## 4 Simulation Results  
### Simulation Environments  
Realistic underwater environments are reflected in the simulation. Parameters used in the simulation are listed in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of sensor nodes (\(M\)) & 10 \\ Number of nodes including sink (\(N\)) & 11 \\ Internode distance (\(D\)) & 100 m \\ Center frequency (\(f_{c}\)) & 6 kHz \\ Bandwidth (\(f_{B\pi}\)) & 2 kHz \\ Symbol rate (symbol/s) & 2 ksps \\ Sound speed & 1500 m/s \\ Frame size (\(T_{f}\)) & 0.067 s \\ Number of symbols in a frame & 120 symbols \\ Transmit power limit & 48 W (46.8 dBm) \\ Additive Gaussian noise & [14] \\ Path loss model & [15,16] \\ Data modulation & Uncoded QPSK \\ Target bit error rate (BER) for one hop & 1\% \\ Channel impulse responses & Generated based on East Sea of Korea \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 10: Decreases in the average power according to the network split. Each parameter is explained. Figure 3a is assumed to reduce the simulation load. The number of sensor nodes is 10 which is the same as the analysis section. The internode distance is 100 m, and the entire distance from the 1 st node to the sink is 1 km. The center frequency and transmission bandwidth are 6 kHz and 2 kHz, respectively. The symbol rate is 2 ksps, which is the same as the bandwidth. The sound speed is assumed to be 1500 m/s, and the frame size is 0.067 s which is the time to travel 100 m. From the frame size and the symbol rate, the number of symbols in a frame is 134, but only 120 symbols are used for transmission and the remaining 14 symbols are reserved for the guard time to combat the delay spread. The maximum possible transmit power of a node is set to 48 Watts following the commercial limit of WHOI Micromodem-2 [17]. The maximum power ranges from 2.4 W to 100 W depending on the products [18]. The power of additive Gaussian noise is calculated through an integration over 5 kHz to 7 kHz in the power spectral density [14]. The path loss is based on Equations (1) and (2) of [15] with \(k=1.5\). The conversion from the electrical power to the acoustic one assumes the projector of [16]. The simulation does not contain channel encoding and decoding procedures because this simulation is not a link-level one but a system-level one. The uncoded QPSK is used for data modulation. The target uncoded BER is set to 1% considering the coded performance and acceptable simulation time. During a preliminary simulation with a raw QPSK symbol transmission without additive Gaussian noise, about 10% of the BER has occurred for the sink reception where the worst error rate is yielded because a real underwater channel in the simulation is very poor. This is similar to a binary symmetric channel (BSC) [19] with 10% error. However, an uncoded 10% error is too much for the coded performance. For example, a 10% error in BSC corresponds to an approximately 10% coded BER for (31, 11, 11) BCH code, which is commonly unacceptable. Less error in BSC results in much less coded BER. A 1% error in BSC yields down to \(10^{-7}\) coded BER. An attempt is made to reduce the uncoded BER for the sink reception in a preliminary simulation, and the repetition and scrambling are applied for the transmission. A repetition of six times is adopted for the transmission from the 10 th node to the sink. The original data is only 20 QPSK symbols among 120 symbols in a frame. As the data of this step is the union of data from the 1 st node to the 10 th node, the amount of data at the 1 st node is only 1/10 of the last step from the 10 th node to the sink. Therefore, repetition at the 1 st node is 60 times to fill an entire frame. With a repetition of 6 times, about 0.03% error is yielded for the sink reception without Gaussian noise. Therefore, 1% BER is set considering the errors due to interference and noise.