## 7 Results of Simulations
### Influence of DT Adaptation on Performance of ED  
The results of the first study presented in Figure 6 show the influence of the DT adaptation on the ED process in RA systems. The results were obtained for a constant Tx power (1 W) of PU, and distinct levels of DT (\(\rho\) /) and NU factors (\(\rho\)). Different NU factors express the influence of the intensity of AWGN variations on the ED of OFDM signals. Additionally, different DT factors represent a versatile level of threshold adaptation capabilities during the ED process. Figure 6 presents the results obtained as ROC curves for the distinct constellations of m-PSK/m-QAM modulations at the location of SU. The results presented in Figure 6 were also obtained for two SNR values (\(-5\) dB, \(-20\) dB) and the unchangeable number of OFDM samples (\(N=128\)). These conditions are typical of real, practical implementations in which ED performance is challenged by different SNRs in the position of SU. The obtained results presented in Figure 6 show that the detection probability (\(P_{d_{i}}\)) is equal for any m-QAM or m-PSK modulation. Hence for any such systems transmitting with a constant Tx power (RA systems), the detection probability does not depend on the mod  
Figure 6: Interdependence between probabilities of detection and false alarm for ED of signals in RA systems, versatile combinations of NU and DT factors, and two distinct SNR levels. consequence of the nature of the PU transmission in the case of RA systems, which is based on the dynamic adjustment of the modulation order while transmitting at the same Tx power. For this reason, the signal energy detected at the location of the SU during the ED in RA systems can only be affected by noise fluctuation. This supports the results presented in Figure 6 showing that, for the same sample quantity, SNR in the position of SU, and the Tx power of PU, the detection probability will be lower for higher noise variations (higher NU factor \(\rho\)). Although in RA systems the adjustment of modulation order during ED does not have any effect on the PU signal detection probability, it can be seen from Figure 6 that DT adjustment can improve ED performance. More specifically, in the case of ED without NU variations and with DT adaptation (\(\rho=1.00\), \(\rho^{\prime}=1.03\)), the detection probability will be the highest for any modulation scheme (Figure 6). However, this scenario is, from a practical point of view, the least realistic. According to Figure 6, the lowest detection probability was obtained for the simulation scenario with significant noise variations (\(\rho=1.05\)), but without DT adaptation (\(\rho^{\prime}=1.00\)). This is expected since the ED of signals impacted by NU and without DT adaptation during the ED process significantly reduces the detection probability. Hence, the improvement of the detection probability in the case of increased NU variations for all modulation schemes (Figure 7) can be expected only if ED is based on DT adaptation (\(\rho^{\prime}>1\)). In Figure 7, the results of the analyses dedicated to the influence of DT adaptation on ED of PU signals in combined MA and RA systems are presented. The results were obtained  
Figure 7: Interdependence between detection and false alarm probabilities for ED of signals in combined RA and MA system under versatile combination of NU and DT factors and PU transmission using: (**a**) QPSK modulation at Tx power of 0.1 W; (**b**) 16 QAM modulation at Tx power of 1 W; (**c**) 64 QAM modulation at Tx power of 10 W and (**d**) 256 QAM modulation at Tx power of 15 W.  
for a fixed SNR (min. \(-15\) dB) at the location of SU, a constant sample quantity (\(N=128\)), and for the four most commonly used OFDM modulations: QPSK and \(16/64/256\)-QAM. The simulation results are presented in Figure 7 as ROC curves for distinct NU levels and DT factors, and the different PU Tx powers and corresponding modulations.