# Interference Mitigation for Metro Train Location Based on Karhunen-Loeve Decomposition
## 2 Signal Model and Interference Modes  
In this section, we introduce the mathematical model of the CPIS and the interference model of the metro train. In our positioning system, the positioning part in CPIS is a system based on DSSS-CDMA, and the navigation message is modulated on the spread spectrum signal by BPSK modulation. The structure of the CPIS base station is shown in Figure 1. The transition of the integrated signal is realized by adding a positioning signal generator to the 5G communication base station. For the communication system, the positioning signal superimposed on the frequency spectrum is the interference signal. We define the ratio of communication signal power to positioning signal power as CPR. Based on a large number of experimental test results, we found that when the CPR is greater than 18 dB, the communication QoS is not affected [28]. For train CPIS positioning terminal, the communication signal is regarded as white Gaussian noise. Without radio frequency signal interference, the signal received by the terminal can be expressed as follows. \[ \begin{split} r_{CPIS}(t)=\sum_{i=1}^{N_{BS}}A^{(i)}d^{(i)}(t)c^{( i)}(t-\tau_{i})\\ \cdot\cos(2\pi(f_{c}+f_{d,i})t+\varphi_{0,i}(t))+\omega(t).\end{split}  \tag{1}\]  
where \(N_{BS}\) represents the number of received integrated signals, \(A^{(i)}\) is the signal amplitude, \(d^{(i)}\) is the navigation message modulated on the positioning part, \(c^{(i)}\) represents the spread spectrum sequence, \(\tau_{i}\) represents the time delay of the signal, \(f_{c}\) and \(f_{d,i}\) are the signal carrier frequency and the doppler frequency shift, respectively, \(\varphi_{0,i}(t)\) is the initial carrier phase, and \(\omega(t)\) is additive white Gaussian noise (AGWN) with variance \(\sigma_{n}^{2}\). Metro train positioning based on CPIS will be inferred by the following two modes of radio frequency signals as shown in Figure 2.  
(a) The interfering signal source is stationary relative to the train positioning terminal. The interference usually comes from radio frequency signals from fixed equipment on the train or from man-carried interference equipment. (b) The interfering signal source moves relative to the train positioning terminal. The interference comes from the radio frequency signal interference generated by the equipment fixed on the rail or the equipment along the track. In the first interference mode, the interference power received by the positioning terminal is constant, resulting in a decrease in positioning accuracy or even inability to output location, which affects the normal operation of the train control system. In the second interference mode, due to the movement of the terminal antenna relative to the interference, there is a difference between the frequency received by the receiver and the frequency of the interfering signal. However, according to the Doppler effect, this difference is negligible, because electromagnetic waves travel much faster than trains run. Figure 1: The structure of the CPIS base station. When the train terminal receives CPIS with an interference signal, it is expressed as follows. \[r(t)=r_{CPIS}(t)+J(t). \tag{2}\]  
where \(J(t)\) represents the interference signal. The types of interference signals in metro train operation environment include single-tone interference, pulse interference, narrowband interference, and broadband interference. This paper mainly studies the mitigation of single-tone signal interference, pulse signal and chirp signal interference. The main characteristic of the single-tone signal is that the energy is concentrated at a single frequency point, which has a significant impact on the dispreading of the positioning signal, and it can be expressed as follows. \[J(t)=\sqrt{2}a\sin\bigl{(}2\pi f_{j}t+\varphi_{j}\bigr{)}. \tag{3}\]  
where \(a\) is amplitude of single-tone signal, \(f_{j}\) is the center frequency of the interfering signal. \(\varphi\) represents initial phase.