## 5 Implementation of the Simulation Algorithm
For the same channel characteristics, the detection probability is equal to the versatile modulation techniques (QPSK, 64 QAM and 16 QAM). This is indicated as the m-PSK/m-QAM in figures presenting ROC curves. According to Figure 4, the higher number of Tx branches on the PU side and Rx branches on the SU side contributes to the improvement of ED efficiency. While the results presented in Figure 4 confirm the weak ED precision in SISO systems (which is no better than a random guess), in Figure 4, for the same operating environment communication system with one additional Tx and Rx branch (2 \(\times\) 2) contributes to the enhancement of ED precision. In Figure 5, even better results are shown for the asymmetric 2 \(\times\) 3 MIMO communication system, which yields the conclusion that an increase in the number of Rx antennas will, for the same radio environment, participate in contributing to the enhancement of the ED precision. Therefore, a larger number of Rx and Tx antennas on both the SU and PU sides has a beneficial influence on the ROC curves in terms of the improvement in the probability of detection for the same probability of false alarm in the MIMO-OFDM wireless system. Figure 4: The ROC curves for various NU and DDT factor combinations in (**a**) SISO and (**b**) 2 \(\times\) 2 MIMO-OFDM systems characterized by transmission with m-PSK/m-QAM modulation, \(N=128\), SNR \(=-15\) dB and \(\mathrm{P_{Tx}}=100\) mW. ### The Role of Various DDT Adaption Levels and NUI Fluctuations on the ED Sensing Efficiency

The effect of various levels of DDT adaptation and NU variation on the detection probability in the ED process is also shown in Figures 4 and 5. The performance of the ED process will be reduced when the NU variation increases for the same channel parameters and when no DDT adjustments are performed (\(\rho=1.05\), \(\rho^{\prime}=1.00\)). Where there is a continual adaptation of DDT in line with the NU changes (\(\rho=1.03\), \(\rho^{\prime}=1.05\) and \(\rho=1.05\), \(\rho^{\prime}=1.03\)), increased detection probability can be attained while maintaining the same value of false alarm probability (Figures 4 and 5). Furthermore, for higher DDT levels of adjustment and lower NU variations (\(\rho=1.03\), \(\rho^{\prime}=1.05\)), a higher detection probability will be obtained and vice versa (\(\rho=1.05\), \(\rho^{\prime}=1.03\)). The highest chance of detection is obtained when DDT adaptation occurs in the absence of NU variations (\(\rho=1.00\), \(\rho^{\prime}=1.03\)). However, this is not common in real-world wireless communication systems which are often characterized by noise power fluctuations. Hence, the results presented in Figures 4 and 5 reveal that the enhanced probability of detection for all modulation techniques can be achieved if the SS process is realized through DDT adaptation. The level of the DDT adjustment needs to be performed according to the level of NU variations. Thus, greater levels of NU variations must be followed with a larger range of possible DDT levels for adjustments and vice versa. The results presented in Figures 4 and 5 also reveal that the OFDM modulation type has no effect on detection probability regarding any false alarm probability. In the case where signals with different modulations (16 QAM, 64 QAM and QPSK) are generated independently, the detection probability is the same for every modulation type denoted as m-PSK/m-QAM. These results are confirmed mathematically with Equations (7), (9), (12), (14), (15), (17), (18) and (23), indicating that adjusting the modulation types in rate-adaptive OFDM communication systems characterized by a constant Tx power does not affect the probability of detection in the ED process. ### The Role of Various PU Transmit Power Levels on the ED Sensing Performance

The influence of the level of the PU TX power on the detection accuracy in the MIMO and SISO transmission systems is elaborated on in this subsection.