RELAY selection provides an attractive way to harvest the

Transcription

1 IEEE TRASACTIOS O VEHICULAR TECHOLOGY, VOL. 66, O. 3, MARCH Buffer-Aided Reay Seection With Reduced Packet Deay in Cooperative etworks Zhao Tian, Member, IEEE, Yu Gong, Gaojie Chen, Member, IEEE, and Jonathon A. Chambers, Feow, IEEE Abstract Appying data buffers at reay nodes significanty improves the age performance in reay networks, but the performance gain is often at the price of ong packet deays. In this paper, a nove reay seection scheme with significanty reduced packet deay is proposed. The age probabiity and average packet deay of the proposed scheme under different channe scenarios are anayzed. Simuation resuts are aso given to verify the anaysis. The anaytica and simuation resuts show that, compared with non-buffer-aided reay seection schemes, the proposed scheme has not ony significant gain in age performance but aso simiar average packet deay when the channe signa-to-noise ratio SR) is high enough, making it an attractive scheme in practice. Index Terms Average deay, buffer-aided reay, reay seection. I. ITRODUCTIO RELAY seection provides an attractive way to harvest the diversity gain in mutipe reay cooperative networks [], [2]. A typica reay seection system is shown in Fig., which incudes one source node S), one destination node D),and reay nodes R k, k ). Anaysis shows that fu diversity order can be achieved with the best seected reay [3] [5]. In the traditiona max min reay seection scheme, the best reay is seected with the highest gain among a of the minima of the source-to-reay and reay-to-destination channe gain pairs [6]. Whie the max min scheme achieves a diversity order of, its performance is practicay imited by the constraint that the best source-to-reay and reay-to-destination inks for a packet transmission must be determined concurrenty. Recent research has, on the other hand, found that introducing data buffers at the reays yieds significant performance advantage in practica systems [7] [0]. Buffer-aided reays have aso been used in ap- Manuscript received March 2, 206; accepted May 8, 206. Date of pubication May 30, 206; date of current version March 0, 207. This work was supported in part by the Engineering and Physica Sciences Research Counci under Grant EP/K04307/2 and in part by the Ministry of Defence s University Defence Research Coaboration in Signa Processing. The review of this paper was coordinated by Prof. R. Jäntti. Corresponding author: Gaojie Chen.) Z. Tian is with Schoo of Engineering and Appied Science, Aston University, Birmingham B4 7ET, U.K. e-mai: z.tian@boro.ac.uk). Y. Gong is with the Advanced Signa Processing Group, Loughborough University, Loughborough LE 3TU, U.K. e-mai: y.gong@boro.ac.uk). G. Chen is with the Department of Engineering Science, University of Oxford, Oxford OX 3PJ, U.K. e-mai: gaojie.chen@eng.ox.ac.uk). J. A. Chambers is with the Communications, Sensors, Signa and Information Processing Group, ewcaste University, ewcaste upon Tyne E 7RU, U.K. e-mai: jonathon.chambers@nc.ac.uk). Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier 0.09/TVT Fig.. System mode of the reay seection system. pications incuding adaptive ink seection [], [2], cognitive radio networks [3], and physica ayer network security [4]. Typica buffer-aided reay seection schemes incude the max max [7] and max-ink [8] schemes. In max max reay seection, at one time sot t, the best ink among a sourceto-reay channes is seected, and a data packet is sent to the seected reay and stored in the buffer. At the next time sot t + ), the best ink among a reay-to-destination channes is seected, and the seected reay which is often not the same reay seected at time t) forwards one data packet from its buffer to the destination. The max max scheme has significant coding gain over the traditiona max min scheme. In the max-ink scheme [8], the best ink is seected among a avaiabe sourceto-reay and reay-to-destination inks. Depending on whether a source-to-reay or a reay-to-destination ink is seected, either the source transmits a packet to the seected reay or the seected reay forwards a stored packet to the destination. As a resut, the max-ink reay seection not ony has coding gain over the max min scheme but aso has higher diversity order than both the max min and max max schemes, making it more attractive than its max max counterpart. The performance gain of either the buffer-aided max max or max-ink schemes is, however, at the price of much increased packet deay. In the non-buffer-aided reay seection scheme e.g., the max min scheme), it aways takes two time sots for every packet passing through the network, corresponding to the source-to-reay and reay-to-destination transmission, respectivey. In the buffer-aided approach, in contrast, when a packet is transmitted to a reay node, it is stored in the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

