## 7 Results of Simulations
### Impact of SNR on the ED Performance
According to Figure 10a-d, the OFDM constellation has no influence on this SNR threshold, since it has no direct impact on the detection probability (which is also confirmed with relations (11), (13), (16), (18), (19), (21), (22) and (24)). The impact of distinct SNR levels and Tx powers on the detection probability of combined MA and RA systems is shown in Figure 11. The results were acquired for distinct SNRs (\(-\)7 dB/\(-\)10 dB/\(-\)25 dB) of the m-PSK/m-QAM signals influenced by the same NU (\(\rho\) = 1.02) in the scenario where the PU signal is being transmitted at different Tx powers (15 W, 10 W, 1 W and 0.1 W). Based on the results obtained, the combination of the level of PU Tx power and SNR at the position of SU has a strong influence on the detection probability for the ED technique. According to expectations, for better SNR and higher Tx power levels, the detection probability will be larger and vice versa. Moreover, in Figure 11a, it can be seen that, for the low Tx power values equal to 100 mW, the detection probability at the location of SU cannot be increased without SNR enlargement (above \(-\)7 dB). Otherwise, in Figure 11d, it can be seen that, for the larger Tx power equal to 15 W, the signal detection  
Figure 10: Impact of SNR on the detection probability of OFDM signals received under versatile combinations of NU and DT factors when PU transmits at: (a) 0.1 W; (b) 1 W; (c) 10 W and (d) 15 W.  
during ED can be ensured (detection probability of \(P_{d_{i}}\)= 100%) for each SNR level higher than \(-\)7 dB. These prove the strong influence of the trade-off between the noise and Tx power on the efficiency of ED. Figure 12 shows the impact of SNR on the detection probability of the MA systems, which transmit at distinct Tx powers equal to 1 W/10 W. Transmission is assumed to occur over a channel with equivalent channel environments (the same NU factor \(\rho\) = 1.01), the fixed false alarm probability (\(P_{fa_{i}}\) = 10%), and versatile OFDM modulations. If the modulated OFDM signals are transmitted with the equal Tx power and influenced by the same NU, the results presented in Figure 12 indicate that the OFDM modulations do not have any influence on the detection probability at any SNR level. Nevertheless, a lower detection probability can be seen for signals of equivalent OFDM constellations transmitted at a lower Tx power. This is because transmission at a lower Tx power degrades the SNR in the position of SU. For higher SNRs in the position of SU (e.g., above \(-\)5 dB), the MA system that transmits with a lower Tx power (1 W) will have a lower detection probability than an MA system transmitting at a larger Tx power having the same SNR in the position of SU. Therefore, in MA systems, transmission at a lower Tx power degrades the detection probability at any SNR in the position of SU. However, transmission at a lower Tx power has a positive impact on the power consumption of the PU device. Figure 11: Interdependence between detection and false alarm probability for ED of m-PSK/m-QAM modulated signals received under different SNR levels when PU transmits at: (**a**) 0.1 W; (**b**) 1 W; (**c**) 10 W and (**d**) 15 W.