## 4 Simulation
### Simulation Results
#### 4.2.1 Collision Probability Behavior According to Sampling and Reasoning Methods  
Here, the collision probability is similar to a sort of outage probability for the PU. However, it is not exactly the same because the collision probability in our paper is nothing but the result of counting the number of time slots where both PU and SU exist together without considering the values such as the signal-to-interference-plus-noise ratio (SINR) or the interference-to-noise ratio (I/N). Thus, even though there is a collision occurring at a certain time slot, the interference may not be harmful to the PU since the level of SINR or I/N is acceptable because those satisfy a priori prescribed requirements. This could possibly happen when the PU is located far from the SU or the SU is intentionally blocked by the clutter.  
In [8], the relationship between the channel availability and the success in channel use was realized by conducting real-world simulation in a testbed. According to the testbed result in [8], it could be confirmed that the success in channel use was becoming below 40% when the channel availability was less than 10%. From the testbed result, there was a significant event that the success in channel use became abruptly degraded when the channel availability dropped at a certain point. Similarly, in our paper, the relationship between \(P_{on}^{Avg}\) like the channel availability in [8] and the collision probability can be translated into the success in channel use in [8] observed in Figure 13, whose trend looks quite similar to that between the channel availability and the success in channel use in [8]. The only difference between the result in [8] and ours in Figure 13 is attributed to the domain, whether PU activity is considered in the temporal domain for the fixed channel or in the spectrum domain for the fixed time interval. Our result focuses on the temporal domain for a certain frequency channel, so that the collision probability is the number of time slots in which the PU and the SU coexist.  
Figure 13 shows the results of collision probability depicted for the purpose of comparison and is tightly associated with the PU traffic model in Figure 12. Along with the simulation test, the CB, RB, WCB, and WRB sampling methods in the learning engine and the rank-sum and prob-sum reasoning methods were each set to have 20 samples, a reasoning period of 20 slots, and a sampling interval of five slots. In the simulation test results in Figure 13, when the PU traffic model's channel occupancy  
Figure 12: Result of traffic model generation according to the average value of the channel occupancy probability of the PU.  
probability value \(P_{on}^{Avg}\) is low, there are many channels available because the occupancy probabilities are relatively low, and the collision probability becomes low for every sampling and reasoning method. Conversely, once \(P_{on}^{Avg}\) gradually increases, the PU traffic becomes dense, and naturally, the probability of a collision increases due to the frequent change in the PU's occupancy pattern.  
With the uniform sampling method, it seems that the PU traffic model results in a relatively low collision probability for \(P_{on}^{Avg}\) values of 0.1, 0.2, or 0.3. This implies that whenever the PU occupancy pattern is sparse, the uniform sampling method gives rise to candidate channels with high fidelity. For the other cases with the weighted sampling method, the collision probability is sustained at a low level compared to the uniform sampling case, even though the \(P_{on}^{Avg}\) values are 0.7, 0.8, or 0.9. This means that the weighted sampling method is superior to the uniform sampling approach in the aspect of the resulting low level of the collision probability whenever there is a continuous PU occupancy pattern.