# Research on Location Selection Model of 5G Micro Base Station Based on Smart Street Lighting System
## 4 Location Selection Model of 5G Micro Base Station
### Location Selection Model Construction
#### 4.2.3 Objective Function  
The objective function of location selection is constructed from the three aspects of coverage, economic cost, and coordination, which are used for iterative optimization of the model to obtain the optimal location selection scheme. In practical, apart from the combined ratio, coupling ratio, and unification ratio of location selection indexes to measure the coordinate equipment capacity, the coverage area of light poles has a significate impact on location selection difficulty. The site selection becomes more complex as the coverage area decreases. The coefficient of location selection difficulty is defined as the ratio of the area covered by the site to the area covered by light poles, as shown in Equation (4). Based on the location selection index of system fusion degree and the coefficient of difficulty, the objective function of the location selection model was constructed. The coefficient of difficulty is as follows:  
\[=\frac{2}{\pi}arctan\frac{S}{S_{\text{g}}} \tag{4}\]  
where \(S\) represents the area of the location selection, \(S_{\text{g}}\) represents the coverage area of the light pole. In this study, the coverage radius of the light pole is the same as that of the target device--the 5G micro base station. Combining capacity \(F_{\text{a}}\): The difference in road network density in the functional area leads to the difference in light pole density, which affects the difficulty of location selection. The higher the density of the light pole per unit area, the lower the difficulty coefficient and the requirement for the combining capacity. That is, the difficulty coefficient is positively  
optimization algorithm is constructed to output the 5G micro-base station location selection scheme with the optimal number \(N\) and location \(L\in(x_{i},y_{i}),\ i=1,2,\ldots,N\). Furthermore, evaluate the performance of the location selection scheme through the analysis of different location selection indexes. In order to reduce the complexity of large-scale location selection and the impact of regional differences on the location selection scheme, the map is firstly pre-processed in blocks, as shown in Figure 3. The black box area in Figure 3 represents the selected area, which is a closed area surrounded by adjacent intersections. The location selection scheme is based on the area's candidate points. The red box represents the affected area, which is the closed area that expands the coverage radius of a base station outward from the area to be selected. The coverage rate \(\gamma\) is defined as the percentage of the coverage area of 5G micro-base stations in the target area and is calculated based on the base stations established in the area. In the iterative process of the binary particle swarm optimization algorithm, the particle near the optimal position is prone to mutation, which is not conducive to later convergence. Changing the particle update method can effectively alleviate the mutation rate [30]. In this study, the particle position update formula \(s(v_{\text{id}})\) and the absolute probability of position change \(x_{\text{id}}\) are shown in Equations (11) and (12). \[s(v_{\text{id}})= \begin{cases}\frac{1-\frac{2}{1+\exp(-v_{\text{id}})}}{1+\exp (-v_{\text{id}})}-1&v_{\text{id}}>0\\ \end{cases}  \tag{11}\]  
\[x_{\text{id}}= \begin{cases}\quad 1&\quad\quad\quad if\ rand()\leq s(v_{\text{id}}) \&v_{\text{id}}>0\\ \quad 0&\quad\quad\quad if\ rand()\leq s(v_{\text{id}})\&v_{\text{id}}<0\\ \quad x_{\text{id}}&\quad\quad\quad otherwise\\ \end{cases}  \tag{12}\]  
where \(v_{\text{id}}\) represents the particle flight speed. In addition, the selection, crossover, and mutation genetic operators are used to generate a new generation of particle swarms. A discrete binary particle swarm optimization algorithm was constructed to solve the location model. The particles in the population were sorted according to the fitness value.