# Energy Efficient Secure Communication Model against Cooperative Eavesdropper
## 2 System Model  
The system model consists of transmitter A, receiver B, jammer J, and eavesdroppers E1 and E2 in a wire tap channel. It is assumed that E1 is closer to A, while E2 is closer to J. A and B use a single input and single output antenna (SISO) system for information transmission and reception. B has an additional antenna for energy harvesting application. J uses the MIMO system for broadcasting jamming signals and it has a separate communication setup to find the location of B and to avoid jamming B. Eavesdroppers use the MIMO system model for receiving information and jamming signals. All the nodes in the system model experience Rayleigh frequency selective fading channels. The SISO channel link between A and B is denoted as \(H_{AB}\), whereas the MIMO channel link between J and E1 is denoted as \(\mathbf{H}_{JE1}\) and, likewise, all the MIMO single inputs with multiple outputs and the multiple inputs with single output channel links are denoted by using \(\mathbf{H}\) and their respective nodes. \(\mathbf{H}_{JE1}\) is characterized as \(\mathbf{H}_{JE1}\sim\mathcal{CN}(0,\sigma_{H,JE1}^{2})\), where \(\sigma_{H,AB}^{2}\) is the channel variance. It is assumed that the expected values of channel variances of all the channel links in the system model are equal. All communication nodes experience additive white Gaussian noise (AWGN) and are modeled as zero mean complex Gaussian random variables. AWGN, experienced by A, is denoted as \(N_{A}\) and is characterized as \(N_{A}\sim\mathcal{CN}(0,\sigma_{N,A}^{2})\), where \(\sigma_{N,A}^{2}\) is the noise variance. Similarly, AWGN is experienced by how all nodes are denoted and characterized. All the legitimate users and jammers are considered to have full channel knowledge. Eavesdroppers are considered to have the channel estimate of all the nodes and this channel estimate depends on the SNR at the eavesdropper node. The channel estimate and the channel estimation error of \(\mathbf{H}_{AE1}\) are denoted as \(\mathbf{\hat{H}}_{AE1}\) and \(\varepsilon_{H,AE1}\), respectively, where \(A\) is the transmitting node and E1 is the receiving node. In similar way, the channel estimate and channel estimation error of the channel between eavesdropper and remaining nodes are denoted. The SNR and SINR of the receiving node E1 are denoted as \(\gamma_{E1}\) and \(\Gamma_{E1}\), respectively. In a similar way, the SNR and SINR are denoted for all the receiving nodes. The SNR of the receiving node considers the power ratio between the received signal and AWGN in an AWGN channel and, therefore, SNR excludes fading coefficient. The SINR of the receiving node considers the power ratio between the received signal and the interference of other signal along with AWGN. The information signal from A, jamming signals from J are denoted as \(X_{I}\) and \(\mathbf{X}_{J}\). The distance between A and E1 is denoted as \(D_{A,E1}\); similarly, the distance between any two nodes in the system model is denoted. In general, the index of transmitting antennas and receiving antennas are denoted as \(t\) and \(r\), respectively, where \(t=1,...,T\) with \(T\) is denoted as the total number of transmitting antennas and \(r=1,...,R\), with \(R\) denoted as the total number of receiving antennas. The total number of transmitting antennas at J is denoted as \(T_{J}\). The total number of receiving antennas at E1 and E2 are denoted as \(R_{E1}\) and \(R_{E2}\), respectively.