## 3 Results
### Research Results  
The CDF of the localization error of the PUFA for the DE algorithm is shown in Figure 4. The population size 'M' is 2, and the crossover rate 'CR' is 0.3. This plot is generated for 50 SUs. We can see that the proposed approach upgraded the limitation precision. Clearly, the higher plot shows that the performance of DE is better. When the CDF is 0.72, the MSE values increase from 0.4 m to 0.8 m. At 0.8 m MSE, CDF starts increasing from 0.72 to 0.91. The figure shows that at 0.91, the value of MSE has a higher increment from 0.8 m to 2.1 m. This increment in MSE increases the position accuracy of the attacker. It shows that increment in the iteration number increases the localization precision. The number of SUs remains 50 for this simulation. The MSE of DE decreases with the increase in the iteration number as shown in Figure 5. Between 0 and 10 iterations, the localization error decreases, and convergence occurs faster and is supposed to be a predictable behavior. From iteration 10 to 30, the error decreases a little bit, and the plot for DE is nearly constant. When the iteration increases from 30 up to 100, the MSE value remains constant. Above 100, the MSE decreases further, but it does not touch 0, as the predictable values used for DE are not true. For FA, the MSE is a constant value above 150 iterations. It is clear from Figure 4 that the proposed DE approach is performing better than the FA. The deviation in MSE with the increment in SNR is shown in Figure 6. The SNR values increase from \(-10\) dB to \(30\) dB where the SUs remain at \(50\). It is obvious from Figure 6 that DE has better performance than FA. The results show that, as the SNR values increase, the MSE declines rapidly for DE and slowly for FA. For FA, when the SNR ranges between \(10\) dB and \(20\) dB, the MSE remains constant and decreases further until \(30\) dB SNR. The MSE for DE declines with the increment in SNR until it reaches \(30\) dB. This decline in MSE shows that the proposed DE model is close to the estimated position of the attacker, as a lower MSE normally specifies an enhanced approximation. The increment in the number of SUs greatly affects the MSE of the attacker position as shown in Figure 7. As the number of SUs is increasing, the MSE value is decreasing. The higher the number of SUs, the lower the MSE will be. The SNR value remains \(10\) for this simulation. It is obvious from Figure 7 that the MSE for DE is less than FA at \(10\) SUs. For FA, the MSE decreases faster up to \(60\) SUs but remains constant until the number of SUs reaches \(90\). After \(90\) SUs, the decline in MSE for FA is not significant. For DE, MSE decreases a little bit and remains constant from \(30\) to \(90\) SUs, but as the number of cooperating users increases, it further declines to some extent. Figure 7 shows that the proposed DE has higher precision than the FA. Figure 4: CDF of localization error for the DE algorithm. Figure 5: Effect on MSE with increase in iterations. The effect of changing the SNR value on the correct detection probability is shown in Figure 8. It is obvious from the graph that as the SNR increases, the likelihood for the correct detection of the PU also increases. This shows that the performance of the proposed technique is good with varying SNR. The SNR ranges from 0 dB to 200 dB, and SUs are 50. The impact of SNR on the false detection probability is shown in Figure 9. As the SNR increases, the probability decreases. It shows that the proposed system is providing free band to SUs for their transmissions because the probability of false detection is decreasing, and the channel is free for SUs. Figure 8: Probability of correct detection against SNR. Figure 6: The deviation in MSE with SNR. Figure 5.0 The deviation in MSE with the variation in the number of SUs. number of SUs for the FA and proposed DE are shown in Figures 5-7, respectively. This comparison shows that the suggested DE model has better performance than FA.