Performance Comparisons without Data Traffic

Next, we compare the performance of SYN, SSCH, L-QCH, RRICH and CACH for various performance metrics, including the average number of co-channel SUs (for a particular SU per time interval), the average number of used channels (per time interval), and the average TTR. In order to see the effects (and the insights) of these rendezvous algorithms, we do this without introducing data traffic, i.e., no data flows.

(a) Effect of the number of SUs on the average number of co-channel SUs.

(b) Effect of the number of SUs on the average number of used channels.

Figure 2.4 Effects of the number of channels on the average number of co-channel SUs and the average number of used channels.

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We first consider the case where six SUs are distributed randomly in a 380mx380m region. Also, the SUs do not change their CH parameters. In this simulation, there are 13 channels and each channel is associated with a PU. The mean OFF period of a PU is set to 10s. The mean of ON periods is set to 10s with probability 1/5 and is set to 30s with probability 4/5. In Fig. 2.4(a), we show the effect of the number of SUs on the average number of co-channel SUs (for a particular SU). A co-channel SU for a particular SU in a particular time interval is an SU that operates on the same channel as that SU in the time interval. To measure this, we choose an arbitrary SU and take the average of the number of co-channel SUs over time. Clearly, the larger the average number of co-channel SUs is, the larger the co-channel interference is. As such, a large average number of co-channel SUs might suffer from the problem of control channel saturation. It can be seen from Fig. 2.4(a) that both RRICH and SSCH have the same average number of co-channel SUs. When the number of SUs is larger than 11, CACH is reduced to RRICH as the number of logical channels is upper bounded by the number of channels. Also, the average number of co-channel SUs for L-QCH is larger than those of RRICH, CACH, and SSCH. Such a result is expected as the system load of L-QCH is larger than the system loads of RRICH, CACH, and SSCH. Since the system load of SYN is 1, the average number of co-channel SUs for SYN increases linearly with respect to the number of SUs. On the other hand, the average numbers of co-channel SUs for RRICH, CACH, SSCH, and L-QCH only increase slowly with respect to the increase of the number of SUs. In Fig. 2.4(b), we further show the effect of the number of SUs on the average number of used channels in a time interval. A channel is said to be used in a time interval if there is (at least) one SU that operates that channel as the control channel in that time interval. To measure this, we count the number of used channels in every time interval and then take its average. Intuitively, a rendezvous algorithm that has a large average number

of used channels tends to distribute its traffic evenly over the channels. It is observed that RRICH, CACH and SSCH have same average number of used channels when the number of SUs is larger than 11. When the number of SUs is only 6, the average number of used channels for RRICH is larger than that of CACH because the system load in CACH is larger than that of RRICH. Also, the average number of used channels for CACH is better than L-QCH, even when the number of SUs is 6. This is because L-QCH only distributes the control traffic over the time (but not over the channels).

In Fig. 2.5(a), we show the effect of the number of channel on the average TTR.

Since SYN allows all SUs to hop to the same channel, it has the lowest average TTR.

Since the worst case TTRs of CACH and L-QCH are independent of the number of (a) Effect of the number of channels on average TTR.

(b) Effect of the PU behavior on the average TTR.

Figure 2.5 Effects of the number of channels and PU behavior on the average TTR.

channels, their average TTRs are also not influenced by the number of channels.

However, the worst case TTRs of RRICH and SSCH depend on the number of channels, and the average TTRs of RRICH and SSCH increases when the number of channels increases. Moreover, since the degree of overlapping of RRICH is N, RRICH has a lower average TTR than SSCH (as SSCH suffers from the PU long-time blocking problem). In Fig. 2.5(b), we measure the effect of the mean ON period (of a PU) on the average TTR. When the mean ON period of each PU is set to 10s, RRICH and SSCH have the same average TTR. However, when the mean of the ON period is increased, the average TTR of SSCH is increased rapidly due to the long-time PU blocking problem. The other channel hopping schemes do not increase their average TTRs quickly because their degree of overlapping are equal to N and then they are immune to the long-time PU blocking problem. In view of Fig. 2.5(a) and Fig. 2.5(b), we note that L-QCH has a lower average TTR than that of CACH.

This is because that L-QCH has a heavier system load than CACH. On the other hand, CACH have a smaller number of co-channel SUs and a larger number of used channels than those of L-QCH.