## 5 Implementation of the Simulation Algorithm
This confirms that the PU occupies the licensed band (Figure 3). In contrast, if the received energy at the SU is lower or equal to the DDT, hypothesis \(H_{0}\) is correct and the PU is not transmitting which allows the SU to reuse the spectrum (Figure 3). Line 9 of the algorithm indicates that for each simulated case, 10,000 Monte-Carlo simulations were run to determine the probability of detection which is according to line 10 in the range [0, 1]. ## 6 Simulation Results and Analysis

This section describes the simulation software used to implement the ED using the SLC approach in the MIMO-OFDM transmission systems and the observations gained from the simulations. The SLC method investigates the performance of the ED process in the SISO, asymmetric and symmetric MIMO systems. The simulation was performed for simulation configuration based on one PU and one SU. Different NU (\(\rho\)) factor values illustrate the effect of the NU variations on the SS process. Additionally, versatile DDT factor values (\(\rho\prime\)) illustrate the effect of NU variations on the SS process. The results demonstrate how the amount of PU and SU communication chains, the amount of detection samples used during SS, the OFDM modulation types, the Tx powers of PU, and the versatile levels of DDT and NU factors affect the accuracy of the ED process expressed with ROC curves. ### Review of the Simulation Software and Parameters

The assessment of ED precision was performed using various operational parameters through simulations using the Matlab software. All parameters utilized in the assessment of the ED performance efficiency are listed in Table 2. The transmission of the PU signals was simulated using the QPSK, 16 QAM, and 64 QAM modulations, which represent the frequently applied modulation constellations in real MIMO-OFDM communication systems. Different numbers of detection samples during the SS equal to 128, 256 and 512 were used for the analysis of the ED performance (Table 2). The SNR values of the received signal at the SU used in the analyses were \(-20\) dB, \(-15\) dB, and \(-10\) dB. They represent typical operating SNR values in MIMO-OFDM communication systems. Furthermore, the false alarm and detection probability intervals based on which the ROC curves will be plotted are in the designated range [0, 1] (Table 2). Specific values for the NU and DDT factors were used to express the impact of variations in noise power and DT adaptation on the sensing performance. More precisely, the values of the factors expressing NU and DDT equal to 1.05 and 1.03 indicate a higher or lesser influence of NU fluctuations and DDT adaptations (Table 2) on the simulated ED process, respectively. As a compromise between simulation quality and simulation time, 10,000 Monte Carlo simulation runs per each case study were employed to get simulation results with an appropriate accuracy (Table 2). Such a large number of Monte Carlo simulations enables the repeating of ED performance tests. However, they can hardly be performed in real practical environments since 10,000 simulations performed for each of 69 case studies analysed in this work (690,000 in total) will be highly time-consuming if it will be performed in a real environment. Hence, Monte Carlo simulations represent an important approach to verifying the confidentiality of obtained results and are a valuable tool for numerical analyses of complex wireless systems [24]. These are the main reasons why practical experiments have not been performed and instead, in further sections we present results obtained through comprehensive Monte Carlo simulations. ### The Role of the Number of Tx-Rx Chains in the ED Sensing Efficiency

Figure 4 shows the ROC curves for various NU and DDT factor combinations in symmetric 2 \(\times\) 2 MIMO and SISO communication systems. The results of the simulations were derived using the same number of detection samples (128), an identical level of SNR (\(-15\) dB), and the same PU Tx power (100 mW).