Radar’s Resolutions

In order to measure the 3-dB-beamwidth of the system, as shown in Fig. 4.16, a corner reflector with a nominal radar cross section of σ0 = 150 m2, is placed in an anechoic

chamber, at a range R = 23.5 m, with Azimuth and elevation angles of φ = 0◦ _and

✓ = 0◦_{, respectively. With the FFT processing and FMCW waveforms’s parameters}

presented in the former sections, a three-dimensional radar image, which contains the information of range, Azimuth and elevation, is calculated.

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Figure 4.16: _{Picture of the anechoic chamber for the measurement of the angular} resolution. The target is placed at a distance of 23.5 meters.

-3 dB

Figure 4.17: _{Azimuth profile, angular section view of the 3D radar image capture of} the target at 23.5 m, in the anechoic chamber.

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-3 dB

Figure 4.18: _{Elevation profile, angular section view of the 3D radar image capture of} the target at 23.5 m, in the anechoic chamber.

Angle in degree

-25 -20 -15 -10 -5

0

5

10

15

20

25

Amplitude in dB

-30

-25

-20

-15

-10

-5

0

Azimuth

Elevation

3-dB

Figure 4.19: _{Superposition of Azimuth and elevation profiles, angular section views} of the 3D radar image capture of the target at 23.5 m, in the anechoic chamber.

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Figure 4.20: _{FFT across range plot, section view of the 3D radar image capture of} the target at 23.5 m, in the anechoic chamber.

Fig. 4.17shows the Azimuth (φ = 0◦_{) profile taken at the range cell of the central target,}

whereas Fig. 4.18 shows the elevation (✓ = 0◦) profile. Under the assumption that the corner reflector represents a point target and that the distance is big enough to be in the far-field region, the theoretical values of the angular resolution of the MIMO virtual array, calculated in Section 4.7, should match with the measured 3-dB beam-width of the target’s main lobe. The measured Azimuth resolution is ∆✓3dBx = 4.7

◦ _{and the}

elevation resolution is ∆φ3dBy = 3.6

◦ _{whereas the calculated is ∆✓}

3dBx = 4.5

◦ _{and the}

elevation resolution is ∆φ3dBy = 3.5

◦_{. As it can be seen, the measured and calculated}

angular resolutions match very well and a difference between the two is expected to arise. This is due to the fact that the equations are an approximation based on a limited number of antenna elements and, additionally, weighting of antenna elements by means of classical windowing functions like the ones used in this algorithm, allows for better side lobe suppression, but at the expense of a slightly reduced angular resolution, due to an enlargement of the width of the main lobe. Additionally, it is important to notice that, in the estimation along the Azimuth direction, the missing element is included, while in the radar beam-forming process, this missing element is calculated as the average of its neighbouring elements. An image, showing the superimposed angular profiles is illustrated in Fig. 4.19, where it can be noticed how the elevation resolution, due to a larger aperture in the Y-direction, is finer, thus resulting in a finer main lobe’s beam-width at 3 dB.

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-3 dB

Figure 4.21: _{Range profile, zoom in of the plot in Fig. 4.20.}

for a capture of the same target at 23.5 m, in the anechoic chamber. The FFT plot is shown in Fig. 4.20, whereas a zoom in of the same plot is shown in Fig. 4.21. As it can be noticed, the effective range resolution is of ∆R = 0.17 m, which is slightly different from the theoretical value calculated in equation (4.9). For the same reason as above, by adopting classical windowing functions like the ones used in this algorithm, a slight increase in the main lobe is expected.

A 2D radar image, cut in the Azimuth plane and the elevation plane, of the complete 3D image obtained through the 3D-FFT beam-forming radar processing, is shown in Fig.

4.22and Fig. 4.23, respectively. The targets, and the side lobes, are clearly visible at a range of 23.5 m.

The overall good imaging performance of the radar is verified as well, by the fact that the walls of the anechoic chamber can also be seen in these images. In Fig. 4.22, the reflections in the picture seem to indicate the presence of a reflecting surface at -4 m and +4 m of cross range (X-Position) and along the range axis (Z-Position), therefore for a total span of 8 m, in accordance to the dimensions of the anechoic chamber shown in Fig. 3.33, subsection A, presented previously. Similarly, in Fig. 4.23, the reflections are at -3 m and +3 m of cross range (Y-Position) and along the range axis (Z-Position), therefore for total span of 6 m, in accordance to the dimensions of the anechoic chamber shown in Fig. 3.33, subsection B.

Finally, a 2D radar image, cut in the range bin of the target, from the complete 3D image obtained through the 3D-FFT beam-forming radar processing, is shown in Fig.

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WALLS

Figure 4.22: _{Azimuth-range section view of the 3D radar image capture of the target} at 23.5 m, in the anechoic chamber.

TARGET TARGET WALLS

Figure 4.23: _{Range-elevation section view of the 3D radar image capture of the target} at 23.5 m, in the anechoic chamber.

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Figure 4.24: _{Azimuth-elevation section view of the 3D radar image capture of the} target at 23.5 m, in the anechoic chamber.

4.24. As it can be noticed, the target is perfectly identifiable at an elevation of φ = 0◦

and Azimuth of ✓ = 0◦, together with its side lobes, along both dimensions.