Figure 2.3: Upper bound on outage performance comparison between the proposed system and the existing PLNC system in terms of data rate
(+ sign indicates γloss=0 dB while• sign indicatesγloss=3 dB).
in performance. N = 2 and ηR = 40 dB are considered for this case. The data rate of PLNC is exceeded by the data rate of the proposed system by a value of 2. This is attributed to the extra bits which are required for antenna activation, which in our case is 1. The increment factor will be 2 since communication is full-duplex in nature. This can be illustrated with an example. For γloss=3 dB and outage probability value of 0.1, PLNC has a data rate of 3.2 bps while SM based DFTWR has a data rate of 5.2 bps.
For different SNR loss factors, γloss=0 dB, γloss=3 dB andγloss = 7dB, the lower bounds on outage probabilities are shown in Fig. 2.4. The target data rate is 3 bps and the SNR at relay node and source nodes are assumed to be equal. N = 2 is considered for this case. The SNR loss factor increment causes the system performance to degrade due to the enhancement in inter-antenna interference, as is evident from the graph. For example, for γloss = 0 dB and outage probability value of 0.01, SNR required is 26 dB while, for γloss = 3 dB, SNR required is 27 dB and for γloss = 7 dB, SNR required is 30 dB.
We can notice that outage probability value increases with an increment in SNR loss factor. As SNR loss factor increases, the relay is unable to decode message properly in the first time slot. Hence in the second time slot, the relay node is incapable of effective transmission of message to the source nodes. The performance of relay node in second time slot mainly governs the system performance, hence the overall performance is affected if relay node is unable to function properly due to presence of high amount of self-interference.
37 2.4. RESULTS AND DISCUSSION
SNR (dB)
0 10 20 30 40
Outage probability
10
-410
-310
-210
-110
0γ
loss=3 dB γ
loss=7 dB
γ
loss=0 dB
Figure 2.4: Lower bound of outage performance of the system with γloss=0 dB,γloss=3 dB andγloss=7 dB(Solid line represents analytical results while + sign indicates simulation results).
The lower bounds on outage probability are plotted for various channel parameters likeN,µ,κrgand α where the parameters have been defined earlier. The impact on lower bounds of outage probability by varyingN,µand α is depicted in Fig. 2.5, Fig. 2.6 and Fig. 2.7 respectively. Relative geometrical gain (κrg) also influences the system performance, as is illustrated in Fig. 2.8. All the nodes are assumed to have same SNR values, while γloss = 0 dB and r=1 values are considered for all the cases. For Fig.
2.5 the parameters are taken as data rate (Rd)=3 bps, α1=2, µ=1 and κrg=0 dB for all links. For Fig. 2.6, where variation of fading parameter (µ) is analyzed, the values are taken as Rd=3 bps, α1=2, N=2 and κrg=0 dB. For comparison of κrg values, the remaining parameters are taken as Rd=3 bps, µ=1, N=2 and α1=2. In Fig. 2.7, the parameters are Rd=3 bps, µ=1, κrg=0 dB and N=2. It can be noticed from Fig. 2.5 that with an increment in the value of number of cascaded components (N), there is an increment in lower bound on outage probability value resulting in degradation of system performance. This is attributed to the fact that increment of N factor results in more fading. The system performance is improved by an increment inµvalue as illustrated in Fig. 2.6. Increment in value ofα1 also improves the system performance, as can be visualized in Fig. 2.7. Impact of variation in relay position is illustrated in Fig. 2.8. From the graph it is evident that κrg=0 dB provides the optimum performance. κrg is varied between 0 dB to 30 dB with increments of 10 dB i.e. relay is brought much closer to MS1. Performance gradually worsens with increase in κrg value. This is because as the relay node is brought closer to MS1, it is not able to receive message properly from MS2 leading to degradation
2.4. RESULTS AND DISCUSSION 38
SNR (dB)
0 5 10 15 20 25 30
Outage probability
10
-310
-210
-110
0N=2 N=3
N=4
Figure 2.5: The impact of N on lower bound of outage performance
(Solid line represents analytical results while∗ sign indicates simulation results).
of system performance. From the results, it can be inferred that the system can yield good performance even when the number of multipath clusters and non-linearity factor are quite high. This validates that the channel model used is suitable for such communication in a high scattering environment. It is to be noted that asymptotic analysis has been included in Fig. 2.6 and 2.7. The asymptotic values in both the figures for different values ofµandα1 converge to the analytical and simulation results at higher values of SNR, thereby validating our analysis. The asymptotic analysis can be obtained in a similar manner for other graphs also, but has not been included to avoid the graphs from getting too clumsy.
The outage probability lower bound is compared for different values of data rates in Fig. 2.9. The values are taken asα1=2,N=2,κrg=0 dB,ηR= 40dB,γloss= 0dB andµ=1 for all links. As the target data rate value increases, the system performance worsens with the increment in outage probability value.
This is due to the fact that it is difficult to achieve higher target data rates and may cause more errors.
The influence of different number of antennas at source and relay node is explored in Fig. 2.10. It is to be noted that number of antenna at any node can only be a power of 2 for SM. Five configurations of antenna are considered in this figure. It is evident that when the equal number of antennas is increased from 2 to 4 and 8, the system performance degrades. This is due to the fact that more antenna gives rise to more interference thereby causing poorer performance. It is also noted that when number of antennas at source node are 4 and only 2 antennas are present at the relay node, then the system performance is almost similar to that of a system having 2 antennas at all the source nodes. Again it can be observed that the performance of a system having 4 antennas at the relay node and 2 antennas at each source
39 2.4. RESULTS AND DISCUSSION
SNR (dB)
0 5 10 15 20
Outage probability
10-6 10-5 10-4 10-3 10-2 10-1 100
µ=1 µ=2
µ=3
Figure 2.6: The impact of fading factor µon lower bound of outage performance
(Solid line represents analytical results, ∗ sign indicates simulation results and dashed line represents asymptotic results).
SNR (dB)
0 5 10 15 20 25 30
Outage probability
10
-410
-310
-210
-110
0α
1=3
α
1=2 α
1=1
Figure 2.7: The effect of α1 on lower bound of outage performance
(Solid line represents analytical results, ∗ sign indicates simulation results and dashed line represents asymptotic results).
node, is similar to that of a system having 4 antennas at each of the 3 nodes. From this it can be inferred that the number of antennas at the relay node basically governs the system performance. This is because in the second stage of the two stage operation, the relay node transmits message. Therefore relay can
2.4. RESULTS AND DISCUSSION 40