## 2 System Model  
As shown in Figure 1, we consider a cooperative communication network consisting a source, \(S\), a destination, \(D\), a relay, \(R\), and a jammer, \(J\). The source, destination, and jammer are assumed to have a fixed power supply such that they always have enough energy for transmission, reception, and jamming. By using the cooperative technique, \(S\) can cooperate with \(R\) to maximize the achievable throughput in the presence of the attack performed by \(J\). The network is assumed to follow a synchronous, time-slotted model with time slot duration \(T\). The channel coefficients between \(S\) and \(D\), \(S\) and \(R\), and \(R\) and \(D\) are denoted by \(h_{SD},h_{SR}\) and \(h_{RD}\), respectively. In this paper, we consider the \"absolute jammer\" who always has enough energy to transmit the interference signals to destroy the channel in target transmission link in a whole time slot duration. Therefore, when the jammer attacks the channel, the direct transmission link from the source to the destination will be blocked; and thus, \(D\) can not receive the data transmitted from \(S\). Fortunately, \(R\) can help the source to forward its data to the destination in this case. However, the relay is assumed to have a limited-capacity battery without any fix powered supplies. Hence, the relay needs to harvest non-RF energy to maintain its long- term operation. The relay is assumed to scavenge energy during a whole time slot \(T\) and the harvested energy is stored in a battery with a finite capacity, \(E_{ca}\). Therefore, at time slot \(t\)th, the amount of energy \(E_{h}(t)\) (energy units) that is harvested by the relay \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Description** \\ \hline \(h_{SD},h_{SR},h_{RD}\) & Channel coefficients between \(S\) and \(D\), \(S\) and \(R\), and \(R\) and \(D\) \\ \(E_{\alpha}\) & Total capacity of the battery \\ \(E_{tr}\) & Transmission energy \\ \(E_{h}(t)\) & Harvested energy at the relay in the timeslot \(t\)th \\ \(e_{mean}^{h}\) & Mean value of the harvested energy \\ \(P_{E_{k}}(t)\) & The probability of the harvested energy in time slot \(t\)th \\ \(T\) & Total time frame \\ \(\tau_{s}\) & The sensing time \\ \(\tau_{SD},\tau_{SR},\tau_{RD}\) & Transmission time between \(S\) and \(D\), \(S\) and \(R\), and \(R\) and \(D\), respectively \\ \(P_{S},P_{R}\) & Transmission power at the source and the receiver \\ \(x_{s}\) & The signal transmitted from the source \\ \(\beta_{r}\) & Amplify scale factor \\ \(\gamma\) & SNR of the channel between the source and the jammer \\ \(\alpha\) & Discount factor \\ \(P_{d},P_{f}\) & Probability of detection and false alarm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The notation list. Figure 1: The system model of the proposed scheme. can be expressed as \(E_{h}\left(t\right)\in\left\{e_{1}^{h},e_{2}^{h},e_{3}^{h},...,e_{v}^{h}\right\},\) where \(e_{1}^{h},e_{2}^{h},e_{3}^{h},...,e_{v}^{h}\) are harvested energy levels, and \(0<e_{1}^{h}<e_{2}^{h}<e_{3}^{h}<...<e_{v}^{h}<E_{ca}\). The probability mass function (PMF) of the harvested energy is given as:  
\[P_{E_{h}}\left(k\right)=\Pr\left[E_{h}\left(t\right)=e_{k}^{h}\right],\text{ \ }k=1,2,3,...,v. \tag{1}\]  
where \(P_{E_{h}}(t)\) is the probability of the harvested energy in time slot \(t\)th. In this paper, we assume that the harvested energy of the relay follows a Poisson distribution where \(E_{h}(t)\) is a Poisson random variable with mean value \(e_{mean}^{h}\), and the PMF in (1) can be rewritten as follows:  
\[P_{E_{h}}\left(k\right)\approx\frac{e^{-e_{mean}^{h}}\left(e_{mean}^{h} \right)^{k}}{k!},k=1,2,...,v. \tag{2}\]  
In order to deal with the jamming attack problem, at the beginning of each time slot, the source needs to determine whether it should use the direct transmission mode or relay-assisted transmission mode to transmit its data to the destination. Figure 2a depicts the time frame structure of the direct transmission mode. For this mode, the frame is divided into two phases: sensing and data transmission.