## 5 Simulation and Discussion  
In this section, the hardware-in-the-loop simulation is used to verify the proposed method to evaluate the interference effect of the pulsed disturbances on RSTT. During this process, we assume that the intermediate-frequency filter of the APD measurement is the same as that of a radio receiver, and the channel symbols of one coding block are modulated in the same way. The test bench employed in this simulation is presented in Figure 10, aiming to test the interference effect of RSTT in a high-speed railway environment. * The radio transmission is established in the MATLAB (MathWorks, Natick, Massachusetts, USA, version R2016b) simulation platform of the computer, as well as the performance evaluation based on statistics;
* The EM disturbance is generated by the National Instruments (NI) NI-5793 radiofrequency transmitter (National Instruments, Austin, Texas, USA) adapter module, which can generate arbitrary waveform;
* The EMI receiver is built on NI FlexRIO architectures, composed of PXIe-1082 chassis, NI 5792 radiofrequency receiver adapter module, PXIe-7966R FPGA module and PXIe-8135 PXI Controller. The signal generator produces pulses with the amplitude of \(A\), the width of \(W\) and the repetition cycle of \(T_{p}\), and the pulses and the AWGN make up the mixed disturbance coupled to the radio transmission. Without a loss of generality, we assume \(A\) obeys Gaussian distribution with the variance of \(\sigma_{h}{}^{2}\), and the variance of is AWGN \(\sigma_{l}{}^{2}\). Thus, the APD curve of the mixed disturbance is demonstrated as  
\[APD_{n}(n)=\rho\text{erf}\left(\frac{n}{\sqrt{2}\sigma_{h}}\right)+(1-\rho) \text{erf}\left(\frac{n}{\sqrt{2}\sigma_{l}}\right)\]  
Figure 9: Illustration of the case that the repeated cycle \(T_{p}\) is much smaller than the length of the code block Q.  
where \(\rho=W/T_{p}\) refers to the duty ratio of the pulses. An example of the pulsed disturbance is shown in Figure 11 when \(\sigma_{l}=1\), \(\sigma_{h}=10\), and \(\rho=0.1\). In particular, the APD curves of interferences are the same if they have equal \(\rho\), \(\sigma_{l}\) and \(\sigma_{h}\), so they can be distinguished by PDD under this circumstance, as illustrated in Figure 12.  
In order to cover the typical cases of interfered encoded RSTT, the interference effect of disturbances with different statistical characteristics in the time domain should be taken into consideration. Nowadays, a turbo code specified by the 3 rd Generation Partnership Project (3 GPP) is widely used in GSM-R and LTE-R systems. Besides, the LDPC code is now used in WLAN and will be applied to 5G-R. Therefore, these popular FEC coding schemes are used in this simulation. As for the disturbances, we set the signal-to-noise ratio of AWGN to be constant \(SNR_{l}=-5\) dB, and observed the predicted transmission error at each \(\sigma_{h}\) level, with a different \(W\) and \(T_{p}\). According to the analysis above, we set the block-length to be \(Q=256\) symbols and the pulse cycle to be \(T_{p}=0.1Q\), \(T_{p}=1.5Q\), \(T_{p}=20Q\) with a duty ratio of \(\rho=0.1\) and \(\rho=0.9\), corresponding to disturbances from different sources. The \(BLER\) performance is estimated by a dynamic MI-based model. For each transmitted symbol, the varying SINR values caused by pulsed disturbances are mapped to instantaneous RBIR by the basic MI-based model. The statistics of block errors are collected and the effective RBIR\({}_{\rm L}\) is computed to look up the \(BLER\) from the AWGN curve. Figure 13 shows the simulated results of a rate-2/3 turbo code with 16 QAM radio signal in the case of \(\rho=0.1\) and \(\rho=0.9\), respectively, and Figure 14 shows the simulated results of LDPC code. From Figure 13a, although the interferences of different repetition cycles have the same APD when SNRh = 2 dB, the difference between their \(BLER\) is as large as almost two orders of magnitude. Therefore, a single APD parameter is not sufficient to evaluate the performance accurately, and may result in considerable errors.