Cooperative Hybrid-ARQ Protocols: Unified Frameworks for Protocol Analysis

Transcription

1 Cooperative Hybrid-ARQ Protocols: Unified Fraeworks for Protocol Analysis Ilu Byun and Kwang Soon Ki Cooperative hybrid-autoatic repeat request (HARQ) protocols, which can exploit the spatial and teporal diversities, have been widely studied. The efficiency of cooperative HARQ protocols is higher than that of cooperative protocols because retransissions are only perfored when necessary. We classify cooperative HARQ protocols as three decode-and-forward-based HARQ (DF-HARQ) protocols and two aplified-andforward-based HARQ (AF-HARQ) protocols. To copare these protocols and obtain the optiu paraeters, two unified fraeworks are developed for protocol analysis. Using the fraeworks, we can evaluate and copare the axiu throughput and outage probabilities according to the SNR, the relay location, and the delay constraint. Fro the analysis we can see that the axiu achievable throughput of the DF-HARQ protocols can be uch greater than that of the AF-HARQ protocols due to the increental redundancy transission at the relay. Keywords: Cooperation, hybrid-arq, half-duplex, decode-and-forward, aplified-and-forward. anuscript received Oct. 5, 010; revised ar. 8, 011; accepted ar. 19, 011. This research was supported by the inistry of Knowledge Econoy (KE), Rep. of Korea, under the Inforation Technology Research Center (ITRC) support progra supervised by the National IT Industry Prootion Agency (NIPA) (NIPA-011-C ). Ilu Byun (phone: , eail: and Kwang Soon Ki (corresponding author, eail: are with the Departent of Electronic and Electrical Engineering, Yonsei University, Seoul, Rep. of Korea. I. Introduction In wireless obile counication systes, various diversity techniques, such as tie, frequency, and spatial diversity techniques, have been investigated to achieve spectrally efficient and reliable counications over fading channels [1]- [4]. Aong the, cooperation diversity techniques, which have been widely studied, can provide spatial diversity by cooperating between users. In cooperative counication systes, distributed antennas of different users are fored as a virtual array by sharing their antennas and tie/frequency resource to achieve the spatial diversity. Autoatic repeat request (ARQ) is a coon technique used to ake a wireless link reliable. The cooperative protocols can adopt the ARQ technique by exploiting feedbacks fro the relay and destinations. Since the relay or source retransits only when the destination wants to, the efficiency of cooperative ARQ protocols is better than that of cooperative protocols without ARQ. This perforance iproveent of cooperative ARQ protocols has been shown in literature [5]-[7]. In [5], it was shown that the increental relaying protocol, which can be viewed as an extension of a hybrid-arq (HARQ) into a cooperative context, outperfors the fixed relaying protocol in ters of its outage behavior. In [6], a dynaic decode-and-forward (DDF)-based ARQ protocol was proposed for two cooperating single-antenna terinals and a double-antenna destination. It was shown that it can achieve the optial diversity-ultiplexing (D-) tradeoff when the nuber of retransissions goes to infinity. In [7], it was shown that the DDF-based ARQ protocol can achieve the optial D- tradeoff in a single user relay channel when the axiu allowable nuber of transissions is greater than. The perforance of a cooperative ARQ protocol and that of a ETRI Journal, Volue 33, Nuber 5, October Ilu Byun and Kwang Soon Ki 759

2 non-cooperative ARQ protocol were also copared in [8]. It was shown that a practical cooperative ARQ protocol using a convolutional code is better than a non-cooperative ARQ protocol. Inspired by these perforance iproveents, extended versions of previous cooperative protocols cobined with ARQ or HARQ schee were proposed and analyzed in [9]- [11]. In [9], three cooperative ARQ protocols, which cobine the increental relaying with the selection relaying, were proposed. Their outage behaviors were shown for a siple ARQ schee without packet cobining. In [10], cooperative HARQ protocols for ultiple relays were proposed for increental redundancy HARQ (IR-HARQ) techniques, and the upper bound of an increental redundancy-based protocol was developed. In [11], the outage probability and the power allocation between the source and relay of a cooperative ARQ protocol were analyzed. The achievable throughput of these cooperative ARQ protocols is changed according to channel odel and environent, such as the relay location, path loss, and signal-to-noise ratio (SNR). Thus, it is difficult to copare these cooperative ARQ protocols using previous analysis ethods such as the outage behavior and the D- tradeoff. In the D- tradeoff analysis, the relay location, which is one of the doinant factors in deterining perforance, is not considered. Soe protocol paraeters, such as the initial transission rate and the axiu nuber of transissions (or the delay constraint), cannot be optiized because