# Acoustic Parametric Signal Generation for Underwater Communication
## 4 Results
### Parametric Studies  
To confirm the non-linear parametric effect and see the applicability of this technique for communication purposes, three different studies have been performed:  
1. Attenuation--as a function of distance.
2. Voltage variation--as a function of the primary beam intensity.
3. Directivity--as a function of the angle of emission.  
The first study analyzes the secondary beam generation in the medium by changing the distance between the emitter and the receiver. The second one aims to compare the amplitudes of the primary and secondary beams by emitting the signal at low intensity (that is, low feeding voltage) and increasing it to demonstrate the non-linear effect. The third study compares the directivity pattern of both beams.  
Figure 6 shows the results varying the distance, \(d\), between the emitter and the receiver from 0.50 to 2.2 m, in steps of 0.10 m. The measurements of both, primary and secondary beams, are adjusted  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Bit Position** & **Bits** & **Detection Time [ms]** & **Amplitude BIT 1 [10\({}^{-4}\)]** & **Amplitude BIT 0 [10\({}^{-4}\)]** & \(RA\) \\ \hline
1 & 1 & 0.634 & 0.4069 & 0.066 & 0.8378 \\
2 & 0 & 1.692 & 0.0661 & 0.3846 & 0.8281 \\
3 & 1 & 2.694 & 0.4198 &  
to a function \(a\cdot d^{-b}\). Neglecting the absorption, for a spherical propagation beam, a value of \(b=1\) is expected. The value for the primary beam is 0.89, so close to 1, however the value for the secondary beam is much smaller, 0.69, and this can be understood as a hint of the parametric generation of the beam in the medium, and therefore there is less attenuation.  
The dependence with respect to the intensity of the primary beam was done by setting the amplitude in the waveform signal generator from 200 mV to 1 V in steps of 100 mV, and studying the received amplitude. As shown in Figure 7, a fit with the function \(a\cdot x^{b}\) was made with data from 600 mV to 1 V. An exponent of 0.99 (linear behavior) is obtained for the primary beam whereas an exponent of 1.98 (square behavior) is obtained for the secondary beam, so agreeing perfectly to the theory of parametric emission.  
The evidence of the parametric effect of the secondary beam is also clearly shown in the directivity study, the results of which are presented in Figure 8. An open angle of \(\pm\)12\({}^{\circ}\) is obtained for the secondary beam, whereas for the primary beam, it is \(\pm\)10\({}^{\circ}\). So, both beams present a quite similar directivity pattern despite the big differences in the frequency content.  
Summarizing, all these effects agree that the signal has been generated parametrically and thus, this technique could be used for underwater acoustic communications in circumstances where highly directive beams are preferable.  
Figure 6: Normalized amplitude of the received signal for primary (red) and secondary (blue) beam as a function of distance between emitter and receiver. Std means the standard deviation. (**a**) for bit 1; (**b**) for bit 0.  
Figure 7: Normalized amplitude of the received signal for primary beam (red) and secondary beam (blue) as a function of voltage sent of emitted signal (i.e., feeding voltage before the amplifier). Std. means the standard deviation. (**a**) for bits 1; (**b**) for bits 0.