# Study and Analysis of Interference Signals of the LTE System of the GNSS Receiver
## 4 Simulation Studies
### Noise in the GNSS Receiver--Identification
It should be noted that the obtainable probability of detecting interference is the greater the more signals of disturbing signals are received and the greater their value \(C/N_{0}\). In the remainder of this work, the element error rate BER will be determined as a function of the ratio \(E_{b}/N_{0}\) (energy per bit to noise density). To describe the relationship between \(E_{b}/N_{0}\) and the signal-to-noise ratio at the demodulator input \(C/N_{0}\), the above relationship, which is true for modulated signals based on the method of bandwidth sharing with division into the frequency OFDM (Orthogonal Frequency Division Multiplexing) method with different guard interval \(D\), symbol duration \(T_{u}\) and code efficiency \(R_{c}\)[44] values can be used. The considered dependence can be written by the following Equation (25):  
\[C/N=\log_{2}M\frac{E_{b}}{N_{0}}R_{c}\frac{1}{1+\Delta/T_{u}} \tag{25}\]  
where \(M\) is the number of modulator states (4 for QPSK, 16 for 16 QAM, and 64 for 64 QAM), whereby QPSK (Quadrature Phase Shift Keying) is a modulation with 2-bit coding of the transmitted signal with four orthogonal phase shifts, and QAM (Quadrature Amplitude Modulation) is amplitude-phase modulation, which is designed to transmit digital data over a radio channel. It should be noted that on the basis of the above dependence (25), it is possible to unequivocally determine \(C/N\) with the help of a known value \(E_{b}/N_{0}\) and vice versa. This will make it possible to move from the receiver signal parameters (useful signal power and noise power) to the value \(E_{b}/N_{0}\) and thus determine the BER value. It should be noted that it is possible to determine the interference power that will prevent the reception of any GNSS satellite signals. According to the official satellite-receiver interface specification [45], the minimum power of the GNSS signal with string \(C/A\) (generally available) at the receiver antenna output should be \(-160\) dBW (\(10^{-16}\) W). With the bandwidth \(B_{C/A}\) of the signal with string \(C/A\), being approximately 2 MHz, the signal power to thermal noise power ratio is \(-19\) dB. Therefore, the signal is received significantly below the noise floor. A measure of the quality of the received GPS signal is the ratio \(C/N_{0}\) of the carrier wave power to the spectral noise power density after focusing the spectrum, which is expressed in dBHz units and can be written as follows (26):  
\[SNR[\mathrm{dB}]=\frac{C}{N}[\mathrm{dBHz}]-10\,\log_{10}\left(B_{\frac{C}{A} }[\mathrm{Hz}]\right)=\frac{C}{N}[\mathrm{dBHz}]-63\,[\mathrm{dBHz}] \tag{26}\]  
where the signal-to-noise ratio (SNR) in the above formula defines the signal-to-noise ratio measured by the GPS receiver. The threshold value \(C/N_{0}\), below which a GNSS receiver is not able to receive the signal correctly depends on its sensitivity and is usually not less than 30 dBHz. This corresponds to a signal-to-noise ratio of \(-33\) dB. Therefore, if the power of the useful signal was e.g., 10 dB greater than the minimum and was \(-150\) dBW, in order to effectively disturb it, it would be enough to transmit a narrowband signal whose power at the receiver input would be \(-150\) dBW + 33 dB = \(-117\) dBW, i.e., about \(2\times 10^{-12}\) W.  
The power of the interfering transmitter obviously depends on the length and nature of the propagation path between this transmitter and the interfered receiver. Nevertheless, a relatively low power transmitter is usually sufficient. It should also be noted that the susceptibility to interference depends on whether the receiver is tuned to the useful signal at the moment of activation of the unwanted signal (i.e., is it in the so-called tracking phase) or is just searching for it (acquisition phase) [43].