## 5 Implementation of the Simulation Algorithm
This is the result of the exploitation of a larger amount of Rx chains and the corresponding antennas at the SU side, which imposes a greater likelihood of detecting the PU signal for an equivalent value of false alarm probability. Because the ED is based on the SLC principle that combines the energy of the received signals at the Rx antennas, a higher number of Rx chains can process a greater number of PU signal streams. This contributes to the increase in the ED sensing capabilities (Figures 7 and 8). As a result, increasing the number of antennas participating in transmission on the PU and particularly SU side contributes to the enhancement of the sensing performance. Figure 7: The ROC curves for various NU and DDT factor combinations in asymmetric MIMO (2 \(\times\) 3 and 3 \(\times\) 2) systems for transmission characterized with QPSK modulation, \(N\) = 128, SNR = \(-15\) dB and \(\rm P_{Tx}\) = 100 mW. ### The Role of Various SNR Levels on the ED Sensing Efficiency

In this subsection, for the SISO and \(2\times 2\) MIMO communication systems, the results show the effect of SNR changes on the SU side on the shape of the ROC curves. The ROC curves were calculated for the communication system characterized by three characteristic SNR levels (\(-20\) dB, \(-15\) dB and \(-10\) dB) at the SU side, the continuous PU Tx power (100 mW), the QPSK modulation, the versatile NU fluctuation, and the DT adjustments levels (\(\rho=1.05\), \(\rho^{\prime}=1.03\); \(\rho=1.03,\rho^{\prime}=1.05\)). The results presented in Figure 9a,b indicate that greater SNR at the SU side increases the detection probability of the SISO and \(2\times 2\) MIMO systems. A higher SNR level (\(-10\) dB) at the SU side leads to a more precise PU signal recognition and a more efficient SS procedure. Furthermore, Figure 9a,b show the degradation of the detection performance at low SNR values, which confirms the strong influence of the SNR level at the SU side on the precision of the SS. Additionally, for the higher SNR levels (greater than \(-10\) dB), the results show that detection probability can be guaranteed (\(P_{d}=1\)) for any MIMO Tx-Rx chain combination. This is due to the high levels of SNRs which correspond to the appropriate signal intensities that ensure excellent PU signal recognition. Figure 8: The ROC curves for various NU and DDT factor combinations in SISO and symmetric MIMO systems for transmission characterized with QPSK modulation, \(N=128\), SNR \(=-15\) dB and \(\rm{P_{Tx}}=100\) mW. Figure 9: The ROC curves for various NU and DDT factor combinations and for different values of the SNRs (\(-20\), \(-15\), and \(-10\) dB) in (**a**) SISO and (**b**) \(2\times 2\) MIMO systems for transmission characterized with QPSK modulation, \(N=128\) and \(\rm{P_{Tx}}=100\) mW. Furthermore, Figure 9 shows that higher NU fluctuations (\(\rho\) = 1.05) reduce the recognition ability of the PU signal by the SU for identical SNRs at the SU antennas and false alarm probabilities. The detection performance can be increased for every SNR level by choosing an appropriate level of DT adaptation (\(\rho^{\prime}\) = 1.03 or \(\rho^{\prime}\) = 1.05). Figure 9 further shows that using the MIMO communication system instead of SISO in conjunction with greater SNR values on the SU side, significantly improves the detection performance. This is due to the possibility of detecting higher levels of PU signal through multiple Rx antenna chains of SU. ### The Role of Various Number of Detection Samples on the ED Sensing Efficiency

The role of a number of detection samples on ED efficiency in the 2 \(\times\) 2 MIMO and SISO systems was analysed in this subsection. The ED efficiency was analysed in simulated SISO and MIMO communication systems characterized by the PU transmission with a 100 mW constant Tx power and use of QPSK modulation, the SNR at the SU side equal to \(-\)15 dB, and various DDT and NU parameters.