5.4 Performance Evaluation
5.4.2 Simulation Results
The performance of the proposed distributed user selection strategy is evaluated by Monte Carlo simulations (ITmax = 104). It is assumed that the maximum outage probabilityq = 1%for both distributed and centralized algorithms. We considered also that the radius of the secondary cell R = 1000 meters and the radius of the primary protection area Rp = 600 meters. The derivation of the maximum number of SUs allowed to transmit using the distributed algorithm is based on the average channel gainsGsuandGpuestimation. From the locations of the users in the two-dimensional plane and the propagation characteristics of the environment, we can estimate the two average channel gains for the downlink and the uplink mode. These values are estimated assuming a wireless ad hoc network affected by a large number of interferers. From simulation results, using M = 500 SUs and one PU, we findG2pu/G2su ' 15 in the downlink mode and G2pu/G2su '20in the uplink mode.
Figure 5.2 shows the behavior of the distributed strategy in comparison with the centralized one, presented in Section 4.7, for both downlink and uplink scenarios. This figure presents the number of active SUs versus the total number of SUs ranging between 1 user and a maximum of 140 users, and using different rate values (0.1,0.3and0.5bits/s/Hz). From this figure, it is clear that the distributed strategy always outperforms the centralized one. Generally, we found out that the distributed scheme presents almost 3 additional active SUs than the centralized scheme. This can be explained by the fact that, the number of active SUs in the centralized case is computed iteratively and in the distributed one, we know in advance the maximum number of active SUs (computed distributively) so, the algorithm is run until the maximum numberM˜theory is reached.
In fact, in the distributed case, we computeM˜theory distributively using the average channel gains Gsu andGpu and if this maximum number of active SUs is reached, all remaining SUs will be considered inactive. As explained in the first paragraph of this section, the two average gains are estimated using a large number of SUs and a number of iteration equal to 106 iterations.
These conditions give more flexibility for the distributed algorithm and we have in this case a broader concept. In the centralized case, however, the proposed algorithm in [76, 77] selects active SUs using an iterative strategy by computing in each iteration the outage probability knowing all channel gains for the selected SUs (active) until this iteration. The majority of classic algorithms derived in the literature do not use the same concept and select active SUs with an exhaustive manner among all SUs. In fact, in the first step of this centralized algorithm, all SUs are taken inactive (”off”) and in each iteration, SUmchecks its power and outage probability constraints. If the two constraints are verified, SUm will be switched ”on” and will be considered active during the next time slot. Here, the last SU entering in the system is removed from the transmission. We also remark from Figure 5.2 that the number of active users in the downlink always outperforms the uplink configuration. This can be explained by the fact that, as far as the downlink system is considered, the power received from BS isK times the power in the uplink. This results on better PU’s QoS guarantee. In fact, at a rate = 0.3bits/s/Hz, 12 SUs are allowed to transmit in the downlink and 7 SUs in the uplink, when we have saturation of the number of active SUs. We also remark that, asymptotically, i.e., as the number of SUs goes large, the number of active SUs keeps constant due to the influence of interference impairments on the PU’s QoS. This tends to confirm the intuition from formula (5.7) where the number of active SUs is always upper-bounded
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(a) Downlink : rate = 0.1bits/s/Hz (b) Uplink : rate = 0.1bits/s/Hz
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(c) Downlink : rate = 0.3bits/s/Hz (d) Uplink : rate = 0.3bits/s/Hz
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(e) Downlink : rate = 0.5bits/s/Hz (f) Uplink : rate = 0.5bits/s/Hz
FIGURE5.2 – Performance evaluation of the distributed user selection strategy in comparison with the centralized one : Number of active secondary users versus total number of secondary users for different rates (0.1,0.3and0.5bits/s/Hz) andq= 1%in the downlink and the uplink mode.
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0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
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(a) Downlink (b) Uplink
FIGURE5.3 – Performance evaluation of the distributed user selection strategy in comparison with the centralized one : Outage probability as function of the number of secondary users for a target outage probability = 1% and a rate = 0.3bits/s/Hz in the downlink and the uplink mode.
byM˜theory in the distributed case, and PU outage probability protection given by the maximum outageq.
In order to validate results in Figure 5.2 and the theoretical derivation given in Section 5.2, we compare the centralized outage probability expressed in (4.16) to the distributed one given in (6.15) usingM˜theory. As an example we carry out simulations for a rate = 0.3bits/s/Hz. First, it is shown from Figure 5.3 that the distributed algorithm guarantees a good protection for the PU as well as the centralized one. We also remark that, for the outage probability of interest (i.e., q = 1%), the number of allowed SUs to transmit is equal to 40 for the downlink and 22 for the uplink. This is exactly what Figures 5.3 (a) and (b) show, respectively, in the saturation state at a rate = 0.3bits/s/Hz. From the presented results, we verified that we can maintain a QoS guarantee to the PU. The question now, under the assumption that the PU outage probability is unaffected, what would be the cognitive system capacity presented by the sum SU’s capacity as expressed in (4.6).
Figure 5.4 (a) depicts the sum SU’s capacity in the case of the distributed strategy for both downlink and uplink, and usingR = 1000meters andRp = 600meters. As expected, it is found that the capacity of the uplink system outperforms that of downlink system. On the other side, increasing the number of SUs yields significantly increase in capacity because the increase in degree of freedom more than compensates for the decrease in SINR due to interference. Howe- ver, reaching a certain number of SUs, the sum SU’s capacity stabilizes. In addition, the current curve claims that in CRN, when one attempts to maximize the number of active SUs, the cognitive capacity degrades asymptotically. Typically, there is a fundamental trade-off between cognitive capacity maximization and number of active SUs maximization. We compute also the SU’s capa- city in the case of the centralized user selection strategy and we find practically the same results.
This confirms the very good matches between the distributed and the centralized method. Now, we change the size of the radius of the secondary cell and the primary protection area toR= 500me- ters andRp = 300meters, respectively. From Figures 5.4 (a) and (b), we remark that, as the radius RandRpdecrease, the sum SU’s capacity becomes more sensitive to the interference impairments leading to a significant decrease in the sum secondary rate.
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(a)R= 1000andRp= 600meters (b)R= 500andRp = 300meters FIGURE 5.4 – Performance evaluation of the distributed user selection strategy in term of sum secondary user’s capacity withq = 1% and a rate = 0.3bits/s/Hz in the downlink and the uplink mode using different radius of the secondary cell and primary protection area : (R= 1000meters, Rp = 600meters) and (R= 500meters,Rp= 300meters).