## 3 Simulation Results and Discussion
### Algorithm Verification  
This paper uses the MAC protocol based on TDMA, and divides each period to nine time slots, and in each time slot, only one node can send or receive a data frame. The authors of [14] presented a model which can be used to quantify the consumption of energy of underwater sensor networks. The following content will describe the model in detail: assume the minimum power of a node receiving packets is \(P_{0}\). If a node sent \(i\) bits packet to the another node at a distance \(l\), the consumption is:  
\[E_{s}(i,l)=iP_{0}l^{k}\alpha^{l} \tag{7}\]  
The consumption of the other node is:  
\[E_{R}(i)=iP_{r} \tag{8}\]  
where \(i\) is the bit rate of the sent packet, \(l\) is the transfer distance, \(\mathrm{P_{r}}\) is a constant parameter which is decided by the receiving device, \(k\) is the energy coefficient (for a cylindrical shape k is 1-1.5 and k is 2 for roundness). \(\dot{a}=10\dot{a}^{\dot{a}(l)/10}\), \(\dot{a}(l)\) is absorption coefficient measured in dB/km relevant to the frequency. Based on the Thorp function we can calculate the absorption coefficient of the frequency range of interest:  
\[\alpha(f)=0.11\frac{f^{2}}{1+f^{2}}+44\frac{f^{2}}{4100+f^{2}}+2.75\times 10^{ -4}f^{2}+0.003 \tag{9}\]  
To simulate the underwater environment, we have to realize the parameters that will affect the simulation first, then enactment these parameters such as bit error rate, network delay, noise, conflict and overhearing. Bit error rate [15] is the indication of the measure exactness of data in the scheduled time:  
\[\mathrm{bit\ error}=\frac{\mathrm{bit\ error\ in\ transmission}}{\mathrm{ total\ bit\ in\ transmission}}\times 100\% \tag{10}\]  
In the application to underwater sensor networks, nodes communicate with each other by sound waves. At the sending terminal, nodes need to transform digital signals into analog signals and amplify them with an amplifier before sending them through a hydrophone. The receiving terminal receives the analog signals and then transforms them into digital signals. The process is shown in Figure 12. The transformations and the complex underwater environment will increase the bit  
Network delay [18] is the time spent to send a packet from a terminal to the other terminals that include sending delay, transmission delay and processing delay. \[\text{total delay}=\text{send delay}+\text{transmission delay}+\text{ process delay}\]  
Sending delay is the time cost of the _D/A_ transform [19], power amplification and underwater transformation. Transmission delay is the time cost caused by the transmission of sound waves underwater. Processing delay is the time cost caused by wave filtering, _A/D_ transform, and digital signal processing. We assume _T1_ is the sum of send delay and processing delay, _T2_ is the transmission delay. Through a large amount of experiments in the actual environment and calculations we set the delay as follows:  
\[ \begin{split} T1&=118 ms\\ T2&=1520\times L\end{split}  \tag{12}\]  
where \(L\) is the distance between any two nodes. Noise [20] is caused by waves, currents, ships and marine organisms. We evaluate it in an actual environment under different weather and sea conditions. We adopt two approximate noise probabilities: the higher noise is 7.6%o and the lower noise is 3%o. If two nodes use the same channel in the same time slot, they will interfere with each other breaking the packet and cause conflict. Because conflict cannot happen between PCs, we have to simulate underwater conflict to test the reliability of protocols. We conclude the conflict situation as follows:  
1. For the packet which has a destination, we only check whether the neighbor nodes are also forwarding the packet to the same destination. 2. To broadcast a packet, we check whether other nodes are sending in the same slot. Figure 12: Communication process of an underwater sensor node. Due to the fact underwater sensor networks share communication channels, nodes perhaps receive some packets that they should not receive.