# Energy Efficient Secure Communication Model against Cooperative Eavesdropper
## 3 Numerical Results
In Figures 4 and 5, for the fixed operating SNR, i.e., 12 dBm, the performance of E2 is measured for \(\beta_{E2}\) values against the expected jamming signal estimate error. Since the jamming signal is random in nature, instead of BER, the expected error for detecting jamming signal is considered for performance measurement. Figure 4 demonstrates that the expected error of the jamming signal estimate error reduces with the increase in \(\beta_{E2}\) value, but the rate of reduction in error saturates with the increase in \(\beta_{E2}\). In this simulation, the performance of E2 can be degraded by increasing \(T_{J}\) at the J. By increasing the \(T_{J}\), we can reduce the SNR of individual jamming signals while keeping the total power of combined jamming signals at constant. In order to use the IBDFE receiver, E2 should satisfy \(R_{E2}\geq T_{J}\). Thus, in this simulation, we set \(R_{E2}=T_{J}\). The observation of the results of Figure 4, based on the increase in \(T_{J}\), degrades the performance of E2, even if \(R_{E2}=T_{J}\), which satisfies (15). Therefore, by increasing \(T_{J}\), J can degrade E2 performance. Figure 5 demonstrates the drastic performance improvement of E2 with the application of the IBDFE decoder over the ZF decoder with the increase in \(R_{E2}\). The increase in \(T_{J}\), degrades SNR, as in (15), but this SNR degradation impact is reduced with the increase in feedback diversity order in IBDFE, due to \(R_{E2}\). Therefore, with the increase in \(R_{E2}\), the performance degradation due to SNR degradation is lower in IBDFE, as compared to ZF. Figure 6 demonstrates the BER results of the information signal after reducing the interference of the jamming signal by using the jamming signal estimate from E2. The expected jamming signal estimate error is tabulated in Table 2. To degrade the performance of E1 and E2, J increases \(T_{J}\), this is observed from the BER results. When \(T_{J}\) is increased, the performance of E2 degrades and the error in the jamming signal estimate feedback increases, as in Table 2. The BER results show that, by increasing the \(\beta_{E1}\) value above 1 and by increasing \(T_{J}\), J can degrade E1 performance. Even though increase in \(\beta_{E1}\) degrades the BER results of E1, it is optimal to set \(\beta_{E1  
Figure 7 demonstrates the advantage of using IBDFE over the ZF decoder at E1. Even though IBDFE performs better than ZF, the increase in \(T_{J}\) can degrade the performance of IBDFE and the performance gap between IBDFE and ZF decreases with the increase in \(T_{J}\). Therefore, with the help of \(T_{J}\) and \(\beta\), J can degrade cooperative eavesdropper performance with the least possible energy expenditure. The comparison of results of the ZF and IBDFE decoder at \(T_{J}=11\) shows that the performance of IBDFE is better than that of ZF. The comparison of IDBFE performance in terms of SNR shows that there is a slight performance degradation at SNR--18 dBm over SNR 15 dBm--and this result is contrary to the expected result. The reason for this unexpected degradation in BER is due to the incorrect noise power input in the feed forward in (12), and for the single antenna case, refer to [6]. The amount of energy saved at J, when \(\beta_{E1}=1\) over \(\beta_{E1}=1. Figure 5: The performance of IBDFE versus ZF at E2, where the feedback of information signal estimate is included to reduce interference. Figure 6: The BER results of E1 with the feedback of jamming signal estimate, where \(T_{j}=R_{E2}\).