## 1 Introduction  
Railway radiocommunication systems between train and trackside (RSTT) carry train control, voice dispatching, command, operational information as well as monitoring data between on-board radio equipment and the related radio infrastructure located along the trackside. In a high-speed railway (HSR) system, RSTT provide improved railway traffic control, passenger safety and improved security for train operations [1]. Therefore, RSTT are considered as \"mission critical\" for train operations in general and the management of train emergency situations [2]. For example, among the dispatching communication functionalities specified for railway, the Global System for Mobile Communications-Railway (GSM-R) [3] provides a railway emergency call service (REC) for drivers and signalers to alert all trains when part of route assigned to them may be occupied and collision risk occurs, so that they can immediately start lowering the speed or braking, depending on the operational rules [4]. The GSM-R REC service has helped to save lives and mitigate the severe consequences of rail accident in many cases [5; 6]. Therefore, the availability of the GSM-R frequencies is essential for safe and interoperable operations [7]. Unfortunately, railway infrastructures operate in a harsh and complex electromagnetic (EM) environment, where interferences are generated both inside and outside the HSR system. While supporting train operations, the electric traction system and high-power electrical appliances radiate strong electromagnetic emission under some unavoidable circumstances, such as the arcs generated during the separation of the pantograph and the contact wire [8]. Additionally, railway is distributed through the public domain and exposed to EM sources at various places, such as public radio transmission equipment [9]. In the HSR EM environment, the EM disturbances can hardly be eliminated from the source, nor be prevented through the coupling path. Thus, the on-board RSTT devices are extremely vulnerable to the surrounding EM disturbances, which may cause transmission errors and even lead to critical communication failures [10]. The communication failures directly cause the operational consequences of the rail network, such as jammed traffic and major delays, which may further result in bad economic and commercial effect [6] and even potential threat to the safety of passengers [11]. The degradation of communication availability or quality due to interferences is not acceptable [12]. Therefore, in order to guarantee the reliability of communication services, the impact of EM disturbances on RSTT should be monitored and supervised. Since the degradation of RSTT caused by different types of interferences is quite different, it is essential to consider the variety of disturbances in the HSR system. There have been several methodologies put forward to monitor the interference effect on RSTT based on the different measuring methods of received disturbances, such as classification based on the time-domain waveform [13], simulation and calculation based on the amplitude probability distribution (APD) detector [14] and the instantaneous frequency histogram [15]. Among these measuring methods, APD reflects the time-domain statistics of EMI and it can capture the dynamic behavior of a time-varying EMI with the measuring apparatus specified in the standards [16]. Besides, as a standard emission limit for EMI sources [17], APD is effective to analyze the effect of interferences. Therefore, statistics stand out as the suitable measuring methodology to characterize the disturbances in the complex HSR environment and to analyze the impact on RSTT. Previous research has proved that the statistics of EMI in the time-domain are directly related to the error performance of digital radiocommunication systems with different modulation and coding schemes (MCSs).