# Analysis of LTE-M Adjacent Channel Interference in Rail Transit
## 3 Interference Analysis of LTE-M Underground System
### Interference Analysis When LTE-M Uses Directional Antenna Radiations Pattern
Assuming that the separation distance between UE and the TE is greater than 50 m, the transmission model uses the Xia.h model [43], such as,  
\[L_{\text{UE-TE}}=-10 lg\bigg{(}\frac{\lambda}{4\pi d}\bigg{)}^{2}-10 lg\bigg{[} \frac{\lambda}{2\pi^{2}r}\bigg{(}\frac{1}{\theta}-\frac{1}{2\pi+\theta}\bigg{)} ^{2}\bigg{]}-10 lg\bigg{[}\bigg{(}\frac{b}{2\pi d}\bigg{)}^{2}\frac{\lambda}{ \sqrt{\Delta h_{m}{}^{2}+b^{2}}}\bigg{(}\frac{1}{\phi}-\frac{1}{2\pi+\phi} \bigg{)}^{2}\bigg{]} \tag{11}\]  
where \(r=\sqrt{(\Delta h_{m}{})^{2}+x^{2}}\), \(\theta=\tan^{-1}(\frac{\Delta h_{m}}{x})\), \(\phi=\tan^{-1}(\frac{\Delta h_{b}}{b})\). \(\lambda\) is the carrier wavelength, \(x\) represents the horizontal spacing between the terminal and the scattered edge, typically 15 m, \(b\) represents the average distance between constructions, with a typical value of 80 m, \(\Delta h_{m}\) represents the average height difference between the base station antenna and the terminal, which is 3.5 m, and \(\Delta h_{b}\) represents the height difference between the base station antenna and the track, and considered as 5 m.  
Under the condition of \(L=\) MCL, the minimum safe distance under different conditions can be achieved after substituting MCL into Equations (8)-(11), as shown in Tables 4 and 5. By taking the transmission power and the antenna gain as dependent variables, the relationship between the transmitting power of interference signal, the antenna gain of BS, the received signal BW, the guard band interval, and the minimum safe distance in different links can be obtained, as shown in Figures 3 and 4. When the transmitting power of interfering signal or antenna gain of BS increases, the minimum safe distance also increases, indicating that lowering them can decrease interference of the LTE-M system. When the received signal BW increases, the minimum safe distance decreases gradually, because \(I_{threshold}\) increases with the increase in the received signal BW. The anti-interference ability of LTE-M BS is improved by 2.88 dB when the received signal BW is 10 MHz compared with 5 MHz, as computed from the MCL in Table 2. When other factors are the same, the minimum safe distance with 5 MHz guard interval is smaller than without guard interval. After the 5 MHz guard interval is implemented, the anti-interference capability of the LTE-M BS improves by 13.65 dB when compared to no guard interval, as computed from the MCL in Table 2.  
Similarly, the LTE FDD UE interfering with LTE-M TE is obtained as shown in Figure 5, and it can be noticed that the main trend is similar to that of LTE FDD UE interfering with LTE-M BS. Regardless of whether the UE is in the platform or inside the carriage, the minimum safe distance is very small, which means that the interference of the UE to the LTE-M system is negligibly small in this case. When all other conditions are equal, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Location of UE** & \multicolumn{4}{c}{**Platform**} & \multicolumn{4}{c}{**Carriage**} \\ \hline Received BW (MHz) & 5 & & 10 & & 5 & & 10 \\ Guard band (MHz) & 0 & 5 & 0 & 5 & 0 & 5 & 0 & 5 \\ Minimum safe distance (m) & 25.87 & 5.41 & 18.70 & 3.86 & 10.30 & 2.15 & 7.44 & 1.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: LTE FDD UE interfering with LTE-M BS. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Location of UE** & \multicolumn{4}{c}{**Platform**} & \multicolumn{4}{c}{**Carriage**} \\ \hline Received BW (MHz) & 5 & & 10 & & 5 & & 10 \\ Guard band (MHz) & 0 & 5 & 0 & 5 & 0 & 5 & 0 & 5 \\ Minimum safe distance (m) & 1.30 & 0.28 & 0.94 & 0.20 & 0.52 & 0.11 & 0.37 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: LTE FDD UE interfering with LTE-M TE. LTE-M TE's anti-interference capability improves by 2.84 dB when the received signal BW is 10 MHz, compared with 5 MHz. It can also be noticed that the anti-interference capability of the LTE-M TE is improved by 13.5 dB after the 5 MHz band guard interval is added compared to when no guard interval is used.