# Acoustic Parametric Signal Generation for Underwater Communication
## 4 Results  
### First Studies  
The study for the parametric generation of a sine sweep signal with the emitting transducer was carried out by emitting frequency-modulated signals with carrier frequency of 200 kHz. Two modulated sine sweep signals were used as basic codification of the information: bit 1, upwards from 4 to 40 kHz, and bit 0, downwards from 40 to 4 kHz, corresponding to Figure 3a,b, respectively. Figure 3c shows the received signal being a mixture of the primary beam at 200 kHz and the secondary beam at low frequency produced by the parametric effect. In order to distinguish the secondary beam, a bandpass filter (2 to 42 kHz) was applied. The secondary beam (yellow) is multiplied by a factor of 20 to be visible along with the original received signal. Figure 1: Pictures of the experimental setup. (**a**) The lake where the position of transducers is indicated with white circles. (**b**) Equipment used for the calibrations and measurements. Figure 2: Airmar P19. (**a**) Picture; (**b**) Transmitting Voltage Response (TVR); (**c**) SPL, highlighting the interesting 200 kHz region for this application. A parametric sine sweep signal with a frequency bandwidth of 4 to 40 kHz with a duration of 1 ms and a carrier frequency \(f_{o}=200\) kHz is then used for the communication study. The idea is to generate a 16-bit string = 1010010110010110, code of ones and zeros with this signal; where bit 1 corresponds to the sine sweep signal from 4 to 40 kHz and bit 0 corresponds to a sine sweep signal from 40 to 4 kHz. Using cross correlation techniques, it is possible to recognize the parametric signal since the correlation produces a clear narrow peak on the signal arrival time, which allows it to be distinguished from near echoes, and increases the signal to noise ratio [8; 11]. The signals emitted for bit 1 and bit 0, as well as the received signal for the string are shown in Figure 3.  
The expected secondary beams, that is, the second derivative of the envelope to the square of the signals emitted are presented in Figure 4a,b for bits 1 and 0, respectively. Figure 4c,d show the results of the cross-correlation between the received signal filtered at low frequency containing the 16-bits string (Figure 3c, yellow) with the expected secondary beams for bits 1 and 0 (Figure 4a,b). Thus, one can observe that correlating with bit 1 the cross-correlation amplitudes for the positions of bit 1 of the string are much greater than the corresponding amplitudes for bit 0. In the same way, the positions of bit 0 are clearly enhanced in the correlation amplitudes when correlating with bit 0. Figure 3: Signal used in the analysis. (**a**) Bit 1: Upwards sine sweep signal; (**b**) Bit 0: Downwards sine sweep signal; (**c**) 16-bit received signal (black) and filtered at low frequencies (multiplied by a factor of 20, yellow). Obtained the amplitude voltage by cross-correlation for the detection of bit 1 and 0, presented in Figure 4c,d, and specified in Table 2, a parameter, called Relative Amplitude \(RA\), is introduced for bit detection analysis. It is defined as:  
\[RA=\frac{V-F}{MAX(V;F)} \tag{12}\]  
where \(V\) is the amplitude for the true bit, that is; the one that should be in correlation with the bit emitted (1 or 0) and \(F\) is a false bit since it is the bit not being emitted. In this sense, if the bit is detected correctly, the value \(V\) will be greater than \(F\) and therefore the \(RA\) values will be between 0 and +1. On the other hand, if \(RA\) is between 0 and -1, it means a wrong detection. In Table 2 the results for a direct communication for transducers at 1 m distance, facing each other, so at 0 degrees, are presented. A detection time of about 0.63 ms is obtained. The Relatives Amplitudes \(RA\) obtained after the cross-correlation and the assigned bit are also presented, showing that the information could easily be extracted. In this sense the \(RA\) is correct for each bit position, oscillating between 0.78 and 0.86, so close to +1. Figure 4: Signal analysis using cross-correlation.