Analysis of Packet Combining for Single Carrier Multi-Relay Broadband System

Transcription

1 Anayss o Packet Combnng or Snge Carrer Mut-Reay Broadband System Houda Chanaj ark At-Idr Ham Yankomerogu + and Samr Saoud Communcatons Systems Department INP Madnat A Irane Rabat Morocco INSIU ELECOM/ ELECOM Bretagne Sgna and Communcatons Department CS Brest Cedex France. + Broadband Communcatons and Wreess Systems (BCWS) Centre Department o Systems and Computer Engneerng Careton Unversty Ottawa Canada Emas: houda.chanajsamr.saoud@teecom-bretagne.eu atdr@eee.org ham@sce.careton.ca Abstract hs paper ocuses on packet combnng or mut-reay systems operatng over mutpe-nput mutpe-put (MIMO) broadband channe. he work presented n ths paper s vad or both ampy-andorward (AF) and decode-and-orward (DF) reayng schemes. Frst we drve a communcaton mode n such a way that the destnaton can see the receved sgnas durng the reayng sots as drect retransmssons rom the source. We then present a mut-sot communcaton mode where transmsson over reayng sots s transated nto vrtua receve antennas and examne the age probabty o derent reayng schemes. Usng smuatons we show that ths schemes perorm each other dependng on the reays ocaton and demonstrate that the mutreay transmssons provde better dversty gan than the conventona hybrd-automatc repeat request (ARQ). Index erms Cooperatve reayng mutpe-antenna systems packet combnng age probabty. I. INRODUCION In wreess networks the presence o dversty between the source and the destnaton s a key requrement to combat channe adng and enabe communcaton at hgh spectra ecences. In ths paper we concentrate on tempora and spata dversty. ARQ combned wth orward error correcton (FEC) s a popuar mechansm to expot tempora dversty. hs mechansm has been studed or many years and s st recevng consderabe attenton ] 2]. However t suers rom tempora dversty mtatons especay n sow adng envronments. In 3] the authors have proposed cooperatve reayng transmsson as a son or mtgatng these dversty mtatons. hs cooperatve dversty verson expots the broadcast nature o the wreess channe and adds spata dversty by ncorporatng reays n the network. he reays pay the roe o packet retransmtters nstead o the source thereby creatng an ndependent channe to ncrease the dversty order. Cooperatve reayng presents a good aternatve to cassca ARQ and s becomng an area o wde nterest or many researchers (see or nstance 4] 5]). In ths new transmsson mechansm one or more reays assst the communcaton between the source and destnaton to orm a MIMO system and thereore bud up space tme dversty branches that are expoted at the destnaton. Severa nterestng reayng schemes have been proposed among whch are two basc modes: ampy-and-orward (AF) and decodeand-orward (DF). he AF strategy represents the smpest way that a reay may cooperate wth the source and the destnaton. Under ths scheme the reay smpy ampes the receved sgna and orwards t towards the destnaton. However n the DF scheme the reay rst decodes the sgna receved rom the source re-encodes and retransmts t to the destnaton. hs approach suers rom error propagaton when the reay transmts an erroneousy decoded data bock 6] 7]. Seectve DF where the reay ony transmts when t can reaby decode the data packet has been ntroduced as an ecent method to reduce error propagaton 8]. However the unsuccessu detecton o the data packet by one or more reays can mt the benet o reayng. In act or each ncorrecty detected packet there s a waste o one tme sot. o prevent the ncurrng sence a moded seectve DF scheme has been proposed n 6] 9]. In ths scheme when the reay as to correcty decode the packet t sends back a negatve acknowedgment (NACK) message to the source that drecty transmts the packet to the destnaton durng the sot aocated to the reay. In ths paper we reer to ths scheme as ACK/NACK-aded DF. In ths paper we consder a broadband mut-reay system operatng under the ramework o protoco