the D- tradeoff provides a fundaental but only asyptotic perforance. Outage behavior is also highly affected by the initial transission rate. Thus, it is necessary to develop unified fraeworks that can analyze and copare protocols considering each protocol s characteristic. In this paper, two unified fraeworks are developed. One is for DF-based cooperative HARQ (DF-HARQ) protocols (DF- HARQs), and the other is for AF-based cooperative HARQ (AF-HARQ) protocols (AF-HARQs). The DF-HARQs are classified into three types, and the AF-HARQs are classified into two types. (They are specifically described later.) The HARQ technique considered in this paper is the IR-HARQ technique due to its better perforance over the Chase cobining HARQ schee [1]. In the DF-HARQs, only the IR-HARQ schee is used. On the other hand, in the AF- HARQs, both the IR-HARQ and the Chase cobining schees are considered because the relay just forwards the aplified packet to the destination. Furtherore, the perforance of each protocol is evaluated under two different power constraint scenarios. One is peak power (PP) constraint, where each terinal uses the sae power for a transission. The other is step power (SP) constraint, where the transission power for each step is preserved. Thus, the analytical fraework provided in this paper is quite eaningful because: (i) it provides a unified approach for the analysis of cooperative HARQ protocols; (ii) it provides actual perforance coparison aong different protocols, which can be only done in an asyptotical anner with previous approaches; and (iii) such an analysis, considering the characteristic of each protocol, can be used to optiize the perforance of each protocol according to channel and environent; and (iv) the fraework can be used for adapting a protocol according to network topology. The rest of this paper is organized as follows. In section II, the signal odel and the cooperative HARQ protocols are described. In section III, the analytical fraeworks are developed for the DF/AF-HARQs. The axiu achievable throughput of the cooperative HARQ protocols are obtained and copared in section IV. Finally, the concluding reark is given in section V. II. Protocol Description and Signal odel 1. Protocol Description In this paper, we consider a single relay network with three half-duplex terinals which consists of a source (S), a destination (D), and a relay (R). Also, we assue block fading channels, which reain constant over a block but varies independently fro one block to another, and the degree of freedo of a block is L. The cooperative HARQ protocols considered in this paper are the extensions of cooperative protocols or the cooperative ARQ protocols. We classify the DF-HARQs into three types, and the AF-HARQs into two types. In the DF-HARQs, DF1 includes the selection and increental relaying DF protocol in [13], protocol 1 in [9], and it is siilar to the AC layer protcol in [0]. DF is an extended version of protocol in [13]. DF3 includes the protocol with a single relay in [11] and the DDF protocol when re 0.5 in [7], [14]. In the AF- HARQs, AF1 includes the selection and increental relaying AF protocol in [5] and protocol 3 in [13]. AF includes protocol 3 in [13] and the NAF protocol when in re 0.5 [14]. In the DF/AF-HARQs, the source and/or relay transit a packet to the destination until the destination decodes or the nuber of transissions reaches the axiu nuber of transissions. The DF/AF-HARQs have two steps for an ARQ round, and the axiu nuber of transissions allowed for each step is. An ARQ round of the DF- HARQs starts fro step 1, and step begins if the relay decodes a packet but the destination does not. They are described as follows: 760 Ilu Byun and Kwang Soon Ki ETRI Journal, Volue 33, Nuber 5, October 011

3 DF1. In step 1, S broadcasts a packet to D and R. In step, S does not transit a packet but R transits a packet to D. DF. In step 1, S transits a packet to R but D does not receive a packet. In step, both S and R transit a packet to D as a virtual array using the Alaouti code. DF3. In step 1, S broadcasts a packet to D and R. In step, both S and R transit a packet to D as a virtual array using the Alaouti code. An ARQ round of the AF-HARQs starts fro step 1. The odd (even) transissions of the AF-HARQs are step 1 (step ). They are described as follows: AF1. In step 1, S broadcasts a packet to D and R. In step, R forwards the aplified packet to D but S does not transit. AF. In step 1, S broadcasts a packet to D and R. In step, both S and R transit a packet to D as a virtual array using the Alaouti code. The destination and relay transit ACK/NACK signals for retransissions. The ACK/NACK signaling is assued to be error-free for siple analysis. The resource spent for signaling ACK/NACK is also ignored since it is typically quite sall copared to that used for data transission.. Signal odel At the source and relay, the b bit inforation is encoded using the channel code with codebook C C LN of length LN over the coplex nubers [15], where N= for