# Energy Efficient Secure Communication Model against Cooperative Eavesdropper
## 3 Numerical Results  
In this section, the BER performance of information signal estimate at E1 and the expected error estimate of Jamming signal estimate at E2 are demonstrated and analyzed by using Monte Carlo simulations. The signal uses a 2.4 GHz frequency band and it is considered that all the communication nodes including the eavesdroppers are operating at line of sight channel condition. As in the Figure 1, \(D_{A,E1}=5\) m, \(D_{A,J}=5\) m, \(D_{E1,E2}=15\) m, \(D_{E1,J}=10\) m, \(D_{E2,J}=5\) m and \(D_{A,E2}=10\) m. The path loss factor for an indoor environment is considered as 2. In the following simulations, the system uses the 4-QAM modulation signal and adopts the IBDFE receiver at E1 and E2 for improving their error rate performance. We have adopted 4-QAM modulation over other higher order modulations because 4-QAM signal has better error-rate performance over other higher-order modulation signals. This approach gives an advantage to eavesdroppers in estimating information signal and, if the jammer can successfully obscure eavesdroppers from estimating the 4-QAM signal, then this jamming approach can be easily adopted for other higher-order modulation signals. The channel estimate error for the channel links between the nearest node to E1 and E2 are considered as 0.01 (In this system model, for the indoor environment with slow varying fading scenario, we consider SC-FDMA model with Rayleigh frequency selective fading channel condition between all the nodes. The channel estimation error of the Rayleigh frequency selective fading channel for the system that uses a robust channel estimation technique is less than 0.01 [5]. Since A and J are in a fixed location, to estimate the channel condition between A and E1, the passive eavesdropper transmits a low power pilot signal to E1 from the location of A, and then E1 estimates the channel condition. Similarly, the channel condition between J and E2 can be estimated. To avoid detection, passive eavesdroppers use a low power pilot signal, but this can lead to an increase in the channel estimation error with the increase in distance between the passive eavesdropper and the active eavesdropper. Therefore, in this system model, the channel estimation between A and E2, and J and E1, are not considered. For the sake of simplicity, the passive eavesdroppers that are used for estimating A to E1, and J to E2 channel links are not mentioned in the system model. ). In the following figures, all BER curves, by default, illustrate the 4 th iteration of the IBDFE decoder unless specified as zero forcing (ZF) decoder and, by default, \(T_{I}=1\). For this system model to find the optimum \(\beta\) value, \(P_{I}\) is changed in order to change the \(\beta\) value,e and \(P_{I}=1\) in all simulations. \(P_{I}\) is constant to avoid performance degradation at an legitimate receiver. Figure 2 demonstrates the BER performance of E1 with \(R_{E1}=2\). In this simulation, E1 does not receive the jamming signal estimate feedback from E2. The BER performance degrades with the increase in \(\beta_{E1}\) value and also by increasing \(R_{E1}\). In Figure 3, the comparison of BER results demonstrates that E1 can improve BER by increasing \(R_{E1}\) when \(\beta_{E1}=0.375\), as compared to that of when \(\beta_{E1}=1\). Figure 2: The BER results of E1 without the feedback of jamming signal estimate, where \(R_{E1}=2\), \(T_{l}=1\). Table 1 is an tabulation of Figure 2 values and, with this, \(\beta_{E1}\) and \(\beta_{E2}\) are calculated based on the path loss factor, distance between signal transmitting node and receiving node, and \(P_{I}\) and \(P_{I}\). Figure 3: The BER results of E1 without the feedback of jamming signal estimate, where \(R_{E1}=2\), \(T_{I}=1\). In the following simulations, \(\gamma_{sys}=12\) dBm is considered as an operating SNR and, for this operating SNR, we determine the optimum \(\beta_{E1}\) that is suitable for legitimate users to degrade the performance of the cooperative eavesdropper.