# Analysis of LTE-M Adjacent Channel Interference in Rail Transit
## 4 Interference Analysis of LTE-M Ground System
### Throughput Calculation  
Taking LTE FDD UE interference with LTE-M BS as an example, the SINR can be calculated as follows:  
\[\text{SINR}_{i}=\frac{P_{i,i}*G_{i}*PL_{i}}{\sum_{k}^{M}\sum_{j}^{N}P_{t:kj}*G _{kj}*PL_{kj}*\text{ACIR}_{kj}+P_{noise}} \tag{17}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**LTE BW**} & **Number of** & \multirow{2}{*}{**Interference BW \(B_{A}\)**} & **ACLR with Interval** & **ACLR with Interval** \\  & & & **Less than \(B_{A}\)** & **Greater than \(B_{A}\)** \\ \hline
5 MHz & 5 & \(5\times 180\) KHz & 30 + X & 43 + X \\
10 MHz & 10 & \(10\times 180\) KHz & 30 + X & 43 + X \\
20 MHz & 20 & \(20\times 180\) KHz & 30 + X & 43 + X \\ \hline \hline \end{tabular}
\end{table}
Table 7: ACLR model for LTE interfere and victim.  
Figure 10: The offset between macro cellular networks.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter Set**} & \multirow{2}{*}{**Gamma (\(\gamma\))**} & \multicolumn{5}{c}{\(PL_{x-ile}\) (dB)**} \\ \cline{3-6}  & & **20 MHz BW** & **15 MHz BW** & **10 MHz BW** & **5 MHz BW** \\ \hline Set 1 & 1 & 109 & 110 & 112 & 115 \\ Set 2 & 0.8 & N/A & N/A & 129 & 133 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Power control parameter sets.  
where SINR\({}_{i}\) represents the received signal to interference noise ratio of the \(i\)-th channel of the base station receiver, \(P_{t,i}\) is the transmission power of the LTE-M TE of the \(i\)-th channel, \(G_{i}\) is the sum of transmitting and receiving antenna gain between the LTE-M TE and LTE-M BS of the \(i\)-th channel, \(PL_{i}\) is the propagation loss between the LTE-M TE of the \(i\)-th channel and the receiving LTE-M BS, \(P_{t,k}\) represents the transmission power of the \(j\)-th FDD UE in the \(k\)-th cell, \(G_{kj}\)  represents the sum of the antenna gains of the \(j\)-th FDD UE in the \(k\)-th cell and the LTE-M BS, \(PL_{kj}\) is the propagation loss of the \(j\)-th FDD UE in the \(k\)-th cell reaching the LTE-M BS, and its propagation model is Equation (10). ACIR\({}_{kj}\) is the ACIR value of the \(j\)-th FDD UE of the \(k\)-th cell and the LTE-M BS, \(N\) is the number of cell users, \(M\) is the number of FDD cells, and \(P_{noise}\) is the receiver noise floor power.  
The approximate throughput is obtained by Shannon mapping expression [39], as given below  
\[\text{TP}=\left\{\begin{array}{c}0\text{ SINR}<\text{SINR}_{min}\\ \alpha\times\text{S(SINR)}\text{ SINR}_{min}<\text{SINR}<\text{SINR}_{max}\\ \text{TP}_{max}\text{ SINR}>\text{SINR}_{max}\end{array}\right. \tag{18}\]  
where \(S\) is Shannon bound as \(\text{S(SINR)}=\log_{2}(1+\text{SINR})\) bps/Hz, \(\alpha\) indicates attenuation factor, \(\text{SINR}_{min}\) is the lower limit of SINR, \(\text{TP}_{max}\) is the throughput upper limit, \(\text{SINR}_{max}\) is the SINR when the throughput limit is obtained. For the given system, the LTE interference link parameters are shown in Table 9.  
According to [39], simulation results with interference shall be expressed as a percentage of throughput reduction compared to simulation results without external interference, with the victim system's throughput loss not exceeding 5%. Therefore, in this paper, 5% relative throughput loss is used as the evaluation criterion of the maximum interference of the external system After each simulation, the SINR on each RB is counted. According to the Shannon mapping method, the SINR is mapped with the throughput of each RB, and the system throughput of one simulation is accumulated. The average throughput \(TP_{loss}\) of the system is obtained by averaging multiple simulations, given as follows  
\[\text{TP}_{loss}=1-\frac{\text{TP}_{multi}}{\text{TP}_{single}} \tag{19}\]  
where \(\text{TP}_{single}\) is the average throughput of a single LTE-M system and \(\text{TP}_{multi}\) is the average throughput of the LTE-M system when interfered by LTE FDD system.