## 7 Results of Simulations
### Impact of the Sample Quantity on the ED Performance  
The following results presented in this section are dedicated to the analysis of the influence of the sample quantity (\(N\)) on the capability of detecting PU during the ED process. The ROC curves for signals transmitted with a constant Tx power equal to 1 W using the m-QAM/m-PSK modulations and detected by a different sample quantity are presented in Figure 13. Analyses were performed for two combinations of NU and DT factors (\(\rho\) = 1.02, \(\rho^{\prime}\) = 1.01 and \(\rho\) =1.05, \(\rho^{\prime}\) = 1.03) and for the case when SNR is fixed in the position of SU equal to \(-15\) dB. Figure 13 shows that the sample quantity has a non-negligible influence on the ED performance of RA systems. When the smaller sample quantity is used in the ED process (\(N\) = 128), the results obtained for the channels with the same channel characteristics (equivalent NU and SNR) showed that the signal detection probability will be lower and vice versa. This result is a consequence of the lower sample quantity, which actually means a lower number of independent trials in a period during which the signal of PU is being sensed. Figure 12: Detection probability vs. SNR for MA system with PU transmitting at distinct Tx powers (1 W/10 W) using four different OFDM modulations. Figure 13: Interdependence between detection and false alarm probabilities for ED of m-PSK/m-QAM modulated signals transmitted with Tx power of 1 W and sensed with the distinct sample quantities. Compared to the detection of signals impacted by a higher NU and somewhat higher DT factor (\(\rho=1.05,\ \rho\ t=1.03\)), the results in Figure 13 show that, for the lower values of NU and DT factors (\(\rho=1.02,\ \rho\ t=1.01\)), a higher detection probability can be obtained with the same sample quantity. This is because the lower NU results in less degradation of the received signal, which demands less sample quantity (sensing attempts) for the accurate ED of the PU signal. To ensure the same probabilities of detection for the same sample quantity, a significant increase of NU must also be followed by an appropriate increase in the DT adaptation. Otherwise, the sample quantity must be increased and this trade-off between sample quantity and DT adaptation range significantly impacts the ED efficiency. ROC curves have been shown in Figure 14a-d for different OFDM modulated signals sensed by a distinct sample quantity and transmitted at four distinct Tx powers. The analysis was performed for the fixed SNR in the position of SU equal to \(-15\) dB and for moderate NU level (\(\rho=1.02\)) with the corresponding DT adaptation (\(\rho\ t=1.01\)). Based on the results presented, the increase in the sample quantity and PU Tx power in combined MA and RA systems led to an increase in the detection probability and vice versa. This was an expected result since relations (11), (16) and (19) confirm that the sample quantity (\(N\)) and the Tx power of PU influence the detection probability. A lower Tx power for some OFDM modulations means weaker signal energy at the location of SU. Furthermore, fewer sample quantity \(N\) results in a lower number of independent trials for the PU ED. Additionally, for analysed combinations of NU, Tx power, and SNR level (higher than the SNR wall) presented in Figure 14d, a threshold \(N\), related to the sample quantity above which the detection probability can be ensured for each OFDM modulation (\(P_{d_{i}}=100\%\)), can be seen. For OFDM modulations transmitted at a higher Tx power (presented in Figure 14), the value of this threshold will be lower. Transmission at larger Tx power means more  
Figure 14: Interdependence between detection and false alarm probabilities for ED of versatile OFDM signals detected with different sample quantities and for PU transmission at Tx power: (**a**) 0.1 \(W\); (**b**) 1 \(W\); (**c**) 10 W and (**d**) 15 W.  
energy at the location of the SU user which requires fewer samples to perform accurate PU detection.