the DF- HARQs and N= for the AF-HARQs. The overall codeword is divided into N blocks of length L sybols, C j, which denotes the j-th code block, j=1,, N. Then, the transission rate of the first block (initial transissoin rate) r is given by r=b/l. If the destination receives the j-th codeword, it decodes using codewords {C 1 C C j }. Let x [ ] (,1[ ],...,, [ ]) T a t = xα t xα L t be the sybol vector of the packet transitted fro terinal α at the t-th block, where α {S, R}. The sybol energy is noralized as T E[ xα[ t] x α [ t]]/ L = 1 except when xα [] t is an aplified packet. The sybol vector x α [] t is changed according to protocols. For the DF-HARQs, xs [] t = Ct in step 1, x R [] t = Ct in step of DF1, and : Ct ( xs[ t], x R[ t]) in step of DF and DF3, where denotes the apping function of the Alaouti code. For the AF-HARQs, x S [] t = C t / in step 1, x R[] t = y R[ t 1] in step of AF1, and :( C t /, yr[ t 1]) ( xs[ t], x R[ t]) in step of AF. Let n [ t] ( n,1[ t],..., n, [ ]) T β = β β L t be a noise vector at terinal β in which the eleents are i.i.d. circular Gaussian rando variable with distribution CN(0, N 0 ), for β {S, R}\α. Also, let E α be the transit energy per sybol at terinal α H [] t = g h [] t be the channel between α and β, and αβ, αβ, αβ, where g α, β is the path loss gain and hαβ, [] t is a circularly Gaussian rando variable with CN(0, 1). Then, the received signal at the relay can be written as [ t] E H [ t] [ t] + [ t] y = x n. (1) R S S,R S R The received signals at the destination in step i, for i=1,, is given by y [ t] = ui E H [ t] x [ t] + v At E H [] t [] t + [] t D, i S S,D S i [] x n, () R R,D R D where u 1 =1, v 1 =0, u =0, and v =1 for DF1 and AF1; u 1 =0, v 1 =0, u =1, and v =1 for DF; and u 1 =1, v 1 =0, u =1, and v =1 for DF3 and AF. The instantaneous channel gain of the α to β link Hα, β[] t Eα can be respectively given by γ α, β[] t =, and the N0 average channel gain is given by γ αβ, = gαβ, Eα / N0. The aplification factor A[t] is 1 for the DF-HARQs, and 1/( γ [ t] + 1) for the AF-HARQs. S,R III. Analytical Fraeworks for DF/AF-HARQs In [15], [16], the throughput of point-to-point HARQ schees is analyzed. The throughput is given by r(1 p ) η =, E [ ] out τ where E[ τ ] denotes the average nuber of transissions and p out denotes the packet outage probability. Thus, the throughput of cooperative HARQ protocols can be obtained by coputing E[ τ ] and p out. In this section, two unified fraeworks for the DF-HARQs and the AF-HARQs are developed to obtain the throughput. 1. Fraework for DF-HARQs In this subsection, a unified fraework for the DF-HARQs is developed using state transition diagra approach. Let i i St( S t ) be the event denoting successful decoding (decoding failure) at the t-th transission of link i, for i=1,, 3. Then, the probability of having successful decoding at the t-th transission of link i, q i (t), is given by i i i i ( ) ( 1 1 ) (3) q t =Pr S,S, L,S,S. (4) i t t and the probability of decoding failure with t received packets of link i is given by i i i ( ) ( 1 t ) p t =Pr S,S, L,S. (5) i Then, q i (t) can be rewritten as q i (t)=p i (t 1) p i (t). The probability functions of the destination and relay in steps 1 and ETRI Journal, Volue 33, Nuber 5, October 011 Ilu Byun and Kwang Soon Ki 761

4 are defined as follows. Respectively, p 1 () and p () are the error probabilities of the destination and relay in step 1 when the -th packet is received fro the source. The outage probability with n received packets of the destination in step, while the relay successfully decodes it with received packets in step 1, is defined as p 3 (, n). Also, q 1 () and q () respectively denote the probabilities of successful decoding at the destination and relay with received packets in step 1, and q 3 (, n) denotes the probability of successful decoding at the destination with resceived packets in step 1 and n received packets in step. Figure 1 shows the state transition diagra of the DF- HARQs. Here, all branches are labeled with the corresponding transition probabilities, ultiplied by duy variables T and U. The exponents of T and U respectively denote the nuber of transissions and the rate during the transition. The states are labeled as follows: starting of one round (X s ); the state when the source transits a packet at the -th transission in step 1 (A ); the state when the relay transits the packet at the n-th transission in step after the relay successfully decodes the received packet at the -th transission (R,n ); and the end of the round when the destination decodes the packet successfully or the nuber of transissions has reached (X e ). The transition probabilities between states are listed in Table 1. In the table, p j ( 1), j=1,, denotes the conditional probability of decoding failure at the -th transission, given that the receiver has not decoded it until the ( 1)th transission, and p 3 (, n, n 1) denotes the conditional probability of decoding failure at the n-th transission in step, given that the receiver has not