Performance Analysis of a Dual-Hop Cooperative Relay Network with Co-Channel Interference

Transcription

1 4 IN LIN, HENG WEI, JIAN OUYANG, KANG AN, CAN YUAN, ANALYSIS OF A DUAL-HOP COOPEATIVE ELAY NETWOK Perormance Analyss o a Dual-Hop Cooperatve elay Network wth Co-Channel Intererence n LIN,, Heng WEI, Jan OUYANG 4, Kang AN, Can YUAN PLA Unversty o Scence and Technology, Nanng, Chna Natonal oble Communcatons esearch Laboratory, Southeast Unversty, Nanng, Chna College o Communcaton Engneerng, PLA Unversty o Scence and Technology, Nanng, Chna 4 Inst. o Sgnal Processng and Transmsson, Nanng Unversty o Posts and Telecommuncatons, Nanng, Chna lnmn6@6.com, weheng6@6.com, ouyangan@nupt.edu.cn, ankang@nuaa.edu.cn, yuancanchna@gmal.com Abstract. Ths paper analyzes the perormance o a dualhop amply-and-orward (AF) cooperatve relay network n the presence o drect lnk between the source and destnaton and multple co-channel ntererences (CCIs) at the relay. Speccally, we derve the new analytcal expressons or the moment generatng uncton (GF) o the output sgnal-to-ntererence-plus-nose rato (SIN) and the average symbol error rate (ASE) o the relay network. Computer smulatons are gven to conrm the valdty o the analytcal results and show the eects o drect lnk and ntererence on the consdered AF relay network. Keywords Amply-and-orward, cooperatve relay network, cochannel ntererence, perormance analyss.. Introducton ecently, the applcaton o relay technology has attracted many researchers as a low-cost strategy to ncrease the capacty, relablty and coverage o wreless networks wthout requrng extra power or bandwdth. (See [], [] and the ctatons theren or example.) Among the commonly used relay protocols, such as amply-and-orward (AF), decode-and-orward (DF) and compress-and-orward (CF), AF scheme s o partcular nterest due to ts smplcty. When only one relay s exploted to amply the sgnal, the conguraton s called as dual-hop relay network. When the channel state normaton (CSI) s avalable, the perormance o dual-hop AF relay networks has been well studed n a large body o open lteratures []-[5]. In practce, however, co-channel ntererence (CCI) due to requency reuse oten severely degrades the perormance o wreless systems. otvated by ths act, the authors o [6] have nvestgated the eect o CCI on a varable gan AF relay network over aylegh adng channels. oreover, the authors n [7] have analyzed the ergodc capacty o AF relay system wth CCI present at both relay and destnaton over Nakagam-m adng channels. By consderng the ont eects o CCI and mperect CSI, the perormance o a dual hop varable gan AF relayng wth BF has been studed n [8], where the outage probablty (OP), average symbol error rate (ASE) and asymptotc analyss at hgh SN have been presented. An extenson o the prevous works to the mult-antenna AF relayng has been presented n [9]-[], respectvely. In [9], the authors have analyzed the perormance o mult-antenna AF relay systems wth eedback delay at the source and CCI at the relay. By assumng that the statstcal CSI s avalable at the relay, the analytcal expressons or the OP, Ergodc capacty, ASE o a mult-antenna AF relay network have been obtaned n []. oreover, both the closed-orm and asymptotc expressons o OP or mult-antenna AF relayng wth have derved n [], where the more general case wth both the relay and destnaton corrupted by multple co-channel ntererers has been consdered. However, n the aorementoned studes, the drect lnk between the source and destnaton s assumed to be unavalable due to heavy shadng, whch s not an actual model n many practcal envronments. In ths paper, unlke the prevous related works, we conduct the perormance o a dual-hop AF cooperatve relay network, where drect lnk exsts between the source and destnaton, and multple CCIs corrupt the receved sgnals at the relay. In partcular, we derve the new theoretcal expressons or the moment generatng uncton (GF) o the output sgnal-to-ntererence-plus-nose rato (SIN) as well as the average symbol error rate (ASE) o the relay system. To the best o our knowledge, ths s the rst tme such analytcal results have been presented.. System odel As shown n Fg., we consder a dual-hop AF relay network, where a source S communcates wth a destnaton D through a relay. We assume that each node s equpped wth a sngle antenna, and there exsts a drect lnk between S and D. Here, all the wreless channels are subect to aylegh adng. The complete communcaton takes place n two tme slots. In the rst tme slot, S broadcasts the sgnal to D and through the adng channels h and h, respectvely. eanwhle, s also mpared

