The second proposed relay selection rule is termed the “bottleneck SNR” approach.
In this approach, we aim to simplify the computation complexity of the throughput-optimal approach. We choose the first relay as in the single relay case. Then we select the second and third relay as follows:
i2 = arg
∀j max{min{SNRs−rj, SNRrj−d}}, j ∈ {decoded node index}, j /∈ {i1} . (4.3) If there are multiple nodes in the decoded set with the maximal throughput, we choose the one with the maximal SNR in the link to the destination as the relay node. The third relay is chosen by:
i3 = arg
∀j max{min{SNRs−rj, SNRrj−d}}, j ∈ {decoded node index}, j /∈ {i1, i2} . (4.4) More relays are chosen in the same manner.
4.3 Numerical Results
In this section, we examine the outage probability and the throughput performance of the proposed relay selection rules and two more relay selection method in the multi-relay case. We consider seven modulation coding schemes (MCSs)in the IEEE 802.16 standard. Table. 3.1 lists the required SINR and net data rate for the seven MCSs [24]. We estimate system capacity with 10% frame error rate
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4.3.1 Outage Probability and Throughput Performance of Relay Selection Rules for Multi-Relay, Best Pair Case
−5 0 5 10
Figure 4.1: Outage Probability comparison for various relay selection rules with mul-tiple relays in the best-pair case.
Fig. 4.1 shows the outage probability of various relay selection rules with mul-tiple relays in the best-pair case. For the throughput-optimal approach, more relay nodes ,poorer the outage probability. For the throughput-optimal approach with 2 relays, at Poutage = 10−2 it needs more 2.57 dBW than the signal-based approach, higher than 2.4 dBW with single relay. This is due to more power consumption and higher chance to choose nodes close to the source. For the bottleneck SNR approach,
−150 −10 −5 0 5 10
Figure 4.2: Throughput comparison for various relay selection rules with multiple relays in the best-pair case for the throughput-optimal approach.
the trends are the same. More nodes, poorer the outage probability. For throughput-optimal approach with 2 relays, at Poutage = 10−2 it needs more 1.57 dBW than the signal-based approach, higher than 0.96 dBW with single relay. The reason is the same as the throughput-optimal approach, there is more chances to choose relay nodes far away from the destination and more relay nodes consume more power.
Fig. 4.2 reveals that the throughput of various relay selection schemes, espe-cially for the throughput-optimal approach with multiple relays in the best-pair case.
We can see that for the throughput-optimal approach, more relay nodes, poorer the throughput. For throughput-optimal approach with 2 nodes, in the considered
con-28
−150 −10 −5 0 5 10
Figure 4.3: Throughput comparison for various relay selection rules with multiple relays in the best-pair case for the bottleneck SNR approach.
sumed power range the average throughput is 4.99 Mbps, lower than 5.18 Mbps in the single relay case. At Pav=6.5 dBW the throughput achieves 161% higher than that of the signal-based approach, lower than that with single relay 165%. This is due to more power consumption from more relays and contributed form more chances to choose relay nodes close to the source or the destination. If a relay node is close to the source or to the destination, then one side of the relay node has a low link throughput. Hence, the overall link throughput is limited.
Fig. 4.3 shows the throughput of various relay selection rules, especially for the bottleneck SNR approach with multiple relays in the best-pair case. For the
bot-tleneck SNR approach, more relay nodes, lower the throughput. For botbot-tleneck SNR approach with 2 nodes, in the considered consumed power range the average through-put is 4.99 Mbps, lower than 5.15 Mbps in the single relay case. At Pav=6.5 dBW the throughput achieves 161% higher than that of the signal-based approach, lower than that with single relay 165%. This is contributed from more power consumption by more relay nodes and due to higher chances to choose relay nodes close to the source or the destination, then one side of the relay node has a poor link throughput.
Therefore, the total link throughput is limited.
From the above three figures, we realize the trend of the outage probability and the throughput for the proposed relay selection rules with multiple relays in the best pair case. We find that as deploying more relay nodes, at the same consumed power level the reliability and throughput performance degrades with the number of relays.
this is due to more power consumption and more chances to choose inappropriate relay nodes.
4.3.2 Outage Probability and Throughput Performance of Relay Selection Rules for Multi-relay, Worst-Pair case
Fig. 4.4 shows the outage probability of various relay selection rules for the multi-relay, worst pair case. For throughput-optimal approach with 2 relays, at Poutage = 10−2 it needs more 4.8 dBW than the signal-based approach, higher than 4.7 dBW in the single relay case. For bottleneck SNR approach with 2 relays, at Poutage = 10−2 it needs more 3.1 dBW than the signal-based approach, higher than 2.9 dBW in the single relay case.
