Performance Evaluation
4.2 Simulation Results
4.2.2 Performance Validation and Comparison under Paired CR Networks
4.2.2.1 Characterization of Channel-Hopping Probability for a Single Chan-nel
In this section, the channel-hopping probability will be characterized for the single channel case under the paired CR networks. Figs. 4.2(a) and 4.2(b) illustrate the throughput performance of CRPs and the average frame delay of the PU over different values of hopping probability pi, respectively. There are total of N = 14 CRPs with sensing thresholds pd = 0.93 and 0.95 under PU’s arrival rate λi = 0.05, 0.2, and 0.4.
As shown in Fig. 4.2(a), the throughput performance will first increase with pi due to the augmented number of CRPs that enlarges the channel utilization. However, the throughput of CRPs decreases with larger pi values owing to the insufficient channel availability. Comparing the two values of pd, the case with pd = 0.95 will result in
0 0.2 0.4 0.6 0.8 1
(a) Throughput vs channel-hopping probability.
0 0.2 0.4 0.6 0.8 1
(b) Average frame delay vs channel-hopping proba-bility.
Figure 4.2: Performance of CRPs for a single channel with pd= 0.93 (dashed line) and pd = 0.95 (solid line) under PU’s arrival rate λi = 0.05, 0.2, and 0.4 denoted by ◦, M, and ¤ curves, respectively.
enhanced throughput under larger value of pi since there will exist additional CRPs to utilize the channels. On the other hand, with smaller value of pi, smaller pd = 0.93 results in smaller pf a which can allow the CRPs to quickly discover the idle slots and consequently increase the channel utilization.
Fig. 4.2(b) shows that the average frame delay is an increasing function of pi which can become significantly large with increased value of pi, i.e., the primary queue can go unstable especially for large PU’s arrival probability λi and small sensing threshold pd. It can be explained that with the larger pi indicates that more CRPs will hop into the ith channel according to HN,n,i as shown in (2.3). Therefore, the transmitted frames from those CRPs will produce more collisions with the PU’s frame which makes the increased time in retransmission and therein the larger average frame delay in the primary network. With smaller detection probability pd, more collisions from the CRPs to the PU can be observed. Furthermore, with larger value of λi, it is intuitive that the long waiting line in the queue will also increase the average frame delay.
4.2.2.2 Performance Validation and Comparison
Two conventional channel-hopping sequences are simulated for comparison purpose as follows: (a) uniform channel-hopping sequence (UCS) with the probability pi = 1/M for i = 1, 2, ..., M , and (b) proportional hopping sequence (PCS) with channel-hopping probabilities proportioning to the complement of λi/µ, where µ represents the service rate. The PCS scheme is designed according to the situation that smaller frame arrival probability is assumed to result in larger channel availability, which can be written as
pi = 1 −λµi PM
i=1(1 −λµi), i = 1, 2, ..., M. (4.1)
0 5 10 15 20 25 30 35 40 45
(a) Aggregate throughput vs number of CRPs.
0 5 10 15 20 25 30 35 40 45
(b) Aggregate frame delay vs number of CRPs.
Figure 4.3: Performance Comparison under pd = 0.93 and number of channels M = 4 with PU’s arrival rate at each channel as λi = 0.05, 0.05, 0.4, 0.4 for i = 1, 2, 3, 4.
It is noted that the service rate is selected as µ = 1 frame/slot which is the stationary idle probability under no collision between the CR and primary network. For validation purpose, it can be seen from both Figs. 4.3(a) and 4.3(b) that the simulation results can match with the analytical results for all the three approaches. Fig. 4.3(a) shows that the proposed OCS can provide higher aggregate throughput compared to the other channel-hopping sequences since it can exactly exploit the potential throughput in multiple channels. It is interesting to note that the aggregate throughput in OCS will saturate after exceeding a certain number of CRPs while the number of the CRPs is large enough to utilize each channel with optimal throughput. In general, the design concept arises from assigning additional CRPs into the virtual channel in order to reduce collision with the PU.
On the other hand, as show in Fig. 4.3(b), the aggregate frame delay of primary network can also be guaranteed by adopting the proposed OCS approach. As a result, even though the delay constraints is not taken into consideration, the OCS still can ensure the QoS requirement of the PUs to a certain level. In order to provide tighter QoS requirement for the PUs, the case with constraints Dc,i = 2 for i = 1, 2, 3, 4 are also shown in both Figs. 4.3(a) and 4.3(b). The effect with delay constraint Dc,i = 2 can be observed with lowered aggregate frame delay of PUs and consequently lowered aggregated throughput of CRPs. With different sensing thresholds pd, the large pd will have enhanced aggregate throughput than the small pd case since the number of CRPs is large enough to exploit channel availability. On the other hand, smaller pd results in smaller pf a which can provide the CRP to quickly discover the idle slots and consequently increase the channel utilization over the large pd which blocks the CRPs’
access into the channel which makes the channel utilization in (2.17) down when the number of CRPs is small.
Furthermore, in Fig. 4.3(a), the aggregate throughput of PCS is better than UCS
first, which can be explained that PCS puts more CRUs into good channels (i.e., with lower arrival probabilities) than UCS, but when too many CRUs are in the good chan-nels, the aggregate throughput will degrade more quickly than UCS due to too much collision in the good channels. On the other hand, in Fig. 4.3(b), UCS will make the primary system unstable quickly due to too much CRUs allocated to the bad channels (i.e., with large arrival probabilities) at first. As a result, the merits of adopting the OCS approach under the paired CR networks can be observed.