# Fast Optimization of the Installation Position of 5G-R Antenna on the Train Roof
## 2 Coupling Coefficient Data  
In order to quickly optimize the installation position of the 5G-R antenna, the coupling coefficient between the pantograph arcing and the roof antenna needs to be collected and analyzed. In this paper, the similar electromagnetic simulation model in references [2; 12] is used to solve the coupling coefficient. Firstly, the simulation model of the coupling coefficient is established by using electromagnetic simulation software. As mentioned above, due to the limitation of the scale and simulation time of the electromagnetic simulation, the model can be simplified to only the case of the roof. The main view and top view of the model are shown in Figure 2.  
In the model, the roof plane of a carriage is set to be 25 m \(\times\) 3 m, given that the pantograph of the \"Fuxing\" train of 17 groups is located in the No. 3 and No. 6 carriages, and the roof antenna of the communication system is mostly located on the top of the first carriage. Therefore, the roof plane in the model is 50 m \(\times\) 3 m, and the co-ordinate system marked in the figure is taken as a reference. The position co-ordinate of the pantograph arcing is (52 m, 0 m), and the roof antenna is located directly below the contact line, and the distance from the roof plane is 3 cm. A thin cylinder with a length of 3 cm is used to simulate the pantograph arcing. A voltage source with an amplitude of 1 kV is set at the center of the thin cylinder as the excitation source port, which is a discrete port. The contact wire is a finite length wire; in order to reduce the influence of the contact wire length on the coupling coefficient, it is necessary to connect the termination resistance at two terminals of the contact line [4]. The length of the contact line in reference [4] is 43 m, and the terminal resistance is set at 200 \(\Omega\). The length of the contact line in the simulation model in this paper is 80 m, so the terminal resistance is set at 250 \(\Omega\). In this paper, probes (with an interval of 1 cm) are set, respectively, near the pantograph arcing and above the roof antenna to collect the electric field intensity E\({}_{1}\) and E\({}_{2}\) at the two places, in units of dBV/m, as shown in Figure 2c. Therefore, in this paper, the coupling coefficient is defined as the difference between the two (S = E\({}_{2}\) - E\({}_{1}\)); the unit is dB, which is used to determine the best installation position of the roof antenna with different operating frequencies, that is, the minimum value of the coupling coefficient [1]. The optimization of the installation position of the roof antenna is influenced by many factors, such as the electromagnetic coupling between the roof antennae, the distribution of electromagnetic field intensity in the roof area, and the installation height or size of the antenna. Among them, the study on the distribution of the radiant electric field intensity on the roof is too general, and can only obtain the change curve of the electric field intensity, failing to take into account the research objectives such as the working frequency and specific position of the roof antenna. In addition, if the parameters are changed, a large number of simulation solutions will be required and the calculation cost will be large. The electromagnetic coupling between the roof antennae and the installation height or size of the antenna need to be studied according to the specific model and the situation of the roof antenna, which is not considered in this paper. Therefore, this paper focuses on the effect of the position co-ordinates (X, Y) of the 5G-R antenna on the coupling coefficient.