## 5 Implementation of the Simulation Algorithm
The results of the simulations were obtained for the radio environment where SS was performed for a constant SNR value at the SU antenna (\(-15\) dB), the PU transmission using QPSK modulation, the fixed number of detection samples (128), and the different NU and DDT factor values. Figure 5: The ROC curves for various NU and DDT factor combinations in asymmetric \(2\times 3\) MIMO systems characterized by transmission with m-PSK/m-QAM modulation, \(N=128\), \(\text{SNR}=-15\) dB and \(\text{P}_{\text{Tx}}=100\) mW. Figure 6 shows the results obtained in the form of ROC curves for the two PU Tx power levels of 10 W and 100 mW and the ED performed in the 2 \(\times\) 2 MIMO and SISO systems. Based on the results presented in Figure 6, the transmission of PU signals at a higher Tx power yields a higher detection probability for a given false alarm probability. These results are predictable since the PU transmission at a higher Tx power eventually results in larger energy for the signal received by the SU Rx chains. However, the OFDM signals transmitted over more Tx and received over more Rx antennas (e.g., for 2 \(\times\) 2 MIMO systems compared to SISO systems) and at a greater Tx power level (e.g., at 10 W compared to 100 mW) can significantly contribute to the amendment of the probability of detection (Figure 6). In Figure 6, the obtained results show that the combination of higher PU Tx power and the number of Tx-Rx antennas at the PU and SU, significantly contributes to the improvement of the ROC curve shape with respect of achieving better probabilities of detection for the same false alarm probabilities. Thus, the performance of ED can be boosted with an enlargement in PU Tx power and through the MIMO transmission, where a larger number of Rx and Tx branches participating in the MIMO transmission represents a more favourable option. Figure 6: The ROC curves for various levels of NU and DDT factors in (**a**) SISO systems with the PU transmitting at 100 mW, (**b**) SISO systems with the PU transmitting at 10 W, (**c**) 2 \(\times\) 2 MIMO systems with the PU transmitting at 100 mW, and (**d**) 2 \(\times\) 2 MIMO system with the PU transmitting at 10 W and for transmission characterized with QPSK modulation, \(N\) = 128 and SNR = \(-\)15 dB. The Role of Different Numbers of Asymmetric and Symmetric MIMO Transmission Branches in the ED Sensing Efficiency

This subsection focuses on the analysis of the effect of the number of SU Rx and PU Tx antennas on the ED efficacy in SISO and asymmetric/symmetric MIMO wireless systems. For the acquired results of the simulations, analyses were performed involving the QPSK-modulated PU signals, the constant number of samples (128), the SNR equal to \(-15\) dB at the SU site, and the constant PU Tx power (100 mW). The results of simulations in the form of ROC curves obtained for transmission in the asymmetric 2 \(\times\) 3 and 3 \(\times\) 2 MIMO communication systems performing ED are presented in Figure 7. The obtained results indicate that asymmetric MIMO systems having a number of Rx antenna chains (\(N\)) that is for one higher than the number (\(N\)) of Tx antenna chains, achieve better results in terms of their ED accuracy in comparison with the systems having a reversed amount of Rx and Tx chains. As the number of SU Rx chains increases, the detection efficiency also increases due to the larger number of Tx antennas and corresponding chains. This can contribute to the higher signal energy detection through SLC at the SU side. More accurate sensing performance and lower false alarm rates are therefore provided for the asymmetric 2 \(\times\) 3 MIMO systems compared to the 3 \(\times\) 2 MIMO systems. Additionally, as illustrated in Figure 8, the results of the simulations in the form of ROC curves for the MIMO systems and SISO systems were presented. The obtained results reveal that the asymmetric 4 \(\times\) 4 MIMO system outperforms the SISO and 2 \(\times\) 2 MIMO-OFDM systems in terms of its detection accuracy.