decoded it until the -th transission in step 1 and the (n 1)th transission in step. As derived in Appendix A, the average nuber of transissions can be calculated using the state transition diagra as 1 [ τ ] =1 + 1( ) ( ) + 1( ) ( ) [ τ '], (6) E p p p q E =1 =1 1 p n 1 3 n = where E [ τ ] = 1 + (, ). Also, the outage probability of a DF-HARQ is given by p = p p + p q p,. (7) ( ) ( ) ( ) ( ) ( ) out =1 By substituting (6) and (7) into (3), the throughput of the DF- HARQs can be obtained. Let J ( γ αβ, [ ]) be the utual inforation between α and β at the -th transission, where J ( γαβ, [ ]) = log (1 + γαβ, [ ]) for Gaussian inputs. Then, the outage probability of the destination and relay are respectively given by p1( ) =Pr J( u1γ S,D[ s] ) < r, (8) s=1 X s a b c c d,n e,n e, a 1 A 1 A A b 1 b R 11 Fig. 1. State transition diagra for DF-HARQs. b X e d 11 d 1 R 1 R 1 R 1 R R R 1 d 1 R c 1 c c e 11 e 1 e 1 e 1 e e e 1 e e Table 1. Transition probabilities for DF-HARQs. Transition probability p 1 ( 1)p ( 1)T p 1 ( 1) (1 p ( 1))T (1 p 1 ( 1)) TU r, for < (1 p 1 ( 1)) TU r +p 1 ( 1)T p 3 (, n, n 1)T (1 p 3 (, n, n 1))TU r, for n< (1 p 3 (,, 1))TU r +p 3 (,, 1)T R p( ) =Pr J( γ S,R[ s] ) < r, (9) s=1 n p3 (, n) =Pr J( u1γs,d[ s] ) + J( uγs,d[ b] + γr,d[ b] ) < r, s=1 b=1 (10) where the instantaneous SNR of the destination in step is given by γs,d[ b] + γr,d[ b] for DF and DF3 since the source and relay transit an Alaouti coded signals. The coputation coplexity of (9)-(11) can be reduced by the Gaussian approxiation. If the su of J ( γ αβ, [ ]) is not sall, the outage probability can be approxiated using the Gaussian approxiation. Let the ean of the utual k inforation be μγ ( 1,..., γk) = EJ [ ( γ[ ])] i 1 i and the = variance of the utual inforation be σ ( γ1,..., γ K ) k = VJ [ ( γ [ ])]. i 1 i Then, the outage probability of the relay = and destination are respectively given by r μ( u1γs,d) p1 ( ) 1 Q, (11) σ ( u1γs,d) 76 Ilu Byun and Kwang Soon Ki ETRI Journal, Volue 33, Nuber 5, October 011

5 r μγ ( S,R ) p ( ) 1 Q, (1) σ ( γs,r ) r μ( u1γs,d) nμ( uγs,d, γr,d) p3 (, n) 1 Q. (13) σ ( u1γs,d) + nσ ( uγs,d, γr,d) For k=1, μ( γ 1) and σ ( γ 1) were calculated in [17]. For k>1, μ( γ1,..., γk ) and σ ( γ1,..., γk ) are obtained using the nuerical integration.. Fraework for AF-HARQs To obtain the throughput and the outage probability of the AF-HARQs, a unified fraework for the AF-HARQs is developed using a state transition diagra. The error probability at the destination is defined as follows. Respectively, p 1 () and p () are the error probabilities of the destination at the -th transission in steps 1 and. Also, q 1 () and q () respectively denote the probabilities of successful decoding of the destination at the -th transission in steps 1 and. Figure shows the state transition diagra for the AF- HARQs. In the state transition diagra, all branches are ultiplied by duy variables T and U as in the case of the DF-HARQs. The states are labeled as follows: the start of a round (X s ); the state when the source broadcasts a packet in step 1 at the -th transission (A ); the state when the relay relays an aplified packet to the destination in step at the -th transission (R ); and the end of the round when the destination decodes successfully or the nuber of transissions has reached (X e ). The transition probabilities between states are listed in Table. As derived in Appendix B, the average nuber of transissions can be calculated using the state transition diagra as E = ( 1) q p 1 p q. 1 1 (14) =1 [ τ ] ( ) ( ) + ( ) ( ) Also, the outage probability of an AF-HARQ protocol is X s A 1 A A a 1 b 1 a a R 1 c 1 d 1 c d c d Fig.. State transition diagra for AF-HARQs. X e R R a b c d d given by Table. Transition probabilities for AF-HARQs. Transition probability p 1 ( 1)T p ( 1)T (1 p 1 ( 1))TU r (1 p ( 1))TU r, for n< (1 p ( 1))TU r +p ( 1)T ( ) ( ) p = p p. (15) out 1 By substituting (14) and (15) into (3), the throughput of the AF- HARQs can be obtained. In the AF-HARQs, the source transits a packet with additional redundancies at odd transissions, but the relay forwards an aplified packet without additional parities at even transissions. Thus, the outage probabilities are given by p1 ( ) = 1 Pr J ( u1γs,d[ s 1] + uγs,d[ s] +Γ [ s] ) + J( u1γs,d[ ] ) < r, s=1 1 S,D S,D s=1 where γs,r γr,d γs,r γr,d (16) p ( ) =Pr J( uγ [ s 1] + u γ [] s +Γ[] s ) < r, (17) Γ [] s = [] s []/( s [] s + [] s + 1). They can be approxiated using the central liit theore as r 0.5( 1) μ( uγ, u γ, Γ) μ( uγ ) p1 ( ) Q 1 S,D S,D 1 S,D =1, 0.5( 1) σ ( u1γs,d, uγs,d, Γ ) + σ ( u1γs,d) r 0.5 μ( uγ, u γ, Γ) p ( ) Q 1 1 S,D S,D =1, 0.5 σ ( u1γs,d, uγs,d, Γ) (18) (19) Here, μ( u1γs,d, uγs,d, Γ) and σ ( u1γs,d, uγs,d, Γ) were obtained fro the analysis in [18], [19] for both u 1 =1, u =0 and u 1 =1, u =1. Because the two fraeworks consist of the error probability of each terinal, the throughput and the outage probability of any cooperative HARQ protocol can be obtained fro knowing of the error probability corresponding to a given protocol at each terinal. Thus, the proposed analysis can be used as fraework for the analysis of any cooperative HARQ protocol. Also, the upper liit of protocol perforance can be obtained fro an inforation theoretic easure as well as the ETRI Journal, Volue 33, Nuber 5, October 011 Ilu Byun and Kwang Soon Ki 763