2 2568 IEEE TRASACTIOS O VEHICULAR TECHOLOGY, VOL. 66, O. 3, MARCH 207 buffer and wi not be forwarded to the destination unti the corresponding reay-to-destination ink is seected. As a resut, different packets in the buffer-aided reay network may endure different deays. To be specific, in either the max max or maxink scheme, the average packet deay increases ineary with reay number and buffer size. On the other hand, to achieve high performance gain, the reay number and the buffer size in the max max or max min scheme are often set as high as possibe. This makes the existing buffer-aided reay seection schemes unsuitabe in most appications, particuary in 5G mobie systems which require utraow atency. Whie packet deay reduction has been investigated in adaptive ink seection with infinite buffer size e.g., []), itte has been done for buffer-aided reay seection with finite buffer size. In this paper, we propose a nove buffer-aided reay seection scheme with significanty reduced packet deay. This is achieved by giving higher priority to seect the reay-todestination than the source-to-reay inks, so that the data queues at reay buffers are as short as possibe. The main contributions of this paper are isted as foows. Proposing a nove reay seection scheme. The proposed scheme provides a simpe yet effective way to reduce the packet deay in the buffer-aided reay seection. Deriving the cosed-form expression for age probabiity. The anaysis is based on the genera asymmetric channe assumption that the source-to-reay and reay-todestination inks may have different average gains. Obtaining the cosed-form expression for the average packet deay. Using Litte s aw, the average packet deay of the proposed scheme is anayticay obtained. Anayzing the asymptotic performance that the channe SR goes to infinity. The asymptotic performances, incuding diversity order, coding gain, and average packet deay for infinite channe SR, are anayzed. The remainder of this paper is organized as foows: Section II proposes the new reay seection scheme; Section III anayzes the age probabiity; Section IV anayzes the average packet deay; Section V anayzes the asymptotic performance; Section VI shows simuation resuts; and Section VII concudes this paper. II. BUFFER-AIDED RELAY SELECTIO WITH REDUCED DELAY The system mode of buffer-aided reay seection is simiar to that shown in Fig., except that every reay is equipped with a data buffer Q k k ) of finite size L. We assume that reays appy the decode-and-forward DF) protoco. The channe coefficients for S R k and R k D inks at time sot t are denoted by h srk t) and h rk dt), respectivey. A channes are Rayeigh fading, and the average channe gains for S R k and R k D inks are given by [ γ sr = E h srk t) 2], γ rd = E [ h rk dt) 2], for a k ) respectivey. We assume with osing generaity that a transmission power and noise variances are normaized to unity. We aso assume that channe gains in either the source-to-reay or reay-to-destination inks are independent and identicay distributed i.i.d.), but in genera γ sr γ rd. In the existing buffer-aided max max and max min reay seection schemes, the average packet deay increases ineary with reay number and buffer size. The arge deay is due to the packets queuing at the buffers. This can be seen, for exampe, in the max-ink scheme with reay number and buffer size L>2. Specificay, we assume that a buffers are initiay empty and a packet s is sent to reay R at time t =. Then, at the next time t = 2, except for R which contains s,a other buffers are sti empty. Thus, there are + ) avaiabe inks for seection in tota: from source-to-reay S R k for a k) inks and one from reay-to-destination R D) ink. Because the max-ink scheme aways seects the strongest ink among a avaiabe inks, the probabiity that R D is seected and s is forwarded to the destination is / + )).In other words, it is more ikey [with the probabiity of / + )]thats remains in R at t = 2, eading to one extra time sot in packet deay. It is cear that this extra deay may be avoided by forwarding s to the destination immediatey at t = 2, once the corresponding R D ink is not in age, even if it is not the strongest ink. This eads to a new principe of buffer-aided reay seection, i.e., to transmit the packets aready in the buffers as fast as possibe. This transates into giving higher priority to seect the reay-to-destination inks: ony when no reay-to-destination ink can be seected are the source-to-reay inks considered. As a resut, the packet queuing engths at the reay buffers are minimized, as we as the average packet deay. To be specific, at time sot t, the ink seection rue is described as foows. ) Choose the ink with the highest channe SR among a avaiabe reay-to-destination inks h rk dt) 2 ). If the chosen ink is not in age, the corresponding reay forwards a packet from its buffer to the destination. 2) Otherwise, if the seected ink in step ) is in age or there are no avaiabe reay-to-destination inks at time t, choose the ink with the highest channe SR among a avaiabe source-to-reay inks h srk t) 2 ). If the seected ink is not in age, the source transmits one packet to the corresponding reay and the packet is stored in the buffer. Otherwise, age occurs. The aforementioned proposed scheme is easy to impement because it requires the same knowedge as that in the existing buffer-aided max max or max min scheme. In the foowing two sections, the age and deay performance of the proposed scheme wi be anayzed, respectivey. III. OUTAGE PROBABILITY The numbers of data packets in a of the reay buffers form a state. With reays and buffer size L, therearel + ) states in tota. The th state vector is defined as s =[Ψ Q ),...,Ψ Q K )], =,...,L + ) 2) where Ψ Q k ) gives the number of data packets in buffer Q k at state s. It is cear that 0 Ψ Q k ) L.

