## 5 Implementation of the Simulation Algorithm
The results shown in Figure 9(a),b demonstrate that increasing the number of detection samples enhances the likelihood of detecting a PU signal for any Tx-Rx antenna combination, as well as any combination of DDT and NU factors. Such a result is supported by Equation (23), which shows that a larger number of detection samples employed in the ED SS improves detection probability. This is expected as a higher number of detection samples used for the ED SS represents an increased number of detection attempts during the PU signal recognition process. This increases the probability that the PU signal will be detected accurately. In addition, the ROC curves presented in Figure 9(a),b show that for identical channel conditions and a higher number of detection samples, the 2 \(\times\) 2 MIMO system outperforms the SISO system in terms of sensing performance. As previously explained, this is due to the diversity gain of the MIMO system. This cognition allows the MIMO system to achieve the same sensing performance as the SISO system using a reduced number of detection samples for the same channel conditions. Figure 10 also shows the ROC curves for various combinations of DDT and NU parameters (\(\rho\) = 1.05, \(\rho^{\prime}\)= 1.03; \(\rho\) = 1.03, \(\rho^{\prime}\) = 1.05). In an operational environment where moderate levels of NU (\(\rho\) = 1.03) impact the PU signal, a higher value of DT adaptation (= 1.05) results in a better detection performance for an equal number of detection samples. The detection probability will decrease where there are higher NU fluctuations ( = 1.05)

Figure 10: The ROC curves for the various NU and DDT factor combinations and distinct number of detection samples (128, 256, 512) in (**a**) SISO and (**b**) MIMO systems for transmission characterized with QPSK modulation, SNR = \(-\)15 dB and \(\rm{P_{Tx}}\) = 100 mW. and lower DDT adaption values (\(\rho^{\prime}\) = 1.03) for any number of the detection samples used for the ED SS. This confirms that larger NU levels have a stronger unwanted impact on the ED process and that more flexible DDT adaptations improve the ED performance in the presence of strong NUs. Therefore, increased NU variation during the ED process must be accompanied by an adequate increase in DDT adaptations. The results presented in Figure 10 also point out that reliable PU signal detection can be enhanced by exploiting more detection samples during the ED SS. This results in a more precise identification of the PU signal at the SU side. Hence, different combinations of triples related to choosing the number of detection samples, the degree of DDT adaptation, and the number of Rx and Tx branches in the MIMO communication system according to the specifics of the radio channel conditions, can contribute to the enhancement of detection probability in the ED SS process. ## 7 Conclusions

The sensing process in realistic CR systems is negatively affected by inconsistent variations in noise power, which are known as NU. A possible approach to reducing the impact of NU on the ED process is the exploitation of DDT adaptations during SS. In this paper, the analysis of the ROC curve shapes for the SS process performed by the energy detector exploiting the SLC technique in MIMO-OFDM CRN has been elaborated on to explore the different impacts of NU variations and the levels of DDT adaptations. To evaluate the proposed ED performance, mathematical models were developed to express the interdependence of the PU detection probability in MIMO systems on essential performance factors such as the PU Tx power, the number of detection samples, the threshold levels, the number of Tx-Rx MIMO branches, and the SNR values. Furthermore, a simulation algorithm for analysing the accuracy of the ED SS employing SLC is presented and exploited for the simulation of different DDT and NU impacts on the shape of the ROC curves.