## 5 Simulation
### Simultaneous Transmission  
To verify the feasibility of simultaneous transmission scheme, we measure the bit error rate (BER) occurs when multiple ANs transmit their packet at the same time. For the simplicity, just direct path is considered, but this is a reasonable assumption since the horizontal communication link is dominantly used in the given network topology. In addition, the used chirp rates in each ANs participating the localization are randomly selected. Therefore, we can evaluate our system based on the unbiased usage of HFM signal. The presented BER is limited to \(10^{-4}\) to ignore outlier.  
Figure 7 shows the BER versus the number of ANs ranging from 3 to 5. As shown in the figure, as the energy per bit (\(E_{b}/N_{o}\)) increase, the BER gradually decreases, and the BER becomes almost  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network size & 300 m, 1500 m \\ Acoustic propagation speed & 1500 m/s (assumed to be constant) \\ Sampling rate & 44 kHz \\ Preamble length & 1.5 s \\ Bandwidth & [10, 30] kHz \\ Sub-channel bandwidth & 2 kHz \\ Number of ANs & 3, 4, 5 \\ AUV’s velocity range & [0, 3] m/s \\ Symbol duration & 20 ms \\ Number of available chirp rates & 10 \\ Number of bits per packet & 100 \\ Number of trials & 1000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of simulation parameters.  
Figure 6: Network topology: Total 5 ANs are deployed on the surface and the location of AUV is randomly selected. The network size is two cases, 300 m and 1500 m.  
zero if the \(E_{b}/N_{o}\) is greater than 12 dB. It is noteworthy that the reliability of our system is preserved even though the number of participating ANs increases. Meanwhile, the acoustic communication channel is vulnerable to the Doppler effect, especially when the transmitter and receiver is mobile node. Therefore, it should be verified that the simultaneous transmission scheme is feasible in the Doppler channel. To show the Doppler tolerance of the proposed system, we distort the frequencies of transmitting signals with the Doppler factors determined by the AUV's velocity and relative locations between the ANs and the AUV. For the simplicity, the Doppler effect caused by the surface movement is ignored. Here, the AUV's velocity changes from 0 to 3 m/s, which is typical velocity range of the commercial AUV. Figure 8 shows the Doppler-tolerance of the proposed transmission scheme. Owing to the good property of HFM signal, Doppler-invariance, our system is rarely affected by the Doppler effect. Although the required \(E_{b}/N_{o}\) to achieve the target BER slightly increases due to the imperfect matched filter design as stated in the previous section, this problem is negligible since the increment of required \(E_{b}/N_{o}\) is trivial.  
From the presented simulation results, it is noted that the HFM-based transmission allows the multiple ANs to transmit their packet at the same time as long as the \(E_{b}/N_{o}\) is sufficiently large. Furthermore, this can be guaranteed regardless of the number of ANs and AUV's velocity. One simple but effective solution to grow \(E_{b}/N_{o}\) is to increase the transmission power. In contrast to the acoustic node, the ANs which are deployed at the sea surface is able to be supplied the stable power via solar panel, consequently the constraint of power consumption is relatively loose. As a result, HFM-based signaling, which reliably supports the simultaneous transmission, is a fairly reasonable approach in AUV localization.  
Figure 7: BER according to the number of ANs participating in the localization.