3 TIA et a.: BUFFER-AIDED RELAY SELECTIO WITH REDUCED PACKET DELAY I COOPERATIVE ETWORKS 2569 Every state corresponds to one pair of Ks S R,Ks R D ), corresponding to the numbers of avaiabe source-to-reay and reay-to-destination inks, respectivey. A source-to-reay ink is considered avaiabe when the buffer of the corresponding reay node is not fu, and a reay-to-destination ink is avaiabe when the corresponding reay buffer is not empty. At state s, the tota numbers of avaiabe source-to-reay and reay-to-destination inks are denoted by Ks S R and Ks R D, respectivey. It is cear that 0 Ks S R and 0 Ks R D. Specificay, if none of the buffers are fu or empty, a inks are avaiabe, such that Ks S R = Ks R D =. Considering a possibe states, the age probabiity of the proposed buffer-aided scheme can be obtained as P = L+) = π p s 3) where π is the stationary probabiity for state s,andp s is the age probabiity at state s. In the foowing two subsections, we derive p s and π, respectivey. A. p s : Outage Probabiity at State s For independent Rayeigh fading channes, the instantaneous SR for every channe, i.e., γ w w {sr k,r k d}), is independenty exponentiay distributed. In the proposed scheme, age occurs if a avaiabe source-to-reay inks and reay-todestination inks are in age. Thus, the age probabiity at state s is given by where p s = ps R p R D 4) On the other hand, because a source-to-reay ink is seected ony when a reay-to-destination inks are in age and not a source-to-reay inks are in age, the probabiity to seect one source-to-reay ink at state s is given by p S R s = = Ks S R p R D Ks S R p S R ) ) e Δ K R D ) ) s K γ rd e Δ S R s γsr. 7) With these observations, the n, )th entry of the state transition matrix A is expressed as p s, if s n = s p R D s A n, = if s n Us R D p S R s, if s n Us S R 8) 0, esewhere where p s, p R D s,andp S R s are given by 4), 6), and 7), respectivey; Us R D and Us S R are the sets containing a states to which s can move when a reay-to-destination ink or a source-to-reay ink is seected, respectivey. Because the transition matrix A in 8) is coumn stochastic, irreducibe, and aperiodic, the stationary state probabiity vector is obtained as see [5]) π =A I + B) b 9) where π =[π,...,π L+) ] T, b =,,...,) T, I is the identity matrix, and B n, is an n a-one matrix. Finay, substituting 8) and 9) into 3) gives the age probabiity as ) K p S R = e Δ S R s γsr ) p R D = e Δ K R D s γ rd 5) P = L+) = π p s = diaga) π =diaga) A I + B) b 0) where p S R and p R D are the probabiities that a avaiabe source-to-reay inks and reay-to-destination inks are in age, respectivey; r t is the target data rate; and Δ=2 r t. B. π : Stationary Probabiity of the State s We denote A as the L + ) L + ) state transition matrix, where the entry A n, = P X t+ = s n X t = s ) is the transition probabiity that the state moves from s at time t to s n at time t + ). We assume that, at time sot t, thestateisats. The probabiity to seect one reay-to-destination ink when not a of the avaiabe reay-to-destination inks are in age is given by p R D s = K R D s = Ks R D p R D ) ) ) e Δ K R D s γ rd. 6) where diaga) is a vector consisting of a diagona eements of A. IV. AVERAGE PACKET DELAY The deay of a packet in the system is the duration between the time when the packet eaves the source node and the time when it arrives the destination. Because it takes one time sot to transmit a packet from the source to a reay node, the average packet deay in the system is given by D = + D r ) where D r is the average deay at the reay nodes. Because the average deay through every reay node is the same, ony the average deay through reay R k is anayzed in Coumn stochastic means that a entries in any coumn sum up to one, irreducibe means that it is possibe to move from any state to any state, and aperiodic means that it is possibe to return to the same state at any steps [5].

