## 3 Intelligent Jamming
### Estimation of jamming Effect
The relationship between the signal ratio from a jammer (interference device) and the network is given in [16]:  
\[\frac{J}{S}=\frac{EIRP_{jammer}}{EIRP_{network}}\frac{4\pi R^{2}}{\lambda}. \frac{BW_{network}}{BW_{jammer}} \tag{3}\]  
where:  
* \(\frac{J}{S}\) is the signal-to-jammer to signal-to-network, also called the SIR (signal-to-interference ratio), and typically refers to the ratio of the desired signal power to the interference power, where the interference includes any unwanted signals or noise that can degrade the quality of the received signal. * \(EIRP_{jammer}\) is the equivalent isotropic radiated power (EIRP) of the jammer. * \(EIRP_{network}\) is the equivalent isotropic radiated power (EIRP) of the network. * \(R\) is the distance between the jammer and the mobile phone. * \(\lambda\) is the wavelength and \(\lambda=c/f\), where \(c=3\times 10^{8}\) m/s is the speed of light and \(f\) is the downlink central frequency (Hz). * \(BW_{network}\) represents the network bandwidth. * \(BW_{jammer}\) represents the jammer bandwidth. In the Matlab simulations, we considered  
\[\text{EIRP}_{\text{jammer}}(\text{dBm})=\text{P}_{\text{Tx}}(\text{dBm})+\text {G}(\text{dBi})=15+7=22(\text{dBm}) \tag{4}\]  
where \(P_{Tx}(\text{dBm})\) is the transmitted power in decibel-milliwatts, \(G(\text{dBi})\) represents the gain (directivity) of the antenna in decibels isotropic, \(EIRP_{network}(\text{dBm})\) is a measure of the effective radiated power from an antenna or transmitter in a specific direction, which is an important parameter in wireless communication systems and was \(-79.5\) dBm at the monitored point. The distance \(R\) was considered to be 1 m, and the wavelength was  
\[\lambda=\frac{c}{f}=\frac{3\cdot 10^{8}}{793.5\cdot 10^{6}}=0.378\cdot BW_{network}= BW_{jammer}=5\text{ MHz} \tag{5}\]  
The path loss formula describes the attenuation of a signal as it propagates through a wireless communication channel. The path loss depends on various factors, including the distance, frequency and environment. One commonly used path loss model is the free-space equation, which is suitable for free-space or open-air scenarios and assumes no obstacles or interference; it is given by Formula (6):  
\[PL(\text{dB})=20\cdot\log_{10}\left(\frac{4\pi df}{c}\right)+G+L_{obstacle} \tag{6}\]  
where \(P_{L}(\text{dB})\) is the path loss in decibels (dB); \(d\) is the distance between the transmitter and receiver in meters (m), where it was considered in the range of 1-8 m (with steps of 0.5 m); \(f\) is the frequency of the signal in hertz (Hz); \(c=3\cdot 10^{8}\)(m/s) is the speed of light represents the antenna gain, which was considered to be +7 dBm; and \(L_{obstacle}\) represents additional losses due to obstacles and the environment, which was considered to be 0. Considering \(EIRP_{jammer}\) at 22 dBm, we could calculate the final \(EIRP_{jammer}\) only after we decreased the value of Hack-RF to 22 dBm for the \(P_{L}\)(dB) and considered the distance from 1 to 8 m with steps of 0.5 m.  
Therefore, Formula (3) can be rewritten as follows, with the same values for \(BW_{network}\) = \(BW_{jammer}\) = 5 MHz and \(\lambda\) = \(\frac{c}{J}\) = \(\frac{3\cdot 10^{8}}{793.5\cdot 10^{6}}\) = 0.378  m considered above:  
\[\text{SIR}=\frac{J}{\text{S}}=\frac{EIRP_{jammer}-P_{L}}{EIRP_{network}} \cdot\frac{4\pi R2}{\lambda}\cdot\frac{BW_{network}}{BW_{jammer}} \tag{7}\]  
Decreasing \(EIRP_{jammer}\) with a negative value leads to an increase. Using Formula (7) for SIR and (6) for PL, and considering SIR = 0 dB as the limit of the effectiveness of jamming. * \(EIRP_{jammer}\) = 22 dBm (maximum level the SDR Hack-RF could generate). * \(EIRP_{network}\)= \(-\)79.5 dBm (maximum level of DL Digi Mobile signal received by TSMA6). * DL channel centre frequency from Digi Mobile = 793.5 MHz. * \(BW_{network}\) = \(BW_{jammer}\) = 5 MHz. * Receiving antenna gain = 7 dB.