## 4 Simulation
### Simulation Results
#### 4.2.2 Collision Probability Behavior According to Reasoning Period for a Fixed Number of Samples  
The simulation results in Figure 14 show the collision probability when the number of samples and the sampling interval are fixed at 20 samples and five slots, respectively, and the reasoning period is enforced to be changed from five to 40 slots. The reasoning period is a critical parameter, where the probability of PU occupancy is calculated and the available channels are determined. To adapt the dynamic PU activity, it is clear that the reasoning period should be adjusted with the help of acquiring current PU occupancy status. Assuming that the channel used for the next reasoning period is determined by conducting a series of the ordering and ranking method proposed in our paper, it can exploit the relationship between the reasoning period and the collision probability shown in Figure 14. Conceptually, for the sake of selecting an appropriate reasoning period, the result as in Figure 14 can be utilized as a referenced guideline subject to obeying the prescribed requirement such as the collision probability. Figure 13: Comparison of collision probability for each sampling method according to changes in the traffic (reasoning period = 20 slots, number of samples = 20 slots, sample interval = 5 slots). In Figure 14, it is evident that the PU collision probability increases as the reasoning period becomes longer for a fixed number of samples taken using the same sampling interval. This means that a highly reliable policy can be established if the reasoning period becomes as short as possible. If the required collision probability level is set to 25%, this implies that the reasoning period must be 25 slots or less. 4.2.3 Collision Probability Behavior According to the Number of Samples for a Fixed Reasoning Period  
In general, the collision probability between the primary user and the CR node user is directly related to the activity of PU's channel occupancy. In other words, if the activity of PU's channel occupation increases, the probability of collision is increased, as shown in Figure 15. Furthermore, it can also be stated that the probability of collision increases as the averaged occupancy probability per PU rises. Therefore, the relevant comparison of the collision probabilities as the indicator for the CR engine proposed in this paper is considered to be reasonable provided that the parameters for verifying the learning engine and the reasoning engine are consistent under the same environment of PU channel occupation. Note that in the field test of the XG project, the target success rate was confined to 60%, which reads 40% of the failure rate in channel use between the CR node and the primary user [8]. Surely, it is critical which value should be determined for the number of samples in order to estimate the value of the probability of PU occupancy accurately. However, due to the dynamic characteristic of PU occupancy, depending on how many samples are used, the collision probability could be altered. Thus, it could not be said that the longer depth of samples is always best for every situation. In other words, once the PU traffic pattern is apprehended by conducting histogram shape matching, referring to the result, an appropriate number of samples should be explored. Accordingly, Figure 15 delivers the meaning of this effect, which resulted from executing the exhaustive work, and it can be clarified that the number of samples can be determined by selecting the value at the point where the corresponding collision probability is the lowest. The simulation test results in Figure 15  
Figure 14: Comparison of collision probability according to reasoning period (number of samples = 20 slots, sample interval = 5 slots). show the collision probability when the reasoning period and the sampling interval are fixed to 20 slots and five slots, respectively, and the number of samples is changed from five to 45.