4 2570 IEEE TRASACTIOS O VEHICULAR TECHOLOGY, VOL. 66, O. 3, MARCH 207 the foowing. Based on Litte s aw [6], the average packet deay at reay R k is given by D r = D k = L k 2) η k where L k and η are the average queuing ength and average throughput at R k, respectivey. The average queuing ength at R k is obtained by averaging the queuing engths at buffer Q k over a states, or L k = L+) = π Ψ Q k ) 3) where Ψ Q k ) gives the number of packets or the buffer ength) of buffer Q k at state s,andπ is given by 9). On the other hand, because the probabiities to seect any of the reays are the same, the average throughput at reay R k is given by η k = η 4) where η is the average throughput of the overa system network. For deay-imited transmission, the average throughput η is obtained as see [7] and [8]) η = R P ) 5) where R is the average data rate of the system with considering the age probabiity). In the proposed scheme, every packet requires two time sots not necessariy consecutivey) to reach the destination, we have R = /2, and thus η k = P 2. 6) Substituting 3) and 6) into 2), and further into ), gives D = + 2 L+) = π Ψ Q k ). 7) P V. A SYMPTOTIC PERFORMACE This section anayzes the asymptotic performance of the proposed scheme when the average channe SR goes to infinity. The average channe SRs for source-to-reay and reay-todestination ink can be respectivey expressed as γ sr = α γ and γ rd = β γ 8) where α and β are positive rea constants, and γ is the normaized average channe SR. In the foowing, we first derive the asymptotic age probabiity for γ, from which the diversity order, coding gain, and average packet deay are obtained. A. Asymptotic Outage Probabiity When γ, it is cear from 6) that im pr D s =, if Ks R D 0. 9) This impies that any packets in the reay buffers wi be forwarded to the destination and a new packet is transmitted to one of the reays ony after a buffers are empty. Thus, when γ, the buffers can ony be in two possibe states, namey, S 0) and S ), corresponding to the cases that a buffers are empty and ony one of the buffers has one packet, respectivey. It is then from 3) that im P = P S 0)) p S0) + P S )) p S) 20) where P S 0) ) and P S ) ) are the probabiities that buffers are in states S 0) and S ), respectivey, and p S0) and p S) are the corresponding age probabiities. Suppose that, at time t, a buffers are empty, so that the state is in S 0). Then, one packet wi be transmitted to a reay at time t + ), and the state moves to S ). From 9), the packet in the buffer must be forwarded to the destination at t + 2), andthe state returns to S 0). This process continues unti a packets are transmitted. Thus, we have P S 0)) = P S )) = 2. 2) When the buffers are in state S 0),thereare avaiabe sourceto-reay inks and no avaiabe reay-to-destination inks, or we have ) p S0) = e Δ γsr. 22) When the buffers are in state S ), there is one avaiabe reayto-destination ink. In addition, the number of avaiabe sourceto-reay inks is denoted by K,whereK = or,for buffer size L = or arger, respectivey. Then, we have p S) = e Δ γsr ) K e Δ γ rd ). 23) Substituting 2), 22), and 23) into 20) gives im P = ) 2 e Δ ) α γ + 2 e Δ K α γ ) e Δ β γ B. Diversity Order The diversity order can be defined as. 24) og P d = im og γ. 25) If the buffer size L =, substituting 24) into 25), and further noting that e x + x for very sma x, wehavethe diversity order for L = as [ og d L=) 2 = im Δ α γ ) Δ α γ + Δ β γ =. 26) og γ If the buffer size L 2, from 24), the asymptotic age probabiity is given by [ ) ) ] im P L 2) Δ β γ +Δ = im 2. 27) α γ β γ Because im ) ] β γ) < im β γ +Δ)< im 2 β γ) 28) the diversity order for L 2 can be obtained as <d L 2) <+. 29)

5 TIA et a.: BUFFER-AIDED RELAY SELECTIO WITH REDUCED PACKET DELAY I COOPERATIVE ETWORKS 257 C. Coding Gain The coding gain is defined as the SR difference in decibes) between the traditiona max min and proposed schemes to achieve the same age probabiity, or CdB) = im Δ P γ) 30) d whered =, which is the diversity order, and Δ P γ) =0 og P max min) γ) 0 og P L=) γ) 3) where P max min) γ) and P L=) γ) are the age probabiities at γ for the max min and proposed schemes, respectivey. For fair comparison, the buffer size is set as L =, so that the diversity order for the max min and proposed schemes are the same as d =. From 24), we have L=) im 0 og P = 0 og [ 2 ) α + im 0 og For the traditiona max min scheme, we have im 0 og P max-min) Δ = im 0 og α γ + Δ β γ = 0 og α + β ) ) + im 0 og ) ] α + β ). 32) Δ γ ) Δ. 33) γ Substituting 32) and 33) into 3) gives [ ) ] im Δ β P γ) = 0 og. 34) 2 α + β Finay, substituting 34) into 30) gives the coding gain of the proposed scheme as [ ) ] 0 og β 2 α+β CdB) =. 