II where the source broadcasts the data packet to both the reay and the destnaton durng the rst sot whe durng the second sot ony the reay sends the packet to the destnaton0]. We ocus on cooperatve ARQ communcaton where the eedback rom the destnaton s expoted and the packet repetton s actvated ony the destnaton as to decode the data packet ] 2]. Frst we derve an uned communcaton mode or the reayng schemes under consderaton n ths paper.e. AF Seectve DF and ACK/NACK-aded DF. We then derve a mut-sots communcaton mode that heps at the destnaton sde to perorm the combnaton o packets receved over mutpe sots. We aso nvestgate the age probabty o derent reayng schemes. o the best o the authors knowedge prevous works that addressed age anayss o reay communcaton systems have ocused on the case o snge reay transmssons (see or nstance 8] and 3]). In ths paper we provde age anayss o mutreay mut-sot cooperatve ARQ. Usng smuatons we show that the studed reayng schemes perorm each other dependng on reay ocatons and demonstrate that the mut-reay transmssons provde better dversty gan than the conventona hybrd-arq. hrough the paper we use the oowng notaton: (.) and (.) H are the transpose and the transpose conjugate o the argument respectvey. denotes the empty set. dag {X X m denote the bock dagona matrx constructed rom X X m C n n 2 respectvey. For x C N x denotes the dscrete Fourer transorm (DF) o x.e. x = U N x wth U N = U I N where I N s the N N dentty matrx U s a untary matrx whose (m n)th eement s (U ) mn = e j(2πmn/ ) j = and denotes the Kronecker product. he remander o the paper s organzed as oows: In Secton II we ntroduce the uned communcaton mode or the reayng schemes together wth the mut-sot bock communcaton mode. In Secton III we nvestgate the age probabty o the consdered reayng schemes. Outage anayss s provded n Secton IV. Fnay the paper s concuded n Secton V.

2 2 II. RELAY SYSEM MODEL A. Mut-Reay ransmsson Scheme We consder a mut-reay-asssted wreess communcaton system where the M S antenna source termna denoted as S transmts normaton bocks to the M D antenna destnaton termna denoted as D wth the assstance o K dedcated reays denoted as R 2 R k R K. Each reay R k s equpped wth M Rk transmt and receve antennas. We consder a reayng system usng up to K sots or sendng one normaton bock rom the source to the destnaton where each sot spans channe uses. Durng the rst sot the source broadcasts the data packet to the K reays and the destnaton. Durng the oowng sots each reay partcpates to the packet retransmsson durng the aocated sot and keeps sent durng the other sots. In ths work we ocus on cooperatve ARQ communcaton where the eedback rom the destnaton s expoted and packet retransmsson s actvated ony the destnaton as to decode the data packet. hereore durng the reayng sots once decodng s successu the destnaton broadcasts a postve acknowedgment (ACK) to the source and the reays to stop reayng the current bock and move on to the next normaton bock. In ths work we suppose perect packet error detecton and assume that the one bt ACK/NACK eedback message s errorree. he source-reay (S R k ) source-destnaton (S D) and reay-destnaton (R k D) nks are assumed to be requency seectve. he channe matrces correspondng to the A B nk are H (AB) 0 H (AB) L AB C M B M A wth L AB denotes the number o symbo-spaced taps A {S R k and B {R k D. her entres are zero-mean crcuary symmetrc compex Gaussan random varabes. Cycc prex (CP)-aded transmsson s assumed or a nks. hs prevents nter-bock ntererence and aows the use o requency doman processng at the recever sde. he average energes o the derent nks are E SRk E SD and E Rk D and take nto account the path-oss and shadowng eects o each nk. We suppose that no channe state normaton at the transmtter (CSI) s avaabe and assume perect channe state normaton (CSI) at the reays and the destnaton. Frst the source encodes ts data bocks usng a space-tme bt ntereaved