Fig. 4.5 reveals the throughput of various relay selection schemes especially for the optimal approach in the multi-relay, worst pair case. For throughput-optimal approach with two nodes, in the considered consumed power range the
av-30
8 10 12 14 16 18 20 22
Figure 4.4: Outage Probability comparison for various relay selection rules with mul-tiple relays in the worst-pair case.
erage throughput is 4.63 Mbps, lower than 4.72 Mbps in the single relay case. At Pav=37.8 dBW the throughput achieves 129% higher than that of the signal-based approach, lower than that with single relay 131%.
Fig. 4.6 says the throughput of various relay selection rules especially for the bottleneck SNR approach in the multi-relay, worst pair case. For bottleneck SNR ap-proach with 2 nodes, in the considered consumed power range the average throughput is 4.63 Mbps, lower than 4.70 Mbps in the single relay case. At Pav=37.8 dBW the throughput achieves 129% higher than that of the signal-based approach, lower than
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Figure 4.5: Throughput comparison for various relay selection rules with multiple relays in the worst-pair case for the throughput-optimal approach.
with single relay 131%.
From the above three figures, we realize the trend of the outage probability and the throughput for the multiple relays, worst pair case. We observe that applying more relay nodes, at the same consumed power level the reliability and throughput performance degrades with the number of relays. this is due to more power consump-tion and more chances to choose inappropriate relay nodes.
Table. 4.1 shows the performance loss of utilizing more relays. It computes that at Poutage = 10−2, how much Pav is increased when the number of relays is from one to two. We can know that the loss of the bottleneck SNR approach is larger than that
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22 24 26 28 30 32 34 36 38
Figure 4.6: Throughput comparison for various relay selection rules with multiple relays in the worst-pair case for the bottleneck SNR approach.
of the throughput-optimal approach. This is because deploying more relays forces the bottleneck SNR approach to have a higher probability to choose relays which is close the the source, this kind of relay has bad effect on outage performance. While the throughput-optimal approach is less sensitive to this situation. From the table we see that the loss in the best-pair case is larger that that in the worst-pair case. In the best-pair case, choosing more relays results in a higher to choose relays which is close the the source, this kind of relay has bad effect on outage performance. While in the worst-pair case this situation is less sensitive since there are many possible candidates between the source and the destination.
Table 4.1: Performance Comparison Between One Relay and Two Relays Throughput-Optimal Bottleneck SNR
Best-Pair -0.17 dB -0.61 dB
Worst-Pair -0.1 dB -0.2 dB
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CHAPTER 5
Effects of Total Relay Transmit Power Constraint for Relay Networks
In this chapter, we investigate the impact of total relay transmit power constraint on relay selection rules. Our goal is to reduce energy consumption, while maintaining throughput.
5.1 Power Allocation for Relay Selection Rules in the Literature
In [7,14,15], power allocation is proved effective in reduce energy consumption. There-fore at the same consumed power level the outage probability becomes lower. In this thesis, we expect that utilizing total relay transmit power constraint on the proposed relay selection rules can achieve lower outage probability at the same consumed power level in addition maintain the throughput performance.
5.2 Total Relay Transmit Power Constraint for Pro-posed Relay Selection Rules
In the traditional method, the transmit power allocated in the relay link from the source is the same as that in the relay link to the destination. Now, we suggest a total relay transmit power constraint to adjust transmit power from the relay as the number of the relays increases. In the suggested constraint, the transmit power of each relay is inversely proportional to the number of relays, and the sum of the total transmit power from the relay is equal to the transmit power from the source.
Ptr = Pts
Nr . (5.1)
where Ptr is the transmit power of a relay. Pts is the transmit power of the source.
Nr is the number of relays.
From the above definition, we know that for the single relay case the transmit power of the relay is equal to the transmit power of the source. However, for multiple relays case, the transmit power of a relay is less than the transmit power of the source. Also, the transmit power of a relay is inversely proportional to the number of relays.The total consumed power of a transmission period before power allocation can be expressed as:
Ptotal = Pt× Nr+ 1 . (5.2)
while after power allocation, the the total consumed power of a transmission period can be expressed as:
Ptotal = Pts× 2 = Ptr× 2 = Pt× 2 . (5.3)
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−5 0 5 10 10−4
10−3 10−2 10−1
Pav(dBW)
Outage Probability
No Cooperation Threshold−Based Throughput−Optimal Bottleneck SNR Threshold−Based 2nodes
3nodes 4nodes 0.57dB
2.88dB
1.43dB
Bottleneck SNR
Throughput
−Optimal
Figure 5.1: The outage probability with multiple relays with the total relay transmit power constraint in the best-pair case.