35) It is interesting to observe that, for symmetric channe configuration with α = β, the coding gain is 3 db. D. Average Packet Deay We have shown that, when γ, the buffer states can ony be in either S 0) or S ), or a buffer can ony be empty or contains one packet. When a buffers are empty, a new packet is transmitted to a reay with probabiity of /. Further from 2) that P S ) )=/2, the probabiity that Q k contains one packet is given by P Q k = ) =P S )) = 2. 36) Thus, when γ, the average buffer ength at reay R k is given by S )) im L k = P Q k = ) =P = 2. 37) TABLE I ASYMPTOTIC PERFORMACE COMPARISO AMOG DIFFERET SCHEMES FOR SYMMETRIC CHAELS From 6), and noticing that im P = 0, the average throughput at reay Q k is given by im η k = im P ) = ) Finay, substituting 37) and 38) into 2), and further into ), gives the average packet deay for γ as im D = + 2) 2) = 2. 39) It is ceary shown in 39) that, when SR is high enough, the average packet deay of the proposed scheme is the same as that for the non-buffer-aided schemes. E. Comparison Between Different Schemes in Symmetric Channe Configuration For the symmetric channe configuration, Tabe I compares the diversity order, coding gain, and average deay for the nonbuffer-aided max min, the traditiona buffer-aided max max and max-ink, and the proposed schemes. Tabe I shows that a buffer-aided schemes have the 3-dB coding gain over the max min scheme. The proposed ink has sighty higher diversity order than the max max scheme but ower diversity order than the max-ink scheme. In either the max max or max-ink scheme, the average packet deay increases ineary with reay number and buffer size L. In the proposed scheme, when γ, the average deay is fixed at 2, which is the same as that for the non-buffer-aided max min scheme. For asymmetric channes, the comparison between schemes is not the same as that shown in Tabe I, and this wi be discussed in the foowing section. VI. SIMULATIOS AD DISCUSSIOS This section verifies the proposed scheme with numerica simuations, where the resuts for previousy described maxink and non-buffer-aided max min schemes are aso shown for comparison. In the foowing simuation, the transmission rates in a schemes are set as r t = 2 b/s/hz, and simuation resuts are obtained with Monte Caro runs. Particuary in the proposed scheme, the simuation resuts aways we match the theoretica anaysis. A. Symmetric Channe Configuration: γ sr = γ rd In the first simuation, we consider a symmetric channe scenario that the source-to-reay and reay-to-destination inks have the same average channe SRs.

6 2572 IEEE TRASACTIOS O VEHICULAR TECHOLOGY, VOL. 66, O. 3, MARCH 207 Fig. 2. a) Outage probabiities and b) average deay among different schemes, where γ sr = γ rd = 0 db. Fig. 3. Average packet deay comparison between the max-ink and proposed schemes. a) Deay versus buffer size, where = 2. b) Deay versus reay number, where L = 0. Fig. 2a) and b) compares the age probabiities and average packet deays for the non-buffered max min, traditiona max-ink, and proposed schemes, respectivey, where the reay number is fixed at = 3, and we et α = β =.5 and γ = 0 db in 8), so that γ sr = γ rd = 5 db. Fig. 2a) shows that, when the buffer size L =, the proposed and max-ink schemes have the same age probabiities, where both have significanty better age performance than the traditiona nonbuffer-aided max min scheme because of the 3-dB coding gain. When the buffer size increases to L = 5, the proposed scheme has sighty better age performance than that for L =. This we matches the asymptotic anaysis that, when L 2, the diversity order is arger than but smaer than + ) for the proposed scheme. On the other hand, for the max-ink scheme, the age performance improves more significanty with arger buffer size. This is because the diversity order of the max-ink scheme goes up with the buffer size, unti it reaches 2 when L.Fig.2b)showsthat,evenforL =, the average deay of the max-ink scheme is at east twice as much as that for the proposed scheme. When the buffer size increases to L = 5, the average packet deay of the proposed scheme sti maintains at 2 in high-sr ranges, which is the same as that for L =. On the other hand, when L = 5, the average packet deay of the max-ink scheme increases to 8 at high SRs, which is nine times arger than that of the proposed scheme. To further compare the deay performance of the max-ink and proposed schemes in symmetric channes, Fig. 3a) and b) shows the average packet deay versus the buffer size and reay Fig. 4. Diversity order and coding gain of the proposed scheme. number, respectivey, where the average channe SRs in both schemes are set as 0 db. In Fig. 3a), the reay number is fixed at = 2, and the buffer size varies from to 20. In Fig. 3b), the buffer size is fixed at L = 0, but the reay number varies from to 0. It is ceary shown in both Fig. 3a) and b) that the average packet deay for the proposed scheme remains at a constant vaue of 2. On the other hand, the packet deay in the max-ink scheme goes up ineary with either or L. To revea the diversity order and coding gain of the proposed scheme, Fig. 4 compares the age probabiities of the proposed and non-buffer-aided max min schemes at very high

