## 3 Cognitive Radio Engine Platform Usage Scenario
### Available Channel Extraction Method via Conducting the Reasoning Engine
#### 3.4.2 Extracting Available Channel Candidates from Reasoning Results  
To exploit the group of available channels for allocation to the cognitive radio nodes, a sequence is first arranged of the PU occupancy probabilities in ascending order, and the ranking of all the channels is decided. This study examined the performance related to the PU collision probability by applying individual sampling methods, including uniform sampling methods (CB and RB) and weighted sampling methods (WCB and WRB), together with rank-sum and prob-sum reasoning methods. In this case, collision probability refers to the probability of the event in which the cognitive radio node incorrectly uses a channel that is already occupied by the PU.  
To this end, the \(j\)th channel is ranked as \(R_{CB}(j)\), \(R_{RB}(j)\), \(R_{WCB}(j)\), and \(R_{WRB}(j)\), which result from the action of the cognition engine followed by the learning engine, and \(R\) is an integer that obeys \(1\leq R\leq N\). For example, the rank of channel \(j\) calculated by executing the CB sampling method is shown in Equation (14) [18]:  
\[R_{CB}\left(j\right)=rank\left(P_{CB}^{j}\right)\,. \tag{14}\]  
Here, the \(rank()\) function is used to decide the ranking of every channel by assessing the occupancy probability, which is calculated and sorted in the learning engine. The range of the rank is shown in Equation (15) and is the same as the overall number of channels based on the following:  
\[Range\left\{R_{CB}\left(1\right),\ldots,R_{CB}\left(N\right)\right\}=N\,. \tag{15}\]  
Furthermore, Equation (16) realizes the proposed rank-sum reasoning approach, which aggregates ranks derived from the execution of each sampling method. As a result, based on this method, the channel with the minimum rank sum is regarded as a candidate channel. This paper denotes this approach as the rank-sum reasoning method, with the relevant formulation given as:  
\[R_{Rank-sum}\left(j\right)=R_{CB}\left(j\right)+R_{RB}\left(j\right)+R_{WCB} \left(j\right)+R_{WRB}\left(j\right)\,. \tag{16}\]  
Besides this, Equation (17) defines the prob-sum reasoning method that specifies the candidate channel by sorting the sum of the occupancy probabilities resulting from each sampling method in ascending order, given by:  
\[R_{Prob-sum}(j)=P_{CB}(j)+P_{RB}(j)+P_{WCB}(j)+P_{WRB}(j)\,. \tag{17}\]  
Similar to the rank-sum reasoning method, the channel with the minimum probability sum is designated as a candidate channel. In the following, Table 4 shows the PU occupancy probabilities represented in percent, which is quantified by adopting the individual sampling method. The rank-sum and prob-sum methods give rise to the composite ranking referred to as CB, RB, WCB, and WRB.  
As shown in Table 4, the reasoning method proposed in this paper for determining candidate channels using prob-sum does not select the channel with the lowest PU occupancy probability for a specific sampling approach, but selects a reliable candidate channel, which is the most competitive channel with respect to either the composite ranking or the aggregated occupancy probability. Moreover, another critical point is how many reliable channels are determined to clarify this; a guideline can be recommended based on the PU reference traffic model containing relevant information corresponding to the traffic-matched subject for minimizing the collision probability.