2 ADIOENGINEEING, VOL., NO. 4, DECEBE 4 5 PS h PS h P h P N S h P h PI, n hi, n n (5) where h, h, h and Fg.. System model o a dual-hop cooperatve relay network wth CCI. by N CCIs through adng channel h I,n (n =,,,N). As such, the receved sgnals at D and can be, respectvely, expressed as y t P h x t n t, () S S S S In, In, In, n N y t P h x t P h x t n t () where P S s the transmt power at S, P I,n s the transmt power o nth-ntererence, x S (t) and x I,n (t) are the transmt sgnal rom S and that rom nth-ntererence, satsyng E[ x S (t) ] = and E[ x I,n (t) ] =, n (t) and n (t) are the zero mean addtve whte Gaussan noses (AWGNs) at D and, obeyng n (t) N c (,σ ) and n (t) N c (,σ ), respectvely, and E[.] denotes the expectaton operator. In the second tme slot, the receved sgnal at s ampled and orwarded to D through the adng channel h. Accordngly, the sgnal receved at D can be wrtten as y t P G h y t n t N PPGhhx t P PGh hx t S S In, In, In, n PGhn n t () where P denotes the transmt power at, n (t) the AWGN at D wth zero mean and varance σ. Furthermore, G s the amply gan at, gven by [9] G N S I, n I, n n P h P h. (4) Followng the applcaton o maxmal rato combnng (C) at D, t s not dcult to nd that the output SIN can be expressed as N h I, n n, n wth P, P S, P S, n I, n and P beng the average sgnal-tonose ratos (SNs). In (5), γ and γ represent the output sgnal-to-nose rato (SN) o drect S-D lnk and the output SIN o the S--D relay lnk at D, respectvely. Note that a smlar expresson has also been derved n [6, equaton 5] or the case o gnorng drect lnk between S and D and nose at the relay, ndcatng that our work extends the study o prevous works to a more general case.. oment Generatng Functon GF s an mportant approach to evaluate the perormance o wreless systems, whch s dened as s r s E e. Clearly, the GF o n (5) can be obtaned as where s s s r se e Ee Ee s s (6) r r s and r r s are the GF o and, respectvely. Snce the S-D lnk undergoes aylegh adng, h has a Ch-square dstrbuton wth degrees o reedom and varance /, the probablty densty uncton (PDF) s gven by x x exp. (7) Thus, the GF o can be obtaned as [4]. (8) s s sx s E e e xdx To obtan the analytcal GF express the upper bound o as r s o, we rst S S P h P P G h h N P P G h h P G h n In, In, ~ mn, mn, (9)

3 6 IN LIN, HENG WEI, JIAN OUYANG, KANG AN, CAN YUAN, ANALYSIS OF A DUAL-HOP COOPEATIVE ELAY NETWOK or mathematcal tractablty. Thus, the GF o can be approxmated as s E s s e sx sx e xdx se F xdx () where F x s the cumulatve dstrbuton uncton (CDF) o, gven by F x F x F x () x and F x wth F beng the CDF o and. N Next, accordng to [], the PDF o h n I, n, n can be wrtten as t C, x x exp x (),!, wth the coecent C, gven by C where vk v tn () v!, s k, k s, k, v v t v s, v denotes the repeated tmes o, satsyng N. Consder the S- lnk experences aylegh adng, the CDF o can be wrtten as Thereore, F x x x exp. (4) F can be calculated as x z F xpr x y zdydz F x z z dz t v x C, exp!, z z exp dz. (5), Wth the help o dentty [, equaton.5.], we have t v x,,. (6) F xexp C eanwhle, the -D lnk s subect