## 3 Statistical Parameters  
As seen in Figure 3, a simple noise baseband model was plotted [17]. Three important characteristics of the electromagnetic noise baseband model were considered: the amplitude of the pulse, the duration of the pulse, and the interval between the two adjacent pulses. Four statistical parameters were employed to analyze the three characteristics of the noise spectrum [17]: amplitude probability distribution (APD), pulse duration distribution (PDD), pulse separation distribution (PSD), and noise amplitude distribution (NAD). The APD and NAD were used to study the amplitude characteristics of pulses, PDD was used to analyze the duration of pulses, and PSD could well characterize the arrival interval of adjacent pulses.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Frequency Band & 300 MHz–3 GHz \\ Mode & Occupied BW \\ Span & 50 MHz \\ RBW(Resolution Bandwidth) & 10 kHz \\ VBW(Video Bandwidth) & 100 kHz \\ Attenuation & 2 dB \\ Preamp & Open \\ Points & 20001 \\ Polarized & Vertically/Horizontally \\ \hline \end{tabular}
\end{table}
Table 1: Parameters of frequency domain measurements.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Frequency & 315 MHz, 779 MHz, 916 MHz \\ Bandwidth & 200 kHz \\ Sampling Rate & 2 MHz \\ Measurement Duration & 134.2 s \\ Mode & Data Collecting \\ Polarized & Vertically/Horizontally \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of time domain measurements.  
The APD and NAD were used to characterize the amplitude of the pulse. The APD represents the probability that the pulse amplitude exceeds a certain threshold value. It can be calculated by the ratio of the total time when the pulse amplitude exceeds the threshold value to the total time measured as [18].  
\[APD(L_{i})=P(\lambda>L_{i})=\frac{1}{T}\sum_{k=1}^{N}t_{k} \tag{1}\]  
where \(\lambda\) is the noise amplitude and \(L_{i}\) is the threshold level; we refer to the method proposed in patent [19] to determine it in the actual measurement and analysis process. \(T\) is the total measurement time, \(t_{k}\) is the duration of a pulse whose amplitude exceeds the fixed value. For instance, the APD of the signal in Figure 3 is \(APD(L)=P(\lambda>L)=(t_{1}+t_{2}+t_{3}+t_{4})/T\). The influence of electromagnetic noise on bit error rate (BER) can be mapped directly to the APD value, which can directly reflect the size of the BER.  
The NAD is defined as the number of pulses whose value is higher than the threshold divided by the total measurement time [20; 21], and is expressed as  
\[NAD(L_{i})=\frac{n(p_{K})}{T} \tag{2}\]  
where \(T\) is the total measurement time and \(n(p_{k})\) is the number of pulses whose value is higher than the threshold. For instance, the NAD of the signal in Figure 3 is \(NAD(L)=n(p_{K})/T=4/T\).  
The PDD is used to analyze pulse duration. It means the probability that the duration of the pulse exceeds a threshold value \(\tau_{d}\), which can be expressed by the ratio of the number of pulses lasting time beyond \(\tau_{d}\) to the total number of pulses as [17]:  
\[PDD(\tau_{d})=\frac{n(t>\tau_{d})}{N} \tag{3}\]  
where \(n(t>\tau_{d})\) is the number of pulses lasting time beyond \(\tau_{d}\) and N is the total number of pulses.  
PSD can well characterize the arrival interval of adjacent pulses. It means the probability that the interval of adjacent pulses exceeds a fixed value \(\tau_{s}\)[16]. It can be expressed as  
\[PSD(\tau_{S})=P(t>\tau_{s}) \tag{4}\]  
where \(P(t>\tau_{s})\) is the probability that the duration of the pulse exceeds the fixed value.  
According to the above theory, the time domain electromagnetic noise signals at 315 MHz, 779 MHz, and 916 MHz frequencies were measured, and the APD, PDD, PSD, and NAD statistical parameters of electromagnetic noises at different frequencies could be extracted.