7 TIA et a.: BUFFER-AIDED RELAY SELECTIO WITH REDUCED PACKET DELAY I COOPERATIVE ETWORKS 2573 Fig. 5. a) Outage probabiities and b) average deay among different schemes, where γ sr = 20 db and γ rd = 0 db. Fig. 6. a) Outage probabiities and b) average deay among different schemes, where γ sr = 0 db and γ rd = 20 db. SRs, where the reay number is set as = 4 and a resuts are from theoretica anaysis. First, the coding gain is ceary 3 db, by comparing the max min and proposed schemes with L =. For exampe, to achieve the age probabiity of 0 34, the SRs for the max min and proposed schemes with L = are ab 85 and 88 db, respectivey. The diversity order of the proposed scheme is aso ceary shown to be, + ) for L 2. For exampe, as iustrated in the figure, for the proposed scheme with L = 8, the SRs to achieve the age probabiities of 35 and 340 db are ab 78 and 84 db, respectivey. Then, according to the diversity order definition in 25), the diversity order is obtained as )/84 78) =4.7, which is ceary between = 4and + = 5. B. Asymmetric Channe Configuration: γ sr > γ rd In Fig. 5, we consider the asymmetric channe assumption that source-to-reay inks are stronger than reay-to-destination inks in average, where we et α = 2, β =, and γ = 0 db in 8), so that γ sr = 20 db and γ rd = 0 db, and reay number is fixed at = 3. It is very interesting to observe in Fig. 5a) that, for both L = andl = 5, the age performance of the proposed scheme is significanty better than the max-ink scheme. This is because, when the source-to-reay inks are stronger than the reay-to-destination inks, the max-ink scheme is more ikey to seect the source-to-reay inks, so that the buffers are more ikey fu. This effectivey decreases the number of avaiabe source-to-reay inks, eading to ower diversity order. On the other hand, in the proposed scheme, whie the channe condition gives higher priority to the source-to-reay seection, the seection rue gives higher priority to the reayto-destination ink seection. This eads to a more baanced buffers at the reays, or fewer fu or empty buffers, which again increases the diversity order. Fig. 5b) shows the average deay of the max-ink even worse than that in symmetric channes. This is because the buffers are more ikey to be fu, or because of higher queuing ength at buffers. On the contrary, the average deay for the proposed scheme is sti as ow as ab 2 at high SR. Therefore, when γ sr > γ rd, the proposed scheme has better performance in both age probabiity and average deay than the max-ink scheme. C. Asymmetric Channe Configuration: γ sr < γ rd Fig. 6 assumes that the source-to-reay ink is weaker than the reay-to-destination ink in average, where we et α =, β = 2, and γ = 0 db in 8), so that γ sr = 0 db and γ rd = 20 db, and reay number is set as = 3.

8 2574 IEEE TRASACTIOS O VEHICULAR TECHOLOGY, VOL. 66, O. 3, MARCH 207 It is interesting to observe in Fig. 6 that, the max-ink and proposed schemes have simiar performance in both age and average deay. This is because stronger reay-to-destination inks naturay give higher priority to seect the reay-todestination inks. However, even under this channe assumption, the average packet deay is sti better constrained in the proposed scheme than in the max-ink scheme, particuary in ow-sr ranges. VII. COCLUSIO This paper has proposed a nove buffer-aided reay seection scheme with significanty reduced packet deays. We have shown the age and average deay performance under different channe configurations. To be specific, for symmetric S R and R D channes, the max-ink scheme has better age performance than the proposed. However, when S R inks are stronger, the proposed scheme performs better in age than the max-ink. On the other hand, when R D inks are stronger, the max-ink and proposed schemes have simiar age performance. Therefore, if the reay nodes are eveny spread within an area as in many practica systems, it is reasonabe to expect that the age performances of the proposed and max-ink