As mentioned in Section 3.2, OR confines the performance of buffer-aided relaying protocols, because it only utilize the diversity gain provided by one of the two hops.
This effect is depicted in Fig. 4.9 by showing the probabilities of using OR in HRS and CRS versus SNR for the toy example. In this simulation, we discuss the condition, Buffer, which means that CRS and HRS switch to OR because the buffers of the chosen relays selected by SILO and MMRS, respectively, are full or empty. It can be seen that Pr(Buf f er) of CRS is always below that of HRS, which shows that CRS reduces Pr(Buf f er) by SILO compared with HRS. Moreover, Pr(Buf f er) of HRS is the same regardless of SNR. However, CRS reduces Pr(Buf f er) by increasing SNR after SNR
= 5 dB. The reasons are as follows. Both of CRS and HRS combine OR with SILO and MMRS respectively. Hence, CRS and HRS achieve the best performance by reducing
0 2 4 6 8 10 12 14 16 18 20 10−6
10−5 10−4 10−3 10−2 10−1 100
SNR (dB)
Pr(Buffer)
HRS CRS
Figure 4.9: Probability of using OR vs. average SNR in the toy example.
the probability of using OR. In HRS, it reduces the the probability of using OR mainly by increasing the initial buffer length and the buffer size. In CRS, it reduces the the probability of using OR mainly by SILO and increasing SNR.
Chapter 5 Conclusions
To best utilize the information of channel and buffer status, this thesis proposed two cooperative relaying schemes called shortest-in longest-out (SILO) relaying and composite relay selection (CRS). Among a set of available relays that can transmit error-free, SILO selects the relays for reception and transmission based on relay buffer lengths. As a result, the transmitting relay might not be the same as the receiving relay. In case the selected relay sees an empty or full buffer, CRS reduces to OR that selects the same relay based on the channel quality only for transmission and reception.
Table 5.1 shows comparisons of different relay selection schemes under SNR = 15 dB and K = 3. In this table, the comparisons include practicability, achievable diversity order, and buffer requirements in terms of buffer size and initial buffer length, and average delay for achieving the minimum outage probability. Comparing with existing buffer-aided relay selection schemes, our results show the following advantages of CRS.
Firstly, CRS with buffer size of 6 achieves the minimum outage probability while HRS requires buffer size of 100 suggesting 94% buffer size reduction, when the number of relays is three. Secondly, CRS only needs the initial buffer size Ninitof 2 to achieve the minimum outage probability, yet HRS needs to fill the buffer to be half full initially, i.e., Ninit = 50. In this case, the delay of CRS and HRS are 6 and 150 slots, respectively.
Overall, CRS significantly reduces the buffer requirements, including buffer size and initial buffer length, and the delay compared with HRS. Moreover, the improvement in terms of buffer size, initial buffer length, and the resultant delay increases as the number of relays increases.
Scheme OR MMRS SILO HRS CRS
Practical Yes No No Yes Yes
Diversity order Full Full Infinite 1 Full Full Buffer requirements to achieve the minimum outage probability Buffer size (Lb) N/A Infinite Infinite 100 6 Initial buffer length (Ninit) N/A Infinite Infinite 50 2 Average delay N/A Ninit× K Ninit× K 150 6
Table 5.1: Comparisons of different relay selection schemes in terms of practicability, achievable diversity order, buffer requirements to achieve the minimum outage proba-bility including buffer size and initial buffer length, and average delay for achieving the minimum outage probability. For HRS and CRS, the listed results are obtained under SNR = 15 dB and K = 3.
5.1 Future Works
Some potential extensions are discussed below. In [1], the same initial buffer length for all relays is assumed and required to achieve the optimal result. In case the source-relay channel quality is not stable, feeding an equal number of packets in each source-relay buffer may consume a significant amount of time. On the contrary, the requirement of identical initial buffer length can be relaxed in the proposed CSI. This can be seen from the state transition diagram of the toy example in Sec. 3.4, which CRS shows that the buffer lengths of different relays tend to the same at equilibrium, regardless the initial buffer lengths. More former proofs to validate this intuition should worth further work.
Our current work considers the fixed transmission rate. A possible extension is to consider the adaptive rate transmission in CRS. Specifically, the transmitter (may be the source or the relay) can adaptive its transmission rate to the instantaneous channel condition, provided with a fast feedback channel. In this way, the chance of empty RS or TS will be reduced even the source-relay channel quality is poor. Since relays buffers may be fed with different number of information bits in each time slot, the buffer length will be changed more dynamically that requires careful designs toward the relay selection policy.
1SILO never incurs outage because it operates only when RS and TS are nonempty.
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Appendix
To ease the derivation, we define the following four probabilities, q1, q2, q3, and Q. The first probability, q1, represents that both instantaneous SNRs of the branches exceed the SNR threshold, γT , 22r− 1, in the single hop, i.e. both γg1 and γg2 exceed γT in hop 1. Thus q1 can be written as
q1 = P (γg1 > γT ∩ γg2 > γT) = P (RS = {R1, R2})
= e−2γT/Γ (A-1)
= P (γh1 > γT ∩ γh2 > γT) = P (TS ={R1, R2}).
The second probability, q2, represents that only either branch 1 or branch 2 has the instantaneous SNR exceeding γT but not both in the single hop, i.e. γg1 but not γg2 exceeds γT in hop 1. Thus, q2 can be written as
q2 = P (γg1 > γT > γg2) = P (RS ={R1})
= e−γT/Γ(1− e−γT/Γ) (A-2)
= P (γg2 > γT > γg1) = P (RS ={R2})
= P (γh1 > γT > γh2) = P (TS ={R1})
= P (γh2 > γT > γh1) = P (TS ={R2}).
The third probability, q3, represents that both the instantaneous SNRs of the branches are below the SNR threshold, γT, in the single hop, i.e. both γg1 and γg2 are below γT
in hop 1. Thus, q3 can be written as
q3 = P (γT > γg1 ∩ γT > γg2) = P (RS =∅)
= (1− e−γ/Γ)2 (A-3)
= P (γT > γh1 ∩ γT > γh2) = P (TS =∅).
The fourth probability, Q, represents that RS, TS, or both is empty, which is the condition Null. In this case, CRS would switch to OR rather than SILO. Thus, Q can be written as
Q = P (RS = ∅ ∪ TS = ∅)
= P (RS̸= ∅ ∩ TS = ∅) + P (RS = ∅ ∩ TS ̸= ∅) + P (RS = ∅ ∩ TS = ∅)
= P (RS̸= ∅) × P (TS = ∅) + P (RS =∅) × P (TS ̸= ∅) + P (RS =∅) × P (TS = ∅)
= [1− P (γT > γg1 ∩ γT > γg2)]× P (γT > γh1 ∩ γT > γh2) + P (γT > γg1 ∩ γT > γg2)× [1 − P (γT > γh1 ∩ γT > γh2)]
+ P (γT > γg1 ∩ γT > γg2)× P (γT > γh1 ∩ γT > γh2)
= (1− q3)× q3+ q3× (1 − q3) + q3× q3
= 2× q3− q32. (A-4)