coded moduaton (SBICM) encoder. he resutng symbo vector at the put o the SBICM encoder s gven by s s 0 s ] S M S () where s s s t s M S ] S M S s the symbo vector at channe use = 0 and S s the symbo consteaton set. Durng the rst sot the source nserts a CP symbo word o ength CP S D max k=2 K (LSR k LSD) then broadcasts the resutng symbo rame. Ater CP deeton the baseband M D sgna vector obtaned at the destnaton sde s gven by where H () y () = E SD L SD =0 H () s ( ) mod + n () (2) = H (SD) and n () N ( ) 0 MD σ 2 I MD s the therma nose. Durng the oowng K sots the transmsson strategy depends on the consdered reayng scheme. Ater CP deeton he M D receved sgna vector at the destnaton sde at each sot k = 2... K can be expressed as = E k L k =0 H (k) s ( ) mod + n (k). (3) hs expresson s vad or both AF and DF schemes: In AF scheme each reay R k ampes and sends the bock o receved sgnas to the destnaton durng the aocated sot. In ths case H (k) n (3) s the th equvaent tap channe matrx correspondng to nk S R k D. It s the convon o the two channes correspondng to nks S R k and R k D. L k = L SRk + L Rk D s the equvaent channe order and E k = E R k DE SRk 4]. M S E SRk +σ 2 In DF schemes the reays transmt usng M S antennas. In the case o seectve DF H (k) = H (R kd) C M D M S L k = L Rk D and E k = E Rk D reay k can correcty decode the packet otherwse the packet retransmsson s not actvated durng sot k. When ACK/NACK-aded DF s consdered both the reay and the source are nvoved durng the oowng K sots. In act at each reay an acknowedgment message s generated ater the normaton bock decodng. I the decodng come s erroneous the reay broadcasts a NACK message to both the destnaton and the source to ndcate that durng the aocated sot the source s gong to drecty send the symbo rame to the destnaton. In ths case H (k) = H (SD) L k = L SD and E k = E SD. he recepton o an ACK message ndcates that durng the aocated sot the source w keep sent whe the reay w transmt the symbo rame to the destnaton whch means H (k) = H (R kd) C M D M S L k = L Rk D and E k = E Rk D. B. Mut-Sot Bock Communcaton Mode Usng the sgna communcaton mode (3) derved n the prevous secton the receved sgnas durng the reayng sots can be vewed as a drect retransmssons rom the source as t s shown n Fg.. In act (3) s o a great mportance as t aows us to vew each reayng sot as an addtona set o vrtua receve antennas at the destnaton sde. hereore ater k sots the system (source k reays and destnaton) can be vewed as a pont to pont MIMO nk wth M S transmt and km D receve antennas. Frst we ntroduce y () C km D (4) where recepton over mutpe sots can be vewed as mut-antenna recepton. We construct the km D bock receved sgna vector as 0 C km D. (5) he bock communcaton mode correspondng to ths k-sot scheme s gven by = H (k) s + n (k) (6) where H (k) C km D M S s a bock crcuant matrx whose rst km D M S bock coumn matrx s H (k) 0 H (k) L 0 ( L)kM D M S (7) wth L = max (L k) k= K H (k) E H () E k H (k) C km D M S (8) correspond to the order and the th tap o the vrtua MIMO channe respectvey. Vector n (k) = n (k) 0 n (k) C km D (9)

3 3 Nose Encoder S Π Mapper CP Inserton X Buer s... s 0 Reayng nk # () () y... y 0 ACK/NACK (rom Destnaton) Nose Reayng nk #k ( y k ) (... y k ) 0 Fgure. S-BICM dagram or mut-reay asssted systems. denotes the therma nose present n the k-sot equvaent MIMO system where n (k) n () n (k) N ( ) 0 kmd σ 2 I kmd. Note that the bock crcuant matrx H (k) can be bock dagonazed n a Fourer bass as H (k) = U H km D Λ (k) U MS. (0) hereore appyng the DF to the k-sot bock sgna vector (6) yeds the oowng requency doman bock communcaton mode = Λ (k) s + n (k) () where { { Λ (k) dag Λ (k) 0 Λ(k) C km D M S Λ (k) and s and n (k) = L =0 H(k) e j(2π/ ) C km D M S are the DF o s and n (k) respectvey. III. OUAGE PROBABILIY (2) he age probabty s regarded as a meanngu too or evauatng the perormance o non-ergodc channes.e. bock adng