussed further in chapter 5.

Also, according to the modelled results, a method for interpolation of the 2D target signa- ture from multiple 1D signatures can be analysed, a multiple-input-single-output (MISO) system, as discussed in section 5.4.

This system will have to rely on the analysis of the 2D image resolution, governed by the Holography principle, 3.2.3. The system will have to deploy multiple receivers in the vertical dimension, to be able to produce the required resolution for recognition of the target and, also, preserve the phase information of the FSCS of the target.

Thus a sufficient number of receivers needs to be present, spaced accordingly. Modelling of the 2D diffraction patterns of the targets were analysed, where a few receivers in the vertical dimension are modelled, thus receiving a number of signals, each consisting of a FS target signature for the same target. The resulting vectors are then interpolated, so that spacing between receivers in the vertical axis corresponds to ∆y ≤ 1/4λ. This spacing between interpolated waves is chosen through qualitative comparison between the solutions of a number of modeled results based on different spacings. It was chosen as a best result for both speed of the solution and the accuracy of the result.

Analysis of this technique can provide with a minimum number for receivers, to provide a visually recognisable target image. Also, considering the resolution equation for DIH, equation 3.21, and target height of 1.8 m, it is expected that for a vertical array of 5.5 m size, the reconstructed image is going to be only two pixels in height, as seen in Fig. 5.13, where a 2D target signature is interpolated across vertical space from ground (0 m) to 5.5 m, by 5 receivers spaced 1.1 m apart (same result is obtained by simulating 4 receivers

spaced by 1.385 m).

(a)

(b)

Figure 5.13: Real part of a two-dimensional target signature - (a), recorded by a sparse array of vertical receivers and the 2D target image reconstructed - (b), for a RR target (4.6 x 1.8 m) for 1 GHz incident radiation at 30 m from receiver.

Thus a relatively large array would be needed for the accurate extraction of 2D target profiles via this method. However a smaller array will still produce a 2D image, which can be used in conjunction with the 1D reconstructed profile. As seen from Fig. 5.13(b), the outline reveals where the top and bottom (wheels) of the car is. The wheels are positioned around 520 and 550 sample on the horizontal axis and haev magnitude of

around 50. As previously mentioned analysis of the number of sidelobes required for the correct extraction of the target profile can be seen in section 7.2.2. The results indicate that at least three sidelobes should be analysed. According to aperture diffraction a width of a lobe is approximately given by:

∆Θ = 2λ

h , (5.17)

where ∆Θ is the spacing between nulls in radians and h is the height of the aperture considered. For the example considered, the width of a lobe for a target of 1.8 m height is around 9 degrees. This would result in minimum receiver height (for the recording of three sidelobes) of around 5 m at a 30 m observation distance.

The analysis regarding the height of the receiver array is based on the analysis of the minimum length of signal needed for the accurate reconstruction done in Chapter 7, where the conclusion is made that at least 3 sidelobes must be recorded.

In this subsection 2D target imaging was discussed. However, there are constraints which do not allow for 2D target imaging in practical applications of FSR, such as the availability of high vertical array of Rx antennas.

In the section the different methods for target imaging (profile reconstruction) in FSR were discussed. It was shown that a novel approach based on holographic principles has at least the same accuracy than previously published SISAR model. The properties of the reconstructed images was discussed, together with the availability of 2D target imaging. In the next section example results for simulated target signatures will be presented.