# Asynchronous Chirp Slope Keying for Underwater Acoustic Communication
## 5 Discussion  
The transmissions in both scenarios (see Figure 10) were demodulated without error in the single and dual-band verification runs. The verification only cover a small range and is not meant to be exhaustive for a characterization of the system. The first point to notice is the relative lack of noise in the signal, which is illustrated by the blue background in Figure 8 over 60 dB below the highest signal levels. If we closely inspect the right edge of the plots in the lower row Figure 8c,d, the long ring-down of the signal spanning over more than 100 ms is visible as a brighter colored leg smearing the stronger power bands in time. This reminiscence of the signal in the channel affects the transmission as inter-signal interference and is the strongest cause of error in our transmission. The channel impulse response itself depends on the geometry of the body of water and the environment conditions, which are not covered by this investigation. However, the general behavior of the proposed communication scheme will hold in similar environments, and improve for less challenging conditions. The phantom bands that appear for higher and lower frequencies around the transmission are caused by the undersampling on reception and are not present in the physical channel. They are removed in the DDC by a narrow bandpass-filter and only will cause the signal to be corrupted, if one of the phantom bands overlap with the intermediate band where most of the signal power is shifted to. When we compare the frequency spectrum in and outside of symbols in Figure 9, the high signal-to-noise ratio becomes more obvious: The noise floor is at approximately 65 dB below the highest signal levels (blue lines), while the interference raises the floor to about -40 dB (red line, outside the intermediate bands). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \(\boldsymbol{q}\) & & \(\boldsymbol{-1}\) & \(\boldsymbol{0}\) & \(\boldsymbol{1}\) & \(\boldsymbol{2}\) \\ \hline \multirow{2}{*}{\(r_{\text{BE}}\)} & \(A_{q}\) & 0.60 & \(-0.65\) & 0.65 & 0.65 \\  & \(B_{q}\) & 9.5 & 50 & 6.8 & 43 \\ \hline \multirow{2}{*}{\(r_{\text{BExc}}\)} & \(A_{q}\) & 1.00 & \(-0.65\) & 0.15 & 1.00 \\  & \(B_{q}\) & 10 & 22 & 10 & 65 \\ \hline \multirow{2}{*}{\(r_{\text{PE}}\)} & \(A_{q}\) & 4.0 & 6.0 & 1.8 & 1.2 \\  & \(B_{q}\) & 25 & 13 & 7.1 & 43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dual-band fit coefficients. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \(\boldsymbol{q}\) & & \(\boldsymbol{-1}\) & \(\boldsymbol{0}\) & \(\boldsymbol{1}\) & \(\boldsymbol{2}\) \\ \hline \multirow{2}{*}{\(r_{\text{BE}}\)} & \(A_{q}\) & 0.95 & \(-0.85\) & 0.8 & 0.5 \\  & \(B_{q}\) & 26 & 50 & 22 & 140 \\ \hline \multirow{2}{*}{\(r_{\text{BExc}}\)} & \(A_{q}\) & 1.3 & \(-0.5\) & 0.8 & 0.02 \\  & \(B_{q}\) & 27 & 50 & 22 & 140 \\ \hline \multirow{2}{*}{\(r_{\text{PE}}\)} & \(A_{q}\) & 0 & 24 & 2.1 & 2.0 \\  & \(B_{q}\) & 0 & 50 & 25 & 140 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Single band BER fit coefficients. If we regard the distributions of the symbols in Figure 10 around the decision threshold, which is at \(y_{\text{drif}}=0\), the single band levels show a multi-modal behavior. In the dual-band case, the distributions in all channels are much closer to uni-modal distributions, which is the ideal case, but are still far from the optimal. Optimal symbol levels would be achieved, if there would be two symmetrical probability bands at the minimal and maximal edge of the differential signal levels. This effect is due to the symbol peaks of up and down chirps not aligning in phase, but are shifted to each other. The symbol synchronization in the superposed signal locks-in on the matched filter output \(y_{\text{flux}}\) that shows the strongest mean correlation, therefore pushing the other symbols out of phase.