# Analysis of LTE-M Adjacent Channel Interference in Rail Transit
## 3 Interference Analysis of LTE-M Underground System
### Interference Analysis When LTE-M Uses Leaky Cable Radiations Pattern  
When the LTE-M system uses the leaky cable radiations pattern, the complete scene of interference is shown in Figure 6.  
The transmission channel based on leaky cable can be divided into the inner channel and the spatial channel. The spatial channel can be conceived as the wireless fading channel, where the signal travels from the slot to the UE. The longitudinal loss inside the leaky cable can be abstracted as linear power attenuation related to the slot period of the leaky cable [44], so the attenuation model can be obtained:  
\[a_{i}=\alpha\cdot p\cdot i \tag{12}\]  
where \(a_{i}\) represents the amplitude of radiation signals from \(i\) slots, \(a\) represents the attenuation factor during longitudinal transmission of leaky cable, and \(p\) is the slot period, as shown in Figure 7.  
When the interfering signal interferes with the Remote Radio Unit (RRU) of the LTE-M BS through the leaky cable, MCL can be estimated as  
\[\mathrm{MCL}=P_{Imax}-\mathrm{ACIR}-I_{threshold} \tag{13}\]  
\[L=L1+L2+L3 \tag{14}\]  
\[L2=L_{2m}+32.44+20\lg(d1)+20\lg(f) \tag{15}\]  
where \(L1\) is the longitudinal transmission loss of leaky cable, \(L2\) is the coupling loss of leaky cable, \(d1\) is the vertical distance between UE and leaky cable, and \(L3\) is the sum of losses due to feeder, splitter, train penetration, and body penetration. The train penetration loss is considered when the source of interference is located inside the train carriage. Considering the most serious interference; that is, the power of the interference signal fed through the last slot of the leaky cable, the longitudinal transmission loss can be obtained by substituting it into Equation (12): \(L1=4\) dB/100 m \(\times\) 0.25 m \(\times\) 1 = 0.01 dB. According to the Table 6, \(L3=0.9\) dB \(+\) 1.4 dB \(+\) 4 dB \(+\) 2 dB \(=\) 8.5 dB. In the case of \(L=\mathrm{MCL}\), the minimum value of \(L2\) can be calculated by Equations (13)-(15) to obtain the minimum safe distance between UE and the leaky cable, as shown in Table 6.  
Figure 6: Interference analysis of LTE-M with leaky cable radiations pattern. Figure 7: Channel transmission in leaky cable. Taking the power of the interference signal and \(L3\) as a dependent variable, the relationship between interference signal transmission power, \(L3\), the received signal bandwidth, and the minimum safety distance (\(d1\)) in different environments can be obtained according to Equations (13)-(15), as shown in Figure 8.  
Similarly, the interference to the LTE-M system can be reduced by reducing the transmitting power. When \(L3\) increases, the minimum safe distance gradually decreases. Because the larger \(L3\) is, the greater the attenuation of interference signal will be, and the interference to the LTE-M system will gradually decrease. It can be seen from Table 6 that the maximum of the minimum safe distance in four given cases is 0.85 m, and the distance between the train and the leaky cable beside the tunnel wall is 2 m, so there is no adjacent channel interference, even in the most severe cases when the interference signal was fed through the last slot of the leaky cable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Interference Link** & \multicolumn{4}{c}{**UE-BS**} \\ \hline Received BW (MHz) & 5 & & 10 & \\ \hline Guard band (MHz) & 0 & 5 & 0 & 5 \\ \hline \(P_{lmax}\) (dBm) & & 23 & & \\ \hline Attenuation factor \(a\) (dB/100 m) & & 4 & & \\ \hline Slot (m) & & 0.25 & & \\ \hline Coupling loss at 2 m \(L_{2m}\) (dB) & & 62 & & \\ \hline Feeder loss (dB) & & 0.9 & & \\ \hline Splitter loss (dB) & & 1.4 & & \\ \hline Train penetration loss (dB) & & 8 & & \\ \hline Body penetration loss (dB) & & 2 & & \\ \hline \(I_{threshold}\) (dBm) & \(-109\) & & \(-106\) & \\ \hline ACIR (dB) & 21.37 & 34.96 & 21.19 & 34.89 \\ \hline MCL (dB) & 110.63 & 97.04 & 107.81 & 94.11 \\ \hline Minimum safe distance (m) & 0.85 & 0.18 & 0.61 & 0.13 \\ \hline \hline \end{tabular}
\end{table}