6 actual perforance fro the easured or siulated error probabilities using practical odulation and coding schees. IV. Siulation Results In this section, siulation is perfored and copared with the analysis for the DF/AF-HARQs. The cooperative syste is assued to be a one-diensional linear relay network for siplicity. Let the distance between the source and the destination be 1 and the distance between the source and the relay be d. The channel is assued to be an i.i.d Rayleigh block fading. The long-ter average channel gain of each link is set to be g S,D =1 for the source-to-destination link, g S,R =d a for the source-to-relay link, and g R,D =(1 d) a for the relay-todestination link, where the path-loss exponent a is set to 4. The optiu initial transission rate is searched stepwisely with high-resolution quantization. We assue that the average transit power of the source and relay are the sae. For perforance coparison, we consider the PP constraint, where the source and relay transit packets with the sae power, and the SP constraint, where the total transission power in a step is constrained and the transission power in step is equally divided to the source and relay. For exaple, in DF3 with the PP constraint, E S in step 1 is equal to E S in step and E R in step. However, in DF3 with the SP constraint, the half of E S in step 1 is equal to E S in step and E R in step. In this section, DF1, DF, and DF3 are obtained fro (6) and (7) shown in subsection III.1, and AF1 and AF are obtained fro (14) and (15) shown in subsection III.. Also, DF siul. and AF siul. are obtained by onte Carlo siulations. 1. Peak Power Constraint In this subsection, we obtain the axiu throughput of the DF/AF-HARQs under the PP constraint. Also, E s /N 0 denotes the long-ter averaged SNR between the source and destination. Respectively, DF siul. and AF siul. denote the throughput obtained fro the siulation of the DF- HARQs and the AF-HARQs. Fro Figs. 3 and 4, it is shown that the analysis for the DF-HARQs atches with the siulation results quite accurately. The analysis of the AF- HARQ protocol is also quite close to the siulation results. The sall deviations in the AF-HARQ case is due to the PDF approxiations in [18], [19]. Such deviation increases as the relay deviates fro the center location. However, it is at ost several percentages as shown in Figs. 3 and 4. Figure 3 shows the axiu throughput of the cooperative HARQ protocols according to d when E s /N 0 is 4 db and 1 db. Aong the DF-HARQs, DF3 outperfors DF over all ranges of d and outperfors DF1 in the region of d 0.5. axiu throughput (b/s/hz) db DF1 DF DF3 DF siul. AF1 AF AF siul db Relay location (d) Fig. 3. axiu throughput coparison aong protocols according to d under PP constraint when =0. axiu throughput (b/s/hz) db DF1 DF DF3 DF siul. 4 db AF1 AF AF siul Relay location (d) Fig. 4. axiu throuhgput coparison aong protocols according to d under PP constraint when =. Where d>0.5, DF1 and DF3 show siilar perforance in which the space-tie code does not iprove the perforance because the source signal is uch ore attenuated than the relay signal. Also, it is observed that although DF1 outperfors DF over all ranges of d when the SNR is high (1 db), DF1 can be worse than DF when the SNR is low and d is sall due to the high error probability at the first transission in DF1. Aong the AF-HARQs, AF outperfors AF1 over all ranges of d, and the perforance difference slightly increases as the relay deviates fro the center region. Under the PP constraint, the average transission energy in step of DF3 and AF is greater than that of DF1 and AF1, which respectively results in better perforance of DF3 and AF over DF1 and AF1. Interesting observation can be obtained by coparing the DF- HARQs with the AF-HARQs. Previously, it was believed that 764 Ilu Byun and Kwang Soon Ki ETRI Journal, Volue 33, Nuber 5, October 011

7 the AF protocol has the sae perforance as the DF protocol in ters of the D- tradeoff [14]. However, cobined with the HARQ schees, the DF-HARQs outperfor the AF-HARQs over all range of SNR when d=0.5. The reason is that, in the AF-HARQs, the relay cannot transit additional redundancy because the relay does not decode but just forwards the aplified packet. However, in the DF-HARQs, the relay can transit additional redundancy. Thus, the perforance of the DF-HARQs is better than that of the AF-HARQs. Figure 4 shows the axiu throughput of the cooperative HARQ protocols according to d when =. Although the axiu throughput of each protocol decreases, the relative perforance aong the DF-HARQs (or the AF-HARQs) is siilar in the case when the axiu nuber of transissions is large (=0). However, in this delay constraint