## 2 Problem Formulation
### Supervising Methodology of RSTT  
To supervise the interference impact on RSTT during the train operations, an on-board supervision methodology for communication quality is proposed, as illustrated in Figure 1. In this method, the disturbances at the input of the receiving antenna ought to be monitored through a coupler, independent of the existing radio receiver. Thus, the performance degradation of the RSTT transmission can be estimated based on the measurement of disturbances. Furthermore, in comparison with the specified requirements in related regulations, it could be determined whether the disturbance is intense enough to threaten the reliability of RSTT [13]. By this means, the operator could get knowledge of the real-time quality of radio transmission, and even receive an early warning before the communication blackout occurs through the driver-machine interface (DMI). The question then becomes: how to establish the relation between the measurement of EMI and real-time performance degradation of interfered radio transmission. Practically, RSTT are responsible for wireless data and voice communication between the train and the station for different railway applications. As stringent requirements for reliability, availability, safety and security are various for different train operations, numerous radiocommunication technologies have been used for railway operational applications and various MCSs have been adopted. For instance, as for dispatching, train control and other operational safety-related and efficiency needs of railway transportation systems, RSTT usually takes the form of dedicated mobile radio systems, such as GSM-R and Long-Term Evolution-Railway (LTE-R). Moreover, the technologies used for train-positioning  
Figure 1: Illustration of the radiocommunication systems between train and trackside (RSTT) monitoring scheme at the on-board train. ATP: automatic train protection; DMI: driver–machine interface; GSM: Global System for Mobile Communications; LTE: long-term evolution. applications are based on radar and short-range radio, while the wireless local area network (WLAN) is used for train remote and surveillance applications [1]. In the complex HSR environment, RSTT suffer from disturbances with diverse statistical characteristics. On board moving trains, the radio receiver is mainly interfered with by transient disturbances occurring between the catenary and the pantograph, as well as permanent disturbances coming from the public mobile network base stations [7], as shown in Figure 1. On-site measurements of typical EMI in the GSM-R frequency band have been performed at the output port of a GSM-R antenna, and the results are shown in Figure 2. The pantograph arcing disturbance, shown in Figure 2a (with data from [24]), is the most typical interference generated in the HSR system. It has a wide frequency range up to several GHz, covering most working bands of the RSTT (with data from [25]). Besides, the on-board antenna of some RSTT network, like GSM-R and LTE-R, is usually fixed on the roof of the train close to the catenary, which makes it prone to emission from the sliding contact between the pantograph and the catenary. In addition, the signal from the public base station near the railroad is a critical external disturbance when it uses the adjacent frequency band of the railway radio service, as shown in Figure 2b [26]. This usually happens when the train is operating in the vicinity of a city, where the number of base stations and users of public mobile network significantly increases. Generally, both transient and permanent disturbances can be modeled as a series of pulses with a repeated cycle \(T_{p}\), pulse amplitude \(A_{i}\) and pulse width \(W_{i}\) in the time domain, expressed as  
\[n(t)=n_{w}(t)+\sum_{i=0}^{\infty}A_{i}p\bigg{(}\frac{t-iT_{p}}{W_{i}}\bigg{)} \tag{1}\]  
where \(n_{w}(t)\) refers to the background additive white Gaussian noise (AWGN), and \(p(t)\) is the unit rectangular pulse function that refers to the single burst.