## 7 Results of Simulations
### Influence of the False Alarm Probability on the ED Performance  
The last group of simulation results is dedicated to the explanation of the impact of the false alarm probability on the detection probability for versatile OFDM-based systems. The false alarm probability (\(P_{fa}\)) is defined (in Section 4.1) as the probability that the SU wrongly concludes that a PU is transmitting when the PU is not active. In the case that a real PU is present and the SU correctly estimates this, the possibility that the SU wrongly concludes that a PU is present starts to increase. This explains why the decrease in the false alarm probability (\(P_{fa}\)) is followed by a decrease in the detection probability (\(P_{d_{i}}\)) and vice versa (indicated in Figures 6-8, 9b, 11, 13 and 14). As mentioned in Section 5.2, performing the ED process based on satisfying the demand for some predefined value of the false alarm probability is the essence of the CFAR ED process. Although the false alarm probability must be as low as possible, in practice a false alarm probability of up to 20% can be tolerated and used. This motivates the selection of such a value in further analyses. In particular, the results of the analysis presented in Figure 16 were obtained for the three characteristic probabilities of false alarms (\(P_{fa_{i}}\)). From the practical point of view, they express low (1%), moderate (10%) and substantial (20%) false alarm probabilities. In Figure 16, for the RA system, the relationship among the detection probability and SNR has been presented with respect to the three values of false alarm probability. The results were obtained for an equal NU factor (\(\rho\) = 1.02), equal sample quantity (\(N\) = 128), and different DT factors (\(\rho\) \(t\) = 1.01, \(\rho\) \(t\) = 1.03). The obtained results showed that, for lower values of SNRs and probabilities of false alarm (1%), the detection probability will be lower and vice versa (Figure 16). As explained in Section 7.2, a low SNR results in a decrease in detection probability (Figures 6-8, 9b, 11, 13 and 14). However, for ED with a low level of PU signal energy in the position of SU, and for a decrease in the false alarm probability to the lowest values, a decrease in detection probability will be obtained (Figures 6-8, 9b, 11, 13 and 14). However, for ED with a higher DT factor (\(\rho\) \(t\) = 1.03), Figure 16 shows a higher detection probability for the same false alarm probability, SNR, and signals impac  
Figure 16: Detection probability vs SNR relationship for RA system with distinct false alarm probabilities and different combinations of NU and DT factors. further proves the importance of DT adaptations, which can improve the ED process for any value of demanded false alarm probability in the case of the CFAR ED approach. The impact of different SNRs on detection probability for combined MA and RA systems transmitting at distinct Tx powers is presented in Figure 17a-d. The results for each of the four simulations were obtained under equal NU variation (\(\rho=1.02\)), the same sample quantity (\(N=128\)), and DT factor (\(\rho=1.01\)). In Figure 17a-d, it can be seen that the combination of a higher Tx power and a higher false alarm probability increases the detection probability for any OFDM constellation. Nevertheless, it must be taken into account that the increase in false alarm probability raises the possibility of incorrect decisions by the SU in the ED process. For this reason, an appropriate trade-off between Tx power and maximal false alarm probability in case of the CFAR ED approach must take place. Additionally, Figure 17a-d show that the SNR threshold (known as the SNR wall) below which accurate PU signal detection is not feasible is influenced by the false alarm probability and PU Tx power. According to Figure 17a-d, the SNR threshold will be lower for signals transmitted with a larger Tx power (\(-5\) dBm for Tx power of 100 mW compared to \(-25\) dB for Tx power of 15 W) and detected by the lower (CFAR) setting of false alarm probability.