# Deployment Strategy of Shore-Based Cooperative Units for the Internet of Inland Vessels
## 3 Deployment Strategy of Shore-Based Collaborative Units  
### Problem Description  
For a channel with a length of S, shore-based collaborative units include a mobile communication base station and a WiFi base station. A two-layer heterogeneous communication network is carried out in the area to ensure signal coverage and meet the communication needs of inland riverboat networking. The deployment strategy is analyzed from the type of the base station and the configuration of the base station.  
The type of the base station is defined from the communication technology used by the base station and the operating frequency band such as a 4G base station with an operating frequency band of 1.9 GHz and a WiFi5 base station with an operating frequency band of 5 GHz, if there are a total of M types of base stations to choose from including \(m_{1}\) types of mobile communication base stations and \(m_{2}\) types of WiFi base stations (\(M=m_{1}+m_{2}\)).  
The configuration of base stations should consider the total bandwidth, transmission power, tower/pole height (the antenna hanging height is consistent with the tower/pole height), and antenna type. For each type of base station, there are \(k_{1}\), \(k_{2}\), \(k_{3}\), and \(k_{4}\) options for its configuration factors. Therefore, each type of base station has \(K=k_{1}\cdot k_{2}\cdot k_{3}\cdot k_{4}\) configurations.  
The selection matrix for available base-station types and configurations is  
\[A=\left(a_{km}\right)_{K\times M}=\begin{bmatrix}a_{11}&a_{12}&\cdots&a_{1m1}& \cdots&a_{1M}\\ a_{21}&a_{22}&\cdots&a_{2m1}&\cdots&a_{2M}\\ \vdots&\vdots&\ddots&\vdots&\vdots&\vdots\\ a_{K1}&a_{K2}&\cdots&a_{Km1}&\cdots&a_{KM}\end{bmatrix} \tag{6}\]  
where \(a_{km}\) is a variable of 0-1, indicating the selection of the communication base station; \(a_{km}=1\) indicates that the first type of configuration is selected; \(a_{km}=0\) indicates no selection. Due to the need to build a two-layer heterogeneous network based on mobile communication and WiFi,  
\[\begin{array}{c}\sum\limits_{m=0}^{m1}\sum\limits_{k=0}^{K}a_{km}=1\\ \sum\limits_{m=m_{1}}^{\text{M}}\sum\limits_{k=0}^{K}a_{km}=1\end{array} \tag{7}\]  
When the first configuration of the \(m\)th type is selected, \(P_{km}\) is the transmission power of the base station and \(B_{km}\) is the bandwidth. According to the signal-coverage link budget and the corresponding propagation model [16], the coverage radius \(r\) of the base station can be obtained.  
The maximum allowable spacing \(d_{s}\) between the network sites of the same layer can be obtained according to the length of the overlapping coverage band, the signal coverage radius, the width of the channel, and the vertical distance from the base station to the edge of the channel (Figure 3).  
\(d_{1}\) represents the length of the overlapping coverage belt; \(d_{2}\) represents the distance between the base station and the edge of the channel; \(d_{3}\) represents the width of the channel; \(r_{km}\) represents the signal coverage radius of the base station. The following relationship exists between the above parameters.  
\[d_{s}=\sqrt{r^{2}-\left(d_{2}+d_{3}\right)^{2}}+\sqrt{r^{2}-d_{2}^{2}}-d_{1} \tag{8}\]  
Therefore, the corresponding number of deployed base stations is  
\[n_{km}=\lceil S/d_{r}\rceil \tag{9}\]  
where \(\lceil\rceil\) means that the value in the symbol is rounded up to an integer.  
Figure 3: Overlapping coverage belt.