case, all DF-HARQs cannot outperfor the AF- HARQs since the perforance gain by additional redundancy fro the relay of DF-HARQs is liited. When the relay is not near the destination, DF1 and DF3 are better than the AF- HARQs. When the SNR is low (4 db), AF outperfors all DF-HARQs in the region where the relay is near the destination. When the SNR is high, the AF-HARQs outperfor DF, except the region where the relay is close to the source. The value of d, which axiizes the throughput of each protocol, ay also change according to the delay constraint. Although DF, AF1, or AF shows its best perforance when the relay is near the center, the value of d axiizing the throughput of DF1 or DF3 oves to the source as the delay constraint becoes tight.. Step Power Constraint Figure 5 depicts the axiu throughput of the DF/AF- HARQs under the SP constraint. It is observed that it is different to that of the PP constraint. Aong the DF-HARQs, DF1 and DF3 outperfor DF over alost all regions of d, but the axiu throughput of DF1 is greater than that of DF3 oppositely to the PP constraint case. Siilarly, the axiu throughput of AF1 is greater than that of AF in the region of d 0.6. On the other hand, the axiu throughput of AF is greater than that of AF1 in the region of d>0.6. The above observations are very interesting because they are different fro the previously known results of coparing cooperative protocols without HARQ. Aong the AF-HARQs, AF1 and AF without an HARQ schee are, respectively, atched to LTW-AF and NAF in [14]. The D- tradeoff of the NAF is also better than that of LTW-AF. However, AF1 can outperfor AF in any cases. The reason is that the transission power is divided to the source and the relays to obtain diversity gain in AF. However, perforance loss by the axiu throughput (b/s/hz) db DF1 DF DF3 AF1 AF db E s /N 0 Fig. 5. axiu throughput coparison aong protocols according to d under SP constraint when =0. path-loss is greater than the diversity gain in any cases. 3. Initial Transission Rate In this subsection, the tradeoff between the initial transission rate (r) and delay ( and the average delay) is shown for DF1 under the PP constraint. Although not shown explicitly, siilar results and discussion can be obtained for other protocols. To copare the throughput aong various s, the worstcase coding-rate, R=r/, is used. Figure 6 shows the throughput of DF1 according to R under the PP constraint. As can be seen in Fig. 6, when R is sall, the throughput increases as R increases. However, when R is large, the throughput decreases as R increases. This is because p out increases as R increases, and it becoes a doinant factor of perforance degradation when R is too large. This trend of DF1 is siilar to that of the IR-HARQ protocol which is shown in [16]. Additionally, it is seen that the region of R, where the throughput decreases sharply, is consistent over all values of. Thus, for a given, the constraint for the initial transission rate can be set to * r < R ( d, SNR), (1) where R * (d, SNR) is defined as the infiu of the worst-case coding-rate yielding zero throughput when goes to infinity, which is a function of the relay location d and the long-ter averaged SNR. Figure 7 shows the optiu initial transission rate r* in ters of the throughput according to under the PP constraint. Fro this figure, it is easily seen that r* increases alost linearly as increases. Thus, r* for, r*(, d, SNR), can be obtained as ETRI Journal, Volue 33, Nuber 5, October 011 Ilu Byun and Kwang Soon Ki 765

8 Throughput (b/s/hz) =1 =5 =10 =0 =100 d=0.5, E s /N 0 =10 db R Fig. 6. Throughput of DF1 according to R under PP constraint. r*(, d, SNR) d=0.1 d=0.5 d=0.9 DF1 1 db 4 db axiu nuber of transissions () Fig. 7. Optiu initial transission rate according to under PP constraint. where r * (, d, SNR)= a( d, SNR), () r * (, d, SNR) adsnr (, )= li. In order to apply the above optiization and tradeoff, R*(d, SNR) and a(d, SNR) should be easily calculated fro the knowledge of d and SNR, which reains for future work. 4. Application Exaple The unified fraeworks also can be used for adapting protocols. The protocol adaptation can be used for carrier sense ultiple access/collision avoidance (CSA/CA)-based cooperative AC protocols which are used for various ad-hoc axiu throughput (b/s/hz) DF adapt. DF1 DF3 =0, E s /N 0 =1 db AF adapt. AF1 AF Fig. 8. axiu throughput when DF-HARQ (AF-HARQ) is adaptively selected according to network topology. networks such as ZigBee, UWB, and wireless local area networks (WLANs). As shown in [1], [], cooperative AC prootcols based on the CSA/CA decides its relay with the request-to-send (RTS) and clear-to-send (CTS) signaling, and an source-destination pair who picks up a relay at first can use the relay. Also, the protocol adaptation can be perfored using the inforation of a protocol (for exaple, protocol index) included in the RTS/CTS signaling. In WLANs, protocols can be adapted according to the network topology. For exaple, DF1 (AF1) can be used to iprove the throughput