## 4 Feasibility Test of the API Protocol via Simulations
### Feasibility Test of Partial Initialization
#### 4.1.2 Results  
We check the similarity between the FI (at the initialization rate of 100%) and the API (at initialization rates (IRs) of 10%, 30%, 50%, and 70%). We analyze the similarity results in the aspect of the initialization rate, the STD of the generated data, the BER, and the number of slave nodes. First, we analyze the similarity in the view of the initialization rate and the STD of the generated data as follows:  
* It can be intuitively predicted that the higher similarity is guaranteed as the initialization rate becomes higher and the STD of the generated data set is lower. This prediction is confirmed in various cases by changing the STD of the generated data and the initialization rate, as illustrated in Figure 4a-d.
* As the number of transmissions increases, the overall similarity pattern fluctuates in the beginning and then converges after a certain number of transmissions. The larger the initialization rate, the smaller the number of transmissions where the similarity converges. * The similarity increases as the initialization rate increases under the given data type and STDs. In addition, as the initialization rate increases, the variation of the similarity with respect to the number of transmissions decreases, as well as the effect of the STD on the similarity is weak. This result is due to the number of samples for which data statistics are obtained. When the initialization rate is high, the number active nodes also increases, which implies the increase of the number of samples. As more samples are accumulated, the similarity between the data statistics of the API and the FI also increases. * Compared with the data with normal distribution, the data with uniform distribution guarantees slightly high similarity in most cases. This result is confirmed by Figures 4-6. However, the similarity difference between two data types is unremarkable except the case where the initialization rate is very low and the standard deviation of the generated data is high, as shown in Figure 4a. When the initialization rate is low, the number of samples also decreases. In this case, the probability, that the data obtained from the active nodes by the API are near the mean, can be high in the normal distribution. This can increase the difference between the data obtained by the API and that by the FI since the FI obtains the data from all nodes. On the other hand, in the uniform distribution, the data are evenly spread depending on the standard deviation. Thus, the difference between the data by the API and that by the FI in the uniform distribution is less significant than that in the normal distribution. This leads to a similarity difference between the two distributions in the case. * It can be seen that, except for the case where the initialization rate is very low, say 10%, the similarity is at least 90% under the given data type and STDs. Although it is confirmed that the API can be feasible to the given data type based on the simulation results, it cannot be generalized that the  
Figure 3: The illustration of generated data to check the feasibility of partial initialization. (**a**) The random data with normal distribution. (**b**) The random data with uniform distribution. API can be effectively applied to all data models. Depending on the underwater application, there can be other data distributions for which the API do not operate properly, and thus the network must be initialized close to the FI (full initialization) by increasing the number of active nodes. Figure 4: Similarities according to the number of transmissions for different data type, initialization rate, and STDs when the BER is \(10^{-3}\) and the number of slave nodes is 30. (**a**) Initialization rate = 10%, (**b**) Initialization rate=30%, (**c**) Initialization rate = 50%, and (**d**) Initialization rate = 70%.