## 7 Results of Simulations
### Impact of SNR on the ED Performance  
Next, simulations were performed with respect to the influence of SNR at the location of SU on the ED performance. The obtained results shown in Figure 9a for the RA systems indicate the effect of SNR on the detection probability of the OFDM signal. The results presented in Figure 9a confirm that, for the constant PU Tx power equal to 1 W and for the unchanged value of the false alarm probability equal to \(P_{fa_{i}}\) = 10%, the detection probability will remain the same for any modulation and corresponding constellation (m-QAM//m-PSK). Nevertheless, Figure 9a shows that for the higher levels of SNR, the detection probability will be better for any modulation order and decrease with the degradation of SNR. This is due to the higher SNR, which results in higher PU signal energy at the location of SU. This improves the ED process and, as a consequence, increases the PU detection probability. In addition, the results presented in Figure 9a confirm that the trade-off between the level of NU variation and DT adaptation has an impact on the detection probability. More specifically, for the higher NU variation range (\(\rho\) = 1.05) and lower DT adaptation range (\(\rho^{\prime}\) = 1.03), the detection probability will be lower compared to the ED of the signals impacted with the lower NU variation (\(\rho\) = 1.03) and ED performed with a higher DT adaptation (\(\rho^{\prime}\) = 1.05). Additionally, the ROC curves for the fixed PU Tx power (1 W) and the versatile SNR values (\(-\)5 dB, \(-\)10 dB, \(-\)25 dB) of OFDM signal influenced with distinct NUs and received with different DT adaptation ranges are presented in Figure 9b. The presented results show that, for channels with a higher SNR in the location of SU (\(-\)5 dB), the detection probability will be higher due to the lower influence of noise on the ED. Although NU variations have an impact on the ED, the total AWGN level has a significant influence on the ED and high levels of noise can largely reduce ED efficiency. This is due to the lower SNR in the position of SU, where the fixed PU Tx power means higher noise. As a consequence, this results in a lower detection probability. Apart from the significant influence of the overall level of AWGN, Figure 9b additionally confirms the non-negligible influence of NU, which further contributes to the degradation of ED efficiency. Figure 9b suggests that, for lower NUs, the detection probability will be higher for signals with a higher SNR. Based on these results, the combination of high SNR with low NU positively influences the ED performance of the RA system. For combined MA and RA systems, the impact of SNR on the detection probability of the OFDM signals affected by distinct NUs is presented in Figure 10a-d. The results show that, independent of the OFDM modulation and PU Tx power, larger noise fluctuations (characterised with a larger NU factor \(\rho\)) decrease the detection probability at any SNR  
Figure 9: (**a**) Detection probability vs. SNR for signals transmitted in RA systems; (**b**) Interdependence between probabilities of detection and false alarm for versatile NUs, DTs and SNRs in the case of RA system. lower than the SNR threshold (confirmed PU detection). The fluctuations of NU influence every OFDM signal, regardless of its modulation order and Tx power. Although for the signals with a lower Tx power this influence is more observable, this is also reflected in the lower detection probabilities (Figure 10a-d). Furthermore, for the distinct levels of Tx power, an SNR threshold higher than some level for which the PU detection probability can be ensured is visible (Figure 10a-d). This SNR threshold is significantly affected by the Tx power level and is reduced for the signals with larger PU Tx (e.g., 5 dB for Tx power of 1 W and \(-\)5 dB for 10 W Tx power).