## 1 Introduction
For whistle classification with the maximum distance, firstly, we set a whistle feature vector (**V**) whose elements present the dominant features of the whistle, e.g., \(L\) frequencies of the whistle, whistle duration, maximum and minimum frequencies, chirp rate, etc., and secondly, we maximize the distances based on the vector(**V**). **V** is set as below,  
\[\textbf{V}=[f(\tau_{1}),\cdots,f(\tau_{L}),\cdots,\text{max}f(t),\text{min}f( t),\cdots] \tag{1}\]  
If **V** consists of the j elements, **V** has a vector space of \(\mathbf{R}^{j}\) and the classification with the maximum distance is performed in \(\mathbf{R}^{j}\) space. For the classification, we change the classification problem of maximizing distances among different whistle groups, to a new problem of minimizing the distances in the same groups. Since the k-means clustering algorithm is known as a good classification method for minimum variance [19; 20], the k-means clustering algorithm is utilized for classifying the whistles as groups. Let \(K_{\text{opt}}\) be the number of groups, in which the variance of whistles in the same group is minimum, and the set of classified groups be \(\textbf{G}=(G_{1},G_{2},\cdots,G_{k},\cdots,G_{K_{\text{opt}}})\). Assume that the \(N\) whistle vector and the average vectors of the \(k\)-th group \(G_{k}\) is \(\mu_{k}\). Then, the k-means algorithm for classifying the whistles is written as [21; 22],  
\[\underset{\textbf{G},K_{\text{opt}}}{\text{argmin}}\sum_{k=1}^{K_{\text{opt}}} \sum_{V_{n}\in\textbf{G}_{k}}\left|\textbf{V}_{n}-\mu_{k}\right|^{2} \tag{2}\]  
Equation (2) minimizes the variance of the vectors (\(\textbf{V}_{n}\)) which belongs to the same group, i.e., the distance among groups is maximized. Then, \(K_{\text{opt}}\) groups are obtained, and the whistles in the same group have similar patterns. For the biomimetic UWA communication, the information bits are allocated to \(\textbf{G}=(G_{1},G_{2},\cdots,\)\(G_{k},\cdots,G_{K_{\text{opt}}})\) and randomly selected whistles in the group are transmitted. When a large number of information bits are inputted and all whistles are transmitted, the large DoM is attained. At the receiver, the conventional maximum likelihood (ML) based detector can be used to estimate the group index (\(k\)) from the received whistles. The ML based detector determines the transmitted bits by extracting the feature vector (\(\textbf{\hat{V}}_{n}\)) in Equation (1) and comparing all feature vectors of the whistles (\(\textbf{V}_{n}\)), finding the closest one. When the conventional ML detector detects the received whistles, the ML detector suffers from two problems: for the first problem, when the number of real whistles is large, a low BER is not obtained. The maximum distance by the k-means algorithm between groups may not be large enough to overcome the background noise and the UWA channel distortions. If some whistles in the group are picked to keep the larger distance and the error correction schemes are used, the BER performance can increase. However, the DoM and the data rate decreases. Thus, we need to develop a communications method without scarifying the DoM and the BER. For the second, when the received whistles are distorted by the UWA channel, the distorted whistles cannot be compensated by the equalizer. Even though the channel is estimated by the pilots, the frequency bandwidth and time duration of the whistles are larger than the coherent frequency and the coherent time, respectively. In addition, the repeatedly transmitted pilots reduce the DoM. The small distance problem may be resolved by the modern machine learning detection scheme, whose detection capability is better than the ML. When the whistle patterns are represented as a 2-D image, e.g., spectrogram, the machine learning technique easily learns the overall contours and the detail features of the whistles. However, the distorted whistle problem of the UWA channels may not be overcome by the conventional machine learning methods.