5.3 Numerical Results
In this section, we investigate the impacts of the total relay transmit power constraint on the proposed relay selection rules. We shall show the influences on the outage probability and throughput performance.
−150 −10 −5 0 5 10
Figure 5.2: Throughput comparison for various relay selection rules with the total relay transmit power constraint in the best-pair case for the throughput-optimal ap-proach.
5.3.1 Outage Probability and Throughput Performance of Relay Selection Rules with Total Relay Transmit Power Constraint, in the Best Pair Case
Fig. 5.1 shows the outage probability of various relay selection rules with the total relay transmit power constraint in the best-pair case. We find that at the same con-sumed power level the outage probability is better than that without power allocation.
For throughput-optimal approach, at Poutage = 10−2 it needs more 1.43 dBW than the signal-based approach, less than that in the case without the total relay transmit
38
−150 −10 −5 0 5 10
Figure 5.3: Throughput comparison for various relay selection rules with total the relay transmit power constraint in the best-pair case for the bottleneck SNR approach.
power constraint 2.57 dBW. For bottleneck SNR approach, at Poutage = 10−2 it needs more 0.43 dBW than the signal-based approach, less than that in the case without the total relay transmit power constraint 1.57 dBW. This can be explained by that in the second phase, if we choose multiple relays and each relay uses the same transmit power as that of the source, the power consumed in the second phase is too much and unnecessary.
Fig. 5.2 reveals the throughput of various relay selection schemes especially for the throughput-optimal approach with the total relay transmit power constraint in the best-pair case. For throughput-optimal approach with 2 nodes, in the considered
consumed power range the average throughput is 4.91 Mbps, lower than 5.18 Mbps in the single relay case. At Pav=6.5 dBW the throughput achieves 161% higher than that of the signal-based approach, lower than that with single relay 165%.
This is due to more power consumption from more relays and contributed form more chances to choose relay nodes close to the source or the destination. If a relay node is close to the source or the destination, then one side of the relay node has a low link throughput. Hence, the overall link is limited to a low throughput.
Fig. 5.3 shows the throughput of various relay selection rules especially for the bottleneck SNR approach with the total relay transmit power constraint in the best-pair case. For bottleneck SNR approach with 2 nodes, in the considered consumed power range the average throughput is 5.02 Mbps, lower than 5.15 Mbps in the single relay case. At Pav=6.5 dBW the throughput achieves 161% higher than that of the signal-based approach, lower than that with single relay 165%.
This is contributed from more power consumption by more relay nodes and due to more chances to choose relay nodes close to the source or the destination, then one side of the relay node has a poor link throughput. Therefore, the total link throughput is limited.
From the above three figures, we find that utilizing power allocation appro-priately can eliminate wasted power and achieve better performance while keep rea-sonable throughput. In Chapter 4, we thought that there is no advantage from using multiple relays. However, after using power allocation we find gains through multiple relays. This is an interesting discovery.
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8 10 12 14 16 18 20 22 10−4
10−3 10−2 10−1
Pav(dBW)
Outage Probability No Cooperation
Threshold−Based Throughput−Optimal Bottleneck SNR Threshold−Based 2nodes
3nodes 4nodes
2.3dB
5.5dB
2.5dB
Bottleneck SNR
Throughput
−Optimal
Figure 5.4: Outage probability with the total relay transmit power constraint in the worst pair case.
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Figure 5.5: Throughput comparison for various relay selection rules with the total relay transmit power constraint in the worst-pair case for the throughput-optimal approach.
5.3.2 Outage Probability and Throughput Performance of Relay Selection Rules with the Total Relay Transmit Power Constraint, in the Worst Pair Case
Fig. 5.4 shows the outage probability of various relay selection rules with the total relay transmit power constraint in the worst pair case. The outage probability is better than that before utilizing the constraint. For throughput-optimal approach, at Poutage = 10−2 it needs more 2.5 dBW than the signal-based approach, less than
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22 24 26 28 30 32 34 36 38
Figure 5.6: Throughput comparison for various relay selection rules with the total relay transmit power constraint in the worst-pair case for the bottleneck SNR ap-proach.
that in the case without the total relay transmit power constraint 4.8 dBW. For bottleneck SNR approach, at Poutage = 10−2 it needs more 2.3 dBW than the signal-based approach, less than that in the case without the total relay transmit power constraint 3.1 dBW.