schemes are simiar. This wi be eft for future study. We aso highight that, in a cases, the proposed scheme has significanty better age performance than the non-buffer-aided schemes, making it an attractive scheme in practica appications. ACKOWLEDGMET The authors woud ike to thank associate editor and anonymous reviewers for significanty improving the manuscript, particuary one of the reviewers for pointing the parae work in the Master s dissertation [9], in which Agorithms 2 and 3 were proposed with simiar ideas to that in this paper. Agorithm 2 which is based on giving higher priority to reays with onger queuing ength) has simiar performance to our proposed scheme, but it is more compicated to impement. Agorithm 3 trades off between age and deay performance and, in some cases, may have onger deay than the standard buffer-aided max-ink scheme. Our work was done independenty from the work in the Master s dissertation. [5] G. Chen, Y. Gong, and J. Chambers, Study of reay seection in a mutice cognitive network, IEEE Wireess Commun. Lett., vo. 2, no. 4, pp , Aug [6] A. Betsas, A. Khisti, D. P. Reed, and A. Lippman, A simpe cooperative diversity method based on network path seection, IEEE J. Se. Areas Commun., vo. 24, no. 3, pp , Mar [7] A. Ikhef, D. S. Michaopouos, and R. Schober, Max-max reay seection for reays with buffers, IEEE Trans. Wireess Commun., vo., no. 3, pp , May 202. [8] I. Krikidis, T. Charaambous, and J. S. Thompson, Buffer-aided reay seection for cooperative diversity systems with deay constraints, IEEE Trans. Wireess Commun., vo., no. 5, pp , May 202. [9] Z. Tian, G. Chen, Y. Gong, Z. Chen, and J. A. Chambers, Buffer-aided max-ink reay seection in ampify-and-forward cooperative networks, IEEE Trans. Veh. Techno., vo. 64, no. 2, pp , Feb [0] Z. Tian, Y. Gong, G. Chen, Z. Chen, and J. Chambers, Buffer-aided ink seection with network-coding in muti-hop networks, IEEE Trans. Veh. Techno., vo. 65, no. 9, pp , Sep []. Zatanov, R. Schober, and P. Popovski, Buffer-aided reaying with adaptive ink seection, IEEE J. Se. Areas Commun., vo. 3, no. 8, pp , Aug [2]. Zatanov, R. Schober, and P. Popovski, Buffer-aided reaying with adaptive ink seection-fixed and mixed rate transmission, IEEE Trans. Inf. Theory, vo. 59, no. 5, pp , May 203. [3] G. Chen, Z. Tian, Y. Gong, and J. A. Chambers, Decode-and-forward buffer-aided reay seection in cognitive reay networks, IEEE Trans. Veh. Techno., vo. 63, no. 9, pp , Mar [4] G. Chen, Z. Tian, Y. Gong, Z. Chen, and J. A. Chambers, Max-ratio reay seection in secure buffer-aided cooperative wireess networks, IEEE Trans. Inf. Forensics Security, vo. 9, no. 4, pp , Apr [5] J. R. orris, Markov Chains. Cambridge, U.K.: Cambridge Univ. Press, 998. [6] J. D. C. Litte, A proof of the queueing formua: L = λω, Oper. Res., vo. 9, no. 3, pp , 96. [7] R. arasimhan, Throughput-deay performance of haf-dupex hybrid- ARQ reay channes, in Proc. IEEE ICC, Beijing, China, May 9 23, 2008, pp [8] G. Chen, Y. Gong, P. Xiao, and T. Rahim, Dua antenna seection in sefbackhauing mutipe sma ce networks, IEEE Commun. Lett., vo. 20, no. 8, pp. 6 64, Aug [9] D. Pouimeneas, Back-pressure-ike mechanisms on reay seection poicies for cooperative diversity systems, M.S. thesis, Dept. Eectr. Eng., KTH Roy. Inst. Techno., Stockhom, Sweden, 205. [Onine]. Avaiabe: &dswid=537%2 REFERECES [] J.. Laneman, D.. C. Tse, and G. W. Worne, Cooperative diversity in wireess networks: Efficient protocos and age behavior, IEEE Trans. Inf. Theory, vo. 50, no. 2, pp , Dec [2] Z. Ding, Y. Gong, T. Ratnarajah, and C. Cowan, On the performance of opportunistic cooperative wireess networks, IEEE Trans. Commun., vo. 56, no. 8, pp , Aug [3] B. Barua, H. Q. go, and H. Shin, On the SEP of cooperative diversity with opportunistic reaying, IEEE Commun. Lett., vo. 2, no. 0, pp , Oct [4] G. Chen and J. A. Chambers, Exact age probabiity anaysis for cooperative AF reay network with reay seection in presence of inter-ce interference, Eectron. Lett., vo. 48, pp , Oct Zhao Tian S 2 M 5) received the B.Eng. degree and the Ph.D. degree in eectronic, eectrica and systems engineering from Loughborough University, Loughborough, U.K., in 202 and 205, respectivey. He is currenty a Knowedge Transfer Project Associate in Computer Science with Aston University, Birmingham, U.K., and IGI Ltd., Birmingham. His current research interests incude the genera fied of wireess communications, with emphasis on bufferaided reaying, machine earning, and data mining. Dr. Tian was a recipient of the Fu Postgraduate Schoarship from the Engineering and Physica Sciences Research Counci whie working toward the Ph.D. degree.

