# Study and Analysis of Interference Signals of the LTE System of the GNSS Receiver
## 4 Simulation Studies  
Protection of the GNSS receiver against interference signals requires the implementation of coupled noise detection and elimination algorithms. The simplest and the least effective detection methods are based on the analysis of time dependencies and parameters related to the power of the received signals. For example, variations in the received signal strength during movement of the receiver are observed, or the relative delay between the signals transmitted at different frequencies is measured. In other methods, both the sample distribution of the maximum of the correlation function at the receiver and the shape of the function are monitored. Unusual indications of these parameters may indicate the presence of higher noise in the GNSS receiver. A more efficient way of detecting interference signals is to compare the position determined from the signals of the GPS system with the position calculated by the receiver of another navigation system. However, it should be taken into account that the signals of another radio navigation system may be disturbed, and if it is a terrestrial system, its range is limited territorially. Another effective way to check whether the received GNSS signals are more \"noisy\" could be to introduce their cryptographic protection while maintaining backward compatibility with the receivers produced so far. The signals broadcast by the satellites reach the receiver from different directions. In turn, the base station of the LTE system transmits all signals through one antenna, which means that they have the same direction of arrival. Thus, the detection of at least four signals with similar directions of arrival may indicate the presence of interference signals. The designed integrated system partially eliminating noise from the GNSS receiver was programmatically implemented in the Matlab/Simulink programming environment and was subjected to simulation tests. The simulation studies consisted of assessing the positioning accuracy using the spatial orientation system, GPS receiver, and the Galileo system. The generated errors of the integrated system elements are expressed in the local coordinate system (LCS). The values of the parameters of the GPS system model were adopted on the basis of observations of the actual measurement errors of the GNSS receiver. The interference signal of the LTE system is interfering with the GNSS receiver, using the correlation outputs (processes performed by the correlator in the GNSS receiver), so in this case, both stages will be analyzed: first, in the acquisition phase, i.e., that the GPS receiver cannot acquire satellites or acquire bad satellites, second, in the tracking and computing steps, the signal from the LTE system may force the GNSS receiver to output bad navigation data or not be able to demodulate the data because the LTE system signal may confuse the GNSS receiver into not finding the preamble. A genuine GNSS signal can be expressed as (17):  
\[r_{s}(t)=\sum\limits_{m=1}^{M}\sqrt{2P_{m}}d_{m}(t-\tau_{m})c_{m}(t-\tau_{m}) \cos(2\pi(f_{L1}+f_{m})t+\theta_{m})+\sum\limits_{k=0}^{N-1}x_{k,l}\phi_{k}(t_ {LTE}-IT), \tag{17}\]  
where \(P_{m}\) is the amplitude of the satellite signal \(m\); \(c_{m}\) is the PRN code of the satellite \(m\); \(d_{m}\) is the navigation message of the satellite; \(\tau_{m}\) is broadcast time; and \(f_{m}\) is the frequency of the Doppler shift. The interference signal can be written as (18):  
\[i(t)=Ac(t-\tau_{\rm{inter}})\cos(2\pi(f_{L1}+f_{\rm{inter}}+f_{LTE})t+\theta_{ \rm{inter}}+\theta_{\rm{LTE}}), \tag{18}\]  
where \(c(t)\) is the PRN code, \(A\) is the amplitude of the interference signal of the LTE system, and \(\tau_{\rm{inter}}\) is the time shift of the interference signal. In the above Equation (18), parameters \(f_{L1}\), \(f_{\rm{inter}}\), and \(f_{LTE}\) mean the frequency of the GPS signal transmitted in the L1 band, the interference signal frequency (GSM UMTS), and the frequency of the LTE signal, respectively.