when a source has two different data streas for two destinations. Let D A and D B be the destinations of a source and R A and R B be respectively the relays for the destinations. Then, the source transits a packet to D A and R A (D B and R B ), while R B (R A ) transits a packet to D B (D A ). In the siilar anner, DF can be used when a destination has two different data streas which are received fro different sources. Figure 8 shows the axiu througput of the DF- HARQs and AF-HARQs with a protocol adaptation under the PP constraint when =0 and E s /N 0 =1 db. It is obtained under the assuption that a source could have at ost two destinations. Here, ρ denotes the ratio of source nodes to destination nodes in a WLAN network. If ρ is greater than 1, a part of source nodes in the network should have two destinations. In Fig. 8, DF adapt. denotes an adaptive protocol between DF1 and DF3 and AF adapt. denotes an adaptive protocol between AF1 and AF. Figure 8 shows that the DF (AF) adapt outperfors the protocols without the protocol adaptation. Fro the result, we can expect that the su throughput of WLANs can be increased by the protocol adaptation according to the network topology. ρ 766 Ilu Byun and Kwang Soon Ki ETRI Journal, Volue 33, Nuber 5, October 011

9 V. Conclusion In this paper, three DF-HARQs and two AF-HARQs were analyzed and copared. A unified fraework was proposed for each type of cooperative HARQ protocols, which can provide actual perforance evaluation with respect to channel and environent. The fraework can be used for adapting a protocol accroding to the network topology. For exaple, a protocol adaptation can be used for a cooperative AC protocol based on the CSA/CA protocol which can be used for ZigBee, UWB, and WLANs. By obtaining real perforance coparisons aong protocols fro the fraework, it was shown that the throughput and relative perforance of the cooperative HARQ protocols varied according to the relay location, the axiu nuber of transissions (or the delay constraint), the initial transission rate, and the power constraint. Interesting observations fro the analysis are as follows: (i) the axiu achievable throughput of the DF-HARQs can be uch greater than that of the AF-HARQs due to the IR transission at the relay; (ii) protocols having worse D- tradeoff without HARQ schee can outperfor protocols having better D- tradeoff in any cases when HARQ schee is cobined; (iii) the region axiizing the throughput of each protocol changes according to the relay location, the axiu nuber of transissions, and the long-ter averaged SNR; and (iv) it was shown that there is an optiu initial transission in ters of throughput, and it is alost a linear function of the axiu nuber of transissions, in which the gradient is the function of the relay location and the long-ter averaged SNR. Developing a siple algorith that evaluates the optiu initial transission rate for a practical syste reains future work. Appendix A Fro the transition probabilities, the probabilities for each state are given as A 1 =X s, A =a 1 A 1, R, 1 =b A, R,n =d,n 1 R,n 1, X e= c 1 A+ e 1 1, nr, n. = = By substituting n= the transition probabilities shown in Table 1 into the, we obtain 1 ( ) ( ) A = p 1 p 1 T A, (3) 1 1 ( )( ( ) ( )) R = p p 1 p T A, (4),1 1 1 n 1 ( ) R = p, n 1 T R. (5) n, 3,1 Using the above equations, X e can be siplified as r X e = A1 q1( ) p( 1) T U X + Z =1 + + =1 n=1 n r R1, q3 (, n) T U Z, (6) 3. The where Z = p ( ) p ( ) T and = (, ) 1 Z p T transfer function of the state transition diagra of the DF- HARQs, f ( TU, ) = X / X, is then given by e s r f ( T, U) = q1( ) p( 1) T U + Z =1 n r p1( ) q( ) T q3( n) T U p3( ) T =1 n=1 +, +,, (7) where the average transission nuber E[ τ ] = df ( T, U )/ dt T = 1, U = 1 and the average transission rate r(1 pout ) = df( T, U) / du T = 1, U = 1 can be obtained by differentiating the transfer function by T and U. The packet outage probability p out can be obtained fro the average transission rate. Appendix B In the state transition diagra of the AF-HARQs, the probabilities of each state are given as A 1 =X s, A =b R 1, R =a A, and X e = c. 1 A + dr = By substituting the transition probabilities shown in Table into the, we obtain A = p ( 1) p ( 1) T A, (8) ( 1) 1 1 R = p ( ) p ( 1) T A. (9) Using the above results, X e can be siplified as 1 r X e = q1( ) p( 1) T U Xs =1 r + p1( ) q( ) T U Xs. (30) Thus, the transfer function of the AF-HARQs, f(t,u)=x e /X s, is given by 1 r 1 1 r =1 f ( T, U) = q ( ) p ( 1) T U + p ( ) q ( ) T U. (31) By differentiating the transfer function by T and U, the average transission nuber E[ τ ] = df( T, U)/ dt T= 1, U= 1 and the average transission rate r(1 pout ) = df ( T, U )/ du T = 1, U = 1 can be respectively obtained. The packet outage probability p out can be obtained fro the average transission rate. ETRI Journal, Volue 33, Nuber 5, October 011 Ilu Byun and Kwang Soon Ki 767

