## 2 System Model
The total signal received by ED\({}_{n}\) is given as follows:  
\[y_{\text{ED}_{n}}(t)=\sqrt{\text{P}_{\text{BS}}}\ x_{\text{BS}}(t)g_{\text{BS- ED}_{n}}+x_{\text{HT}}(t)g_{\text{HT-ED}_{n}}+\sqrt{\text{P}_{\text{j}}}x_{ \text{j}}(t)g_{\text{j-ED}_{n}}+n_{n}(t). \tag{1}\]  
where \(x_{\text{BS}}(t)\) and \(x_{\text{j}}(t)\) are the information signal sent by the BS and jammer, respectively. \(\text{P}_{\text{BS}}\) is the signal transmission power of the BS and \(\text{E}(\left|x_{\text{BS}}(t)\right|^{2})=\text{P}_{\text{BS}}\), \(\text{P}_{\text{j}}\) is the signal transmission power of the jammer and \(\text{E}(\left|x_{\text{j}}(t)\right|^{2})=\text{P}_{\text{j}}\). The number of EDs in the system is \(N\) and \(n=1\), \(2\), \(\ldots\), \(N\). \(n_{n}(t)\) is a additive white Gaussian noise with zero mean. \(\sigma_{\text{ED}_{n}}^{2}\) is  
Figure 1: The proposed system model. the noise power at ED\({}_{n}\). The channel gain between BS-ED\({}_{n}\), HT-ED\({}_{n}\) and jammer-ED\({}_{n}\) is expressed as \(g_{\text{BS-ED}_{n}}\), \(g_{\text{HT-ED}_{n}}\), \(g_{\text{j-ED}_{n}}\), respectively. The signal transmitted by the HT to the ED\({}_{n}\) is given as follows:  
\[x_{\text{HT}}(t)= \begin{cases}\sqrt{P_{\text{BS}\;Z}}\;x_{\text{BS}}(t)\,g_{ \text{BS-HT}}\;y_{\text{HT}}(t),&\text{passive signal transmission ( relay mode)}\\ \sqrt{P_{\text{active}}}\,y_{\text{HT}}(t),&\text{active signal transmission}\end{cases}  \tag{2}\]  
where \(y_{\text{HT}}(t)\) is the information signal of HT. The channel gain between BS and HT is \(g_{\text{BS-HT}}\). \(z\) is the power reflection coefficient of HT and \(z\in[0,1]\). \(P_{\text{active}}\) is the transmission power of the signal sent by HT during active signal transmission. If the total signal received by EDs is generalized, the total signal obtained with the wiretap channel in the system model is expressed as follows:  
\[y_{\text{ED}}(t) =\sum_{n=1}^{N}y_{\text{ED}_{n}}(t) \tag{3}\] \[=\sum_{n=1}^{N}\Bigl{(}\sqrt{P_{\text{BS}}}\;x_{\text{BS}}(t)g_{ \text{BS-ED}_{n}}+x_{\text{HT}}(t)g_{\text{HT-ED}_{n}}+\sqrt{P_{\text{j}}}x_{ \text{j}}(t)g_{\text{j-ED}_{n}}+n_{n}(t)\Bigr{)}\]  
\(\beta_{0}\) : Spectrum sensing time \(\beta_{1}\) : The HT helps signal transmission of the BS through backscatter communication. In other words, HT works like a relay. \(\
u\beta_{2}\) : The HT transmits signal to the IR with active communication. The BS works like a jammer and helps HT by reducing the SNR value of the signal reaching the ED. \(\beta_{0}\) + \(\beta_{1}\) + \(\beta_{2}\) : WiFi access point operates for one full period \(1\) - \(\beta_{0}\) : Jammer operating time \(T\) period : Period of the normalized dynamic time allocation scheme. Figure 2: Dynamic time allocation scheme for spectrum sensing-based PLS. Energy detection-based spectrum sensing is considered due to its many benefits, including easy implementation and minimal computational complexity [45]. In the scenario where there are sensing errors, the probabilities of the BS being active-passive and the probability of the HT detecting the activity of the BS are included in the mathematical equations. \(P(H_{0})\) is the probability of the BS being inactive. \(P(H_{1})\) is the probability of the BS being active. \(P_{f}\) is the probability of a false alarm. \(P_{d}\) is the probability of signal detection at the HT. It is observed that because of the sensing mechanism, the communication link between BS and HT and the sensing accuracy determine the average throughput. The four scenarios that follow can be applied to proposed system model.