9 TIA et a.: BUFFER-AIDED RELAY SELECTIO WITH REDUCED PACKET DELAY I COOPERATIVE ETWORKS 2575 Yu Gong received the B.Eng. and M.Eng. degrees in eectronic engineering from the University of Eectronics and Science Technoogy of China, Chengdu, China, in 992 and 995, respectivey, and the Ph.D. degree in communications from the ationa University of Singapore, Singapore, in After Ph.D. graduation, he took severa research positions with the Institute of Infocomm Research, Singapore, and aso with Queen s University of Befast, Befast, U.K. From 2006 and 202, he was an Academic Member with the Schoo of Systems Engineering, University of Reading, Reading, U.K. He has been with the Schoo of Eectronic, Eectrica and Systems Engineering, Loughborough University, Loughborough, U.K., since Juy 202. His research interests are in the area of signa processing and communications, incuding wireess communications, cooperative networks, noninear and nonstationary system identification, and adaptive fiters. Gaojie Chen S 09 M 2) received the B.Eng. and B.Ec. degrees in eectrica information engineering and internationa economics and trade from the orthwest University, Shaanxi, China, in 2006 and the M.Sc. Distinction) and Ph.D. degrees in eectrica and eectronic engineering from Loughborough University, Loughborough, U.K., in 2008 and 202, respectivey. From 2008 to 2009, he was a Software Engineering with DTmobie, Beijing, China, and from 202 to 203, he was a Research Associate with the Schoo of Eectronic, Eectrica and Systems Engineering, Loughborough University, Loughborough, U.K. From 204 to 205, he was a Research Feow with the 5G Innovation Centre, Facuty of Engineering and Physica Sciences, University of Surrey, Surrey, U.K. He is currenty a Research Associate with the Department of Engineering Science, University of Oxford, Oxford, U.K. His current research interests incude information theory, wireess communications, cooperative communications, cognitive radio, secrecy communication, and random geometric networks. Jonathon A. Chambers S 83 M 90 SM 98 F ) received the Ph.D. and D.Sc. degrees in signa processing from the Imperia Coege of Science, Technoogy and Medicine Imperia Coege London), London, U.K., in 990 and 204, respectivey. From 99 to 994, he was a Research Scientist with the Schumberger Cambridge Research Centre, Cambridge, U.K. In 994, he returned to Imperia Coege London as a Lecturer in signa processing and was promoted to Reader Associate Professor) in 998. From 200 to 2004, he was the Director of the Centre for Digita Signa Processing and a Professor in signa processing with the Division of Engineering, King s Coege London. From 2004 to 2007, he was a Cardiff Professoria Research Feow with the Schoo of Engineering, Cardiff University, Cardiff, U.K. In , he ed the Advanced Signa Processing Group, the Schoo of Eectronic, Eectrica and Systems Engineering, Loughborough University, Loughborough, where he is now a Visiting Professor. In 205, he joined the Schoo of Eectrica and Eectronic Engineering, ewcaste University, ewcaste upon Tyne, U.K., where he is a Professor in signa and information processing and heads the Communications, Sensors, Signa and Information Processing Research Group ComS 2 IP). He is aso a Guest Professor with Harbin Engineering University, Harbin, China. He is a coauthor of the books Recurrent eura etworks for Prediction: Learning Agorithms, Architectures and Stabiity ew York, Y, USA: Wiey, 200) and EEG Signa Processing ew York, Y, USA: Wiey, 2007). He has advised more than 60 researchers through to Ph.D. graduation and pubished more than 400 conference proceedings and journa artices, many of which are in IEEE journas. His research interests incude adaptive and bind signa processing and their appications. Dr. Chambers is a Feow of the Roya Academy of Engineering, U.K., and the Institution of Eectrica Engineers. He was the Technica Program Chair of the 5th Internationa Conference on Digita Signa Processing and the 2009 IEEE Workshop on Statistica Signa Processing, both hed in Cardiff, U.K., and a Technica Program Cochair of the 36th IEEE Internationa Conference on Acoustics, Speech, and Signa Processing, Prague, Czech Repubic. He received the first QinetiQ Visiting Feowship in 2007, for his standing contributions to adaptive signa processing and his contributions to QinetiQ, as a resut of his successfu industria coaboration with the internationa defense systems company QinetiQ. He has served on the IEEE Signa Processing Theory and Methods Technica Committee for six years and the IEEE Signa Processing Society Awards Board for three years. He is currenty a member of the IEEE Signa Processing Conference Board and the European Signa Processing Society Best Paper Awards Seection Pane. He has aso served as an Associate Editor for the IEEE TRASACTIOS O SIGAL PROCESSIG for three terms over the periods and and since 20 as a Senior Area Editor.