## 4 Numerical Results and Discussion
Importantly, the result validates that it is necessary to consider the optimal number of channels subject to the considered network and sensing parameters in order to achieve the optimal sum utilization performance. Figure 5: Sum utilization of spectrum for single- and multiple-channel scenarios under the topology-1 model. Figure 6: Sum utilization of spectrum for single- and multiple-channel scenarios under the topology-2 model. the spectrum utilization performance for the PU is considered to be the same because of the fixed targeted detection probability. However, longer PU mean inactive durations cause more spectrum utilization opportunities for the SU, and hence the probability of sum utilization of spectrum increases. It can also be observed that the increase in the sum utilization of spectrum with the PU mean inactive durations is dominant when the SU uses the channel more actively. However, the performance of the sum utilization of spectrum converges when the PU uses the channel more actively. The reason is that the SU's utilization of spectrum is at a minimum when PU uses the channel more actively, and the PU mean inactive durations only affect the utilization performance of the SU. The results validated that it is important to identify the range of PU states probabilities subject to the targeted detection probability and PU states mean durations to achieve the required sum utilization performance. Figure 8: Probability of sum utilization of spectrum with different PU states mean durations for single- and multi-channel scenarios under topology-2. Figure 9: Probability of sum utilization of spectrum with different PU active state probabilities for single-channel scenarios under topology-1. Figures 11 and 12 show the probability of sum utilization of spectrum with different PU active state probabilities for single- and multiple-channel scenarios under topology-1 and topology-2, respectively. In the multi-channel scenario, two narrowband channels are considered, and the utilization probability over the two channels is summed. As explained previously, the number of transmitted bits are fixed for the first channel. Moreover, the number of transmitted bits in the second channel is adjusted as per the available transmission duration, and the weighting factor is added to consider the utilization as per the transmitted number of bits. It can be seen in Figures 11 and 12 that for a given PU mean inactive duration, the sum utilization of spectrum for the multi-channel scenario also increases when the PU uses the channel more actively. The reason is the same, as the PU contributes more to the overall sum utilization of spectrum because of the targeted detection probability. The performance improvement for the multi-channel scenario is achieved for any model of channel status, i.e., different PU states probabilities. The reason is that the handoff probability is considered to be the same for any PU channel status. Hence, the transmission of a packet in the next channel for each PU interruption is considered, and the sum utilization gain is achieved. Figure 11: Probability of sum utilization of spectrum with different PU active state probabilities for single- and multiple-channel scenarios under topology-1. Figure 10: Probability of sum utilization of spectrum with different PU active state probabilities for single-channel scenarios under topology-2.