10 References [1] G.J. Foschini, Layered Space-Tie Architecture for Wireless Counication in a Fading Environent When Using ulti- Eleent Antennas, Bell Lab Tech. J., Autun 1996, pp [] S.. Alaouti, A Siple Transit Diversity Technique for Wireless Counication, IEEE J. Sel. Areas Coun., vol. 16, Oct. 1998, pp [3] V. Tarokh, H. Jafarkhani, and A.R. Calderbank, Space-Tie Block Codes fro Orthogonal Designs, IEEE Trans. Infor. Theory, vol. 45, July 1999, pp [4] L. Zheng, D.N.C. Tse, and G.W. Wornell, Diversity and ultiplexing: A Fundaental Tradeoff in ultiple-antenna Channels, IEEE Trans. Infor. Theory, vol. 49, ay 005, pp [5] J.N. Lanean, D.N.C. Tse, and G. W. Wornell, Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior, IEEE Trans. Infor. Theory, vol. 50, Dec. 004, pp [6] Y.-H. Na et al., Cooperation through ARQ, Proc. IEEE Signal Proc. Adv. Wireless Coun., New York, NY, June 005, pp [7] K. Azarian, H.E. Gaal, and P. Schniter, On the Optiality of the ARQ-DDF Protocol, IEEE Trans. Infor. Theory, vol. 54, no. 4, Apr. 008, pp [8] E. Zierann, P. Herhold, and G. Fettweis, The Ipact of Cooperation on Diversity-Exploiting Protocols, Proc. IEEE Veh. Technol. Conf., vol 49, ilan, Italy, ay 004, pp [9] G. Yu, Z. Zhang, and P. Qiu, Cooperative ARQ in Wireless Networks: Protocols Description and Perforance Analysis, Proc. IEEE Int. Conf. Coun., vol. 8, Istanbul, Turkey, June 006, pp [10] I. Stanojev, O. Sieone, and Y. Bar-Ness, Perforance Analysis of Collaborative Hybrid-ARQ Increental Redundancy Protocols over Fading Channels, Proc. IEEE Signal Proc. Adv. Wireless Coun., Cannes, France, July 006, pp [11] S. Lee et al., Cooperative Decode-and-Forward ARQ Relaying: Perforance Analysis and Power Optiization, IEEE Trans. Wireless Coun., vol. 9, no. 8, Aug. 010, pp [1] T.E. Hunter, S. Sanayei, and A. Norsratinia, Outage Analysis of Coded Cooperation, IEEE Trans. Infor. Theory, vol. 5, no., Feb. 006, pp [13] R.U. Nabar, H. Bölsckei, and F.W. Kneubühler, Fading Relay Channels: Perforance Liits and Space Tie Signal Design, IEEE Trans. J. Sel. Areas Coun., Aug. 004, pp [14] K. Azarian, H. El Gaal, and P. Schniter, On the Achievable diversity-ultiplexing Tradeoff in Half-Duplex Cooperative Channels, IEEE Trans. Infor. Theory, Dec. 005, pp [15] G. Caire and D. Tuninetti, The Throughput of Hybrid ARQ Protocols for the Gaussian Collision Channel, IEEE Trans. Infor. Theory, vol. 47, no. 5, July 001, pp [16] S. Sesia, G. Caire, and G. Vivier, Increental Redundancy Hybrid ARQ Schees Based on LDPC Codes, IEEE Trans. Coun., vol. 5, no. 8, Aug. 004, pp [17] W. Peng, Perforance of Hybrid-ARQ in Block-Fading Channels: A Fixed Outage Probability Analysis, IEEE Trans. Cou., vol. 58, no. 4, Apr. 008, pp [18] P.A. Anghel and. Kaveh, Exact Sybol Error Probability of a Cooperative Network in a Rayleigh-Fading Environent, IEEE Trans. Wireless Coun., vol. 3, no. 5, Sept [19].O. Hasna and.s. Alouini, A Perforance Study of Dual- Hop Transissions with Fixed Gain Relays, IEEE Trans. Wireless Coun., vol. 3, no. 6, Nov. 004, pp [0] C. Nie et al., CoopAX: A Cooperative AC with Randoized Distributed Space-Tie Coding for an IEEE Network, Proc. IEEE Conf. Int. Conf. Coun., Dresden, Gerany, June 009, pp [1] P. Liu et al., CoopAC: A Cooperative AC for Wireless LANs, IEEE J. Sel. Area Coun., vol. 5, no., Feb. 007, pp [] H. Shan, W. Zhuang, and Z. Wang, Distributed Cooperative AC for ultihop Wireless Networks, IEEE Coun. ag., vol. 47, no., Feb. 009, pp Ilu Byun received the BS and S in electrical and electronic engineering fro Yonsei University, Seoul, Rep. of Korea, in 005 and 007, respectively. Since 007, he has been pursuing the PhD at Yonsei University. His current research interests include ratecopatible channel codes, ad-hoc networks, and hybrid networks. Kwang Soon Ki received the BS (sua cu laude), SE, and PhD in electrical engineering fro Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Rep. of Korea, in February 1994, February 1996, and February 1999, respectively. Fro arch 1999 to arch 000, he was with the Departent of Electrical and Coputer Engineering, University of California at San Diego, CA, USA, as a postdoctoral researcher. Fro April 000 to February 004, he was with the obile Telecounication Research Laboratory, ETRI, Daejeon, Rep. of Korea, as a senior eber of research staff. Since arch 004, he has been with the Departent of Electrical and Electronic Engineering, Yonsei University, Seoul, Rep. of Korea, where he is now is an associate professor. He was a recipient of the postdoctoral fellowship fro Korea Science and Engineering Foundation (KOSEF) in Ilu Byun and Kwang Soon Ki ETRI Journal, Volue 33, Nuber 5, October 011

11 He received the Outstanding Researcher Award fro ETRI in 00 and the Jack Neubauer eorial Award (Best Syste Paper Award, IEEE Transactions on Vehicular Technology) fro IEEE Vehicular Technology Society in 008. His research interests include counication theory, channel coding, ultiuser/ulticell IO, capacity and cross-layer optiization of wireless networks, and crosslayer optiization of heterogeneous cellular networks. ETRI Journal, Volue 33, Nuber 5, October 011 Ilu Byun and Kwang Soon Ki 769