# Analysis of LTE-M Adjacent Channel Interference in Rail Transit
## 2 LTE-M Adjacent Channel Interference
### Principle of Adjacent Channel Interference  
ACI is mainly determined by the characteristics of the transmitter and receiver filters. In Figure 1, A is the fraction of the interference power of the transmitter entering the targeted frequency band due to out-of-band radiation characteristics, and B is the fraction of the interference signal power that the receiver can receive in the adjacent channel due to imperfect filtering characteristics. Adjacent channel leakage ratio (ACLR) is the ratio of the filtered mean power centered on the assigned channel frequency to the filtered mean power centered on adjacent channel frequency, which is used to measure the out of band propagation characteristics of the transmitter and can be shown as  
\[\text{ACLR}=\frac{P}{A}=\frac{1}{\int_{f_{max}+\Delta f}E_{f_{i}}(f)df} \tag{1}\]  
where \(E_{f_{i}}(f)\) is the power spectral density of the transmission filter of LTE FDD system, \(f_{max}\) is the nominal upper cut-off frequency of the filter, and \(\Delta f\) is the guard interval between LTE FDD and LTE-M. Adjacent channel selectivity (ACS) represents the ratio of the receive filter attenuation on the targeted channel to that on the adjacent interference channel, which is used to measure the receiver's performance in the targeted band, can be shown as  
\[\text{ACS}=\frac{P}{B}=\frac{1}{\int_{-\infty}^{f_{min}-\Delta f}E_{f_{o}}(f)df} \tag{2}\]  
where \(E_{f_{o}}(f)\) is the power spectral density of the receiving filter of LTE-M system, \(f_{min}\) is the nominal lower cut-off frequency of the filter. Adjacent channel interference ratio (ACIR) is the ratio of the total interference power received by the targeted signal receiver to the total interference power sent by the adjacent signal transmitter [35]. The linear value of ACIR can be expressed as  
\[\text{ACIR}=\frac{P}{A+B}=\frac{P}{\frac{P}{\text{ACLR}}+\frac{P}{\text{ACS}}} =\frac{1}{\frac{1}{\text{ACLR}}+\frac{1}{\text{ACS}}} \tag{3}\]  
The value of ACIR (dB) derived from Equation (3) can be re-written as  
\[\text{ACIR}\ (\text{dB})=-10\text{lg}(10^{-\frac{\text{ACLR}}{10}}+10^{- \frac{\text{ACS}}{10}}) \tag{4}\]  
LTE-M base station and LTE-M vehicle terminal (TE) has tolerable interference signal noise power threshold \(I_{threshold}\) in dBm; once the noise power exceeds this threshold, it will block the reception of the targeted signal [36]. The threshold is related to the performance of the receiver, which is specifically manifested in the sensitivity loss of the receiver \(S\). \(I_{threshold}\) can be written as  
\[I_{threshold}=P_{noise}+10\text{lg}(10^{\frac{S}{10}}-1) \tag{5}\]  
Figure 1: Power distribution of transmitting and receiving signals. According to [37], the sensitivity loss \(S_{BS}\) of base station receiver is generally 0.8 dB, and the sensitivity loss \(S_{TE}\) of the vehicle terminal receiver is generally 3 dB. The receiver noise floor power \(P_{noise}\) is related to the system receiving bandwidth (BW) and the receiver noise value \(N_{F}\)[38], as shown below  
\[P_{noise}=-174\ \mathrm{dBm}+10\mathrm{lgBW}+N_{F} \tag{6}\]  
where the thermal noise floor level throughout a 1 Hz bandwidth at 27 \({}^{\circ}\)C is \(-174\) dBm and the noise coefficient \(N_{F\_BS}\) of the base station receiver is 5 dB and that of the vehicle terminal receiver \(N_{F\_TE}\) is 9 dB [39]. This paper selects the transmission link with the most serious interference; that is, one with the highest transmission power \(P_{Imax}\) and the highest transceiver antenna gain \(G_{TR}\). In the transmission process, the transmitter transmits the interference signal, and the signal arrives at the receiver after passing through the transmitting antenna, spatial wireless transmission, channel attenuation, and receiving antenna.