Fig. 5.5 reveals the throughput of various relay selection schemes especially for the throughput-optimal approach with the total relay transmit power constraint in the worst pair case. For throughput-optimal approach with 2 nodes, in the considered consumed power range the average throughput is 4.60 Mbps, lower than 4.72 Mbps in
Table 5.1: The Performance Comparison Before and After Applying Total Relay Transmit Power Constraint for Two-Relays Case
Throughput-Optimal Bottleneck SNR
Best-Pair 1.14 dB 1 dB
Worst-Pair 2.3 dB 0.8 dB
the single relay case. At Pav=37.8 dBW the throughput achieves 129% higher than that of the signal-based approach, lower than that with single relay 131%.
Fig. 5.6 says the throughput of various relay selection rules especially for rule 2 with the total relay transmit power constraint in the worst pair case. For bottleneck SNR approach with 2 nodes, in the considered consumed power range the average throughput is 4.64 Mbps, lower than 4.70 Mbps in the single relay case. At Pav=37.8 dBW the throughput achieves 129% higher than that of the signal-based approach, lower than that with single relay 131%.
From the above three figures, we find that utilizing power allocation appro-priately can eliminate wasted power and achieve higher reliability while maintain acceptable throughput. In Chapter 4, we thought that there is no advantage from using multiple relays. However, after using the total relay transmit power constraint, we find gains through multiple relays. This is an interesting discovery.
For the bottleneck SNR approach with 2 or 3 relays with power allocation, at the same consumed power level the outage probability is even better than that with single relay. And the throughput is maintained in a reasonable range. Therefore, we would recommend the bottleneck SNR approach with 2 relays with the total relay transmit power constraint as the best throughput-oriented relay selection rule.
Table. 5.1 shows the performance gain of using the total relay transmit power constraint. It computes that at Poutage = 10−2, how much Pav is reduced by using
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the total relay transmit power constraint in the two-relays case. We can know that the gain of the throughput-optimal approach is larger than that of the bottleneck SNR approach. This is because throughput-optimal approach uses transmit power in a more inefficient way than the bottleneck SNR approach. From the table we do not see significant difference between the best-pair case and the worst-pair case.
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CHAPTER 6
Conclusions and Future Research Suggestions
There are three main contributions in this thesis. First, we propose two throughput-oriented relay selection rules to get higher throughput. In the literature, many studies design relay selection schemes aiming at achieve better outage probability. However, there is little effort on analyze how to obtain higher system throughput in the relaying networks. Therefore, in this work we propose two relay selection schemes to achieve higher throughput while maintain reliability. The throughput-optimal approach we suggested has the best throughput, but the outage probability is relatively poor and the computational cost is relatively high. Therefore, we propose the bottleneck SNR approach, which is more simpler and has better outage than the throughput-optimal approach while keeping a similar throughput.
Second, we extend the number of relays from one to multiple. We deploy multi-ple relays to see if there is any improvement in the outage probability or throughput.
However, the simulation results are disappointing. At the same consumed power level the outage probability and throughput are both degraded while deploy multiple relays. More relays, poorer outage probability and throughput.
Last but not least, we present the impacts of power allocation on the proposed relay selection rules. We suggest a simple power distribution algorithm here. Excit-ingly, we find that at the same consumed power level power allocation can improve
the outage probability in the multi-relay case while keeping similar throughput. The result for the bottleneck SNR approach with two nodes with power allocation is even better than that of it with single relay. This discovery shows that appropriately utilize power distribution can eliminate unnecessary power and obtain better performance.
6.1 Throughput-Oriented Relay Selection Rules
In Chapter 3, we propose two partner selection methods. The first one is to cal-culate throughput corresponding to each relay, and then choose the relay achieving the maximal throughput. Though this method can achieve the highest throughput, computation cost is quite high. In the second method, we first compare the SNRs of the link from the source to relay with that from the relay to the destination, and designate the smaller one as the bottleneck SNR associated with that relay. The bottleneck SNR of each relay is recorded and compared. The relay with the largest
In Chapter 3, we propose two partner selection methods. The first one is to cal-culate throughput corresponding to each relay, and then choose the relay achieving the maximal throughput. Though this method can achieve the highest throughput, computation cost is quite high. In the second method, we first compare the SNRs of the link from the source to relay with that from the relay to the destination, and designate the smaller one as the bottleneck SNR associated with that relay. The bottleneck SNR of each relay is recorded and compared. The relay with the largest