## 5 Experimental Investigation
### Returning Signal Dependance with Antenna Dimensions  
The most dramatic issue when burying the sensor is the impact of the variable permittivity of the surrounding environment on the operating frequency of the fixed-length dipole antenna \(2l\). Figure 7 summarizes the impact of varying dipole length on the returned signal level depending on the surrounding medium. This experiment simulates the varying permittivity of the environment  
Figure 5: Experimental measurement of returned echoes as a function of depth (Z) of the sensor below the antennas (**a**), and as a function of antenna position along the scan axis (X) in a two-way pattern (positions 0 to 150 are right to left and positions 150 to 0 are left to right as seen in Figure 4). The shallowest sensor (**a**) exhibits a lower returning power due to its position forward from the antenna and not directly below the radiation pattern. (**b**) is a radargram recorded with the sensor buried 61 cm in gravel.  
since the electromagnetic velocity as seen by the dipole antenna decreases to the same extent as the square root of the surrounding media permittivity:  
\[\sqrt{\varepsilon}=\frac{c_{0}}{4l\times f} \tag{6}\]  
with \(c_{0}=300\) m/ us the electromagnetic velocity in free space and \(f\) the central frequency of the pulse, here 190 MHz. The sensor buried in gravel exhibits an optimal antenna length equal to 60 cm (two radiating elements of \(l=30\) cm long each), suggesting a relative permittivity of \(\epsilon_{gravel}\simeq 1.7\), close to the value tabulated in [46]. Sand exhibits a slightly higher value since the optimum dipole length is observed to be \(2l=55\) cm, suggesting a relative permittivity of the medium of \(\epsilon_{sand}\simeq 2\).  
This result illustrates the challenge of designing a single antenna geometry compatible with various sub-surface environments, and most significantly with varying moisture content and the associated strong variation in permittivity and, hence, of electrical length of the dipole. While the  
Figure 6: Experimental measurement of returning echoes as a function of the position of the sensor along the pipe (Y), moving in a direction parallel to the length of the dipole. (**a**) for a sensor buried 61 cm in gravel, (**b**) for a sensor buried 103 cm in gravel.  
Figure 7: (**a**) Returned signal level as a function of dipole length, for a sensor buried 61 cm deep in gravel. (**b**) Evolution of the signal amplitude as a function of dipole length, for a sensor buried under gravel and a sensor buried in sand.  
varying link budget will not prevent the measurement thanks to the fine analysis of echo delays rather than returned magnitude as observed through the RADAR cross-section, the deteriorated signal to noise ratio on the analog radiofrequency measurement will degrade the measured physical quantity signal to noise ratio. Indeed, both quantities are related by the signal processing procedure. While the sensor intrinsic characteristics do not require ultra-wideband antenna design, keeping an acceptable link budget in varying surrounding permittivity conditions requires broadening the antenna operating frequency range in order to keep an acceptable efficiency at the fixed SAW sensor operating frequency band.  
Assuming the signal has been coupled to the cooperative target, which then returns echoes whose delays are representative of the acoustic velocity, i.e., physical quantity, the remaining issue is whether the time delay can be measured accurately enough to identify the acoustic sensor properties, rather than the measuring instrument (GPR receiver) drift.