quas-statc channes as t provdes a ower bound on the bock error rate (BLER) 5 p. 87]. For a gven sgna to nose rato (SNR) γ per receve antenna the age probabty o the drect nk (.e. S D nk) at a target transmsson rate R s dened as the probabty that the mutua normaton I between the transmtter aphabet and the receved sgna s beow R Drect (R γ k = ) = Pr { I(s y () Λ () γ) < R (3) where s s the requency doman transmtted symbo vector y () s the requency doman receved sgna over nk S D (durng sot k = ) and Λ () s the correspondng channe requency response (CFR). In ths work we are nterested n anayzng cooperatve ARQ communcatons where packet reayng s actvated ony the destnaton as to decode the ntay transmtted data packet. In such a scenaro packet combnng starts when the drect nk s n age.e. k 2. At each sot k 2 k copes o the transmtted packet are avaabe at the destnaton sde one rom the drect nk and k rom reayng nks except or seectve DF scheme where the number o transmtted packet copes depends on the quaty o S R nk reazatons. In act or seectve DF packet retransmsson does not occur at sot u (2 u k) the S R u nk s n age. However or the sake o smpcty we assume that sot u s aocated or packet retransmsson even when reayng s deactvated. hereore the k-sot reayng system can be vewed as a repetton codng scheme where k parae sub-channes are used to transmt one symbo message 5 p. 94]. Usng the uned communcaton mode () the age probabty o the studed reayng schemes can be expressed as n 6].e. P (R γ k) = { Pr k I(s Λ (k) γ) < R A A k (4) where A u denotes the event that the destnaton sends a NACK message at sot u. In the case o ndependent and dentcay dstrbuted (..d) crcuary symmetrc compex channe nputs the mutua normaton I(s Λ (k) γ) n (4) can be expressed as n 7].e. I(s Λ (k) γ) = =0 og 2 (det ( I kmd + γ )) Λ (k) Λ (k)h. (5) M S Moreover n the speca case o DF schemes the age probabty can be expressed usng the age probabtes o S R nks. For DF modes the receved sgnas avaabe at the destnaton sde ater k sots depend on the quaty o S R nks. Let E k denote the event that the reayng system {Source k reays destnaton s n age at sot k and C kτ denote the event that τ source-reay nks among the k avaabe source-reay nks (.e. S R 2 S R k ) are n age. he age probabty o the DF reayng system at sot k can be expressed as k DF (R γ k) = Pr {E k C kτ A A k. (6) In the case o seectve DF mode packet retransmsson does not occur at sot u (2 u k) the S R u nk s n age. Let R kτ {R 2 R k denote the set o τ reays nvoved n event C kτ and R kτ {R 2 R k \ R kτ. For seectve DF reayng the age probabty (6) can then be expressed as k P SDF (R γ k) = P SRkτ D R kτ where s computed as P = Pr In (8) y (SR) R R kτ R R kτ ) ( (7) denotes the age probabty o the S R nk and { k I(s y (SR) Λ (SR) γ) < R A A k. (8) denotes the requency doman receved sgna over the S R nk and Λ (SR) s the correspondng CFR. Whe P SR kτ D s the age probabty o the system ater combnng at sot k usng reays n set R kτ. It s computed smary to (4) usng R D nk channe matrces correspondng to reays n set R kτ. Note that when

4 4 R k0 = and R kk = the correspondng mutpcatve terms n (7) are assumed equa to. In the case o ACK/NACK-aded DF mode the packet s drecty retransmtted by the source durng sot u the nk S R u s n age. Let S kτ denote the set o τ tme sots durng whch the source s nvoved n the packet retransmsson. he age probabty (6) can be expressed as k P ACK/NACK DF (R γ k) = P Skτ Rkτ D R kτ R R kτ R R kτ ) ( (9) where P S kτ R kτ D denotes the age probabty o the system ater combnng at sot k usng τ packet copes rom S D nks and k τ copes rom R D nks where R R kτ. IV. OUAGE ANALYSIS In ths secton we anayze the age probabty o the studed reayng schemes. We use Monte Caro smuatons to evauate system age probabty gven by (4). Frst we generate MIMO channe matrces correspondng to the S D nk and compute the mutua achevabe rate usng (5) or k =. I the achevabe rate s greater than R the system s decared n a non age reayng s thereore deactvated and the system moves on to the transmsson o the next bock. However the target rate R s not reached when k = the rst reayng nk MIMO channe matrces are generated dependng on the reayng scheme n use and the mutua achevabe rate s re-cacuated or k = 2. he reayng process s stopped and the processng o the next bock transmsson s started ether because the achevabe rate s greater than kr at sot k K or the system s n age.e. the achevabe rate s beow KR at the ast sot K. For smuatons we choose = 258 channe use. For the sake o smpcty we assume that a reays are at the same dstance rom both the source and the destnaton. We consder a homogeneous case where the dstances between the source and reay SR reay and destnaton RD and source and destnaton SD are normazed n such a way that SR + RD = SD =. A nks have the same requency-seectve adng channe proe.e. L = 3 equa power paths wth the same path oss exponent κ = 3. he nk average energy s E AB = ( AB) κ wth A = S or R and B = R or D. Frst we consder a one-reay cooperatve ARQ system (K = 2 sots) where a nodes are equpped wth two antennas.e. M S = M R = M D = 2 and the target rate s R = 2. In Fg. 2 we report the age probabty versus SR or S D nk SNR.e. = 3dB. In the egend ACK/NACK-DF (Sow Ch) and ACK/NACK- DF (ast Ch) denote the ACK/NACK-aded DF scheme operatng over an S D ong-term statc channe where the channe s constant over K consecutve sots and a S D short-term statc channe where the channe ndependenty changes rom sot to sot respectvey. From Fg. 2 we notce that the optma reay ocaton or a studed schemes s SR = 0.5. Moreover the resuts show that AF and DF reayng perorm each other dependng on the reay ocaton. In act AF scheme seems to be more sutabe or ocatons cose to the destnaton.e. SR > 0.6. However or ocatons cose to the source the reay experences better rado condtons and the probabty o successu data packet decodng becomes hgher. In ths case DF schemes are more sutabe. Furthermore the studed DF schemes have smar perormances when SR < 0.6. For reay ocatons where SR > 0.6 ACK/NACK-aded DF scheme ceary perorms seectve DF scheme. However when the S D nk experences sow adng the gap becomes too sma. In ths case Outage Probabty 0 0 =3dB ACK/NACK DF (Fast Ch) ACK/NACK DF (Sow Ch) Seectve DF AF sr Fgure 2. Outage probabty versus SR or M S = M R = M D = 2 K = 2 L = 3 and the path oss exponent κ = 3. seectve DF can be consdered as the best DF reayng scheme as t does not nvove the source durng the reayng sots. Now we consder a mut-reay cooperatve ARQ system where the source and the reays are equpped wth two antennas.e. M S = M R = 2 and the target rate s R = 2. In Fg. 3 and Fg. 4 we pot age probabty versus at SR = 0.5 or one and two-reay cooperatve ARQ systems (K = 2 and K = 3). In both gures we use conventona hybrd ARQ as a reerence to evauate the behavor o the studed reayng schemes. In ths conventona packet retransmsson scheme the packet s drecty retransmtted by the source wth reay assstance. In the oowng we assume that the S D nk experences short-term quas-statc adng. hs corresponds to the best scenaro or conventona hybrd ARQ where re-transmsson rounds see derent and ndependent channe reazatons. In Fg. 3 a nodes are equpped wth two antennas. In ths case or K = 2 the SNR gan due to packet retransmsson dversty n conventona hybrd ARQ s ess than db at 0 3 age compared wth K =. However when reays are ncorporated n the network to pay the roe o packet re-transmtters ths gan s ncreased to more than 2dB or AF reayng scheme and 5dB or DF. hs hgh dversty gan can be reached when the reay s at the optma ocaton SR = 0.5. Aso note that n conventona hybrd ARQ transmsson the age perormance saturates ater K = 2 whe or reayng transmsson the two-reay system has a dversty gan o 0.5dB at 0 3 age compared to the onereay system. In Fg. 4 we notce that or overoaded mut-reay cooperatve ARQ systems.e. M S = M R = 2 and M D = the dversty gan s ncreased to db or DF reayng schemes. he throughput curves o baanced conguraton wth two reays are reported n Fg. 5. We observe that the benets o ncorporatng reays n the network appear n the regon o ow to moderate SNR where mutpe transmssons are requred to hep correct packets erroneousy receved durng the rst sot. V. CONCLUSION In ths paper we nvestgated the ssue o mut-reay communcaton over broadband MIMO channes. Frst o a we derved an uned communcaton mode or AF Seectve DF and ACK/NACKaded DF. We presented a mut-sot communcaton mode where

5 Outage Probabty 0 2 Drect nk K = Drect nk K = Drect nk K = 3 AF K = 2 AF K = 3 Seectve DF K = 2 Seectve DF K = 3 ACK/NACK DF K = 2 ACK/NACK DF K = hroughput Drect nk AF SDF ACK/NACK DF Fgure 3. Outage probabty versus or M S = M R = M D = 2 SR = 0.5 L = 3 and the path oss exponent κ = 3. Fgure 5. hroughput versus or M S = M R = M D = 2 SR = 0.5 L = 3 and the path oss exponent κ = Outage Probabty Drect nk K = Drect nk K = Drect nk K = 3 AF K = 2 AF K = 3 Seectve DF K = 2 Seectve DF K = 3 ACK/NACK DF K = 2 ACK/NACK DF K = Fgure 4. Outage probabty versus or M S = M R = 2 M D = SR = 0.5 L = 3 and the path oss exponent κ = 3. transmsson over reayng sots s transated nto vrtua receve antennas hen we examned the age probabty o derent studed reayng schemes. Usng smuatons we showed that the studed reayng schemes perorm each other dependng on reay ocatons. We aso showed that the mut-reay-asssted communcatons provde better dversty gan than the conventona hybrd-arq. REFERENCES ] S. Ln D. J. Costeo and M. J. Mer Automatc repeat-request error contro schemes IEEE Communcatons Magazne vo. 2 pp. 5-7 Dec ] G. Care and D. unnett ARQ protocos or the Gaussan coson channe IEEE rans. In. heory vo. 47 no. 4 pp Ju ] E. Zmmermann P. Herhod and G. Fettwes he mpact o cooperaton on dversty-expotng protocos IEEE VC-sprng Man Itay May ] J. N. Laneman G. W. Worne and D. N. C. se An ecent protoco or reazng cooperatve dversty n wreess networks IEEE Internatona Symposum on Inormaton heory (ISI) Washngton DC June ] A. Sendonars E. Erkp and B. Aazhang User cooperaton dversty Part I & Part II IEEE rans. Commun. vo. 5 pp Nov ] J. N. Laneman D. se and G. W. Worne Cooperatve dversty n wreess networks: Ecent protocos and age behavor IEEE rans. Inorm. heory vo. 50 no. 2 pp Dec ] J. Boyer D. D. Faconer and H. Yankomerogu Muthop dversty n wreess reayng channes IEEE rans. on Comm. vo. 52 pp Oct ] F. Atay Onat H. Yankomerogu and S. Peryawar Reay-asssted spata mutpexng n wreess xed reay networks IEEE GLOBECOM San Francsco USA Nov.- Dec ] G. Yu Z. Zhang and P. Qu Cooperatve ARQ n wreess networks: Protocos descrpton and perormance anayss IEEE Internatona Conerence on Communcatons (ICC) Istanbu urkey June ] R. U. Nabar F. W. Kneubher and H. Boecske Perormance mts o ampy-and-orward based adng reay channes IEEE Internatona Conerence on Acoustcs Speech and Sgna Processng (ICASSP) Montrea Canada May ] Y. Zhang H. H. Chen and M. Guzan Cooperatve Wreess Communcatons Auerbach Pubcatons ] B. Zhao and M. C. Vaent Practca reay networks: A generazaton o hybrd-arq IEEE J. Seect. Areas. Comm. vo. 23 no. Jan ] H. V. Khuong and. Le-Ngoc A Bandwdth-ecent Cooperatve Reayng Scheme wth Lmted Feedback Inormaton 24th Benna Symposum on Communcaton 2008 pp June ] H. Chanaj. At-Idr Ham Yankomerogu and S. Saoud Jont urbo Equazaton or Reayng Schemes over Frequency-Seectve Fadng Channes n Proc ACM Intern. Wreess Commun. Mobe Comput. Con. (IWCMC 09) Lepzg Germany Jun ] D. se and P. Vswanath Fundamentas o wreess Communcaton Cambrdge Unversty Press May ]. At-Idr and S. Saoud urbo Packet Combnng Strateges or the MIMO-ISI ARQ Channe IEEE rans. Commun. vo. 57 no. 2 pp Dec ] H. E Gama A. R. Hammons Y. Lu M. P. Ftz and O. Y. akeshta On the desgn o space tme and space requency codes or MIMO requency-seectve adng channes IEEE rans. Inorm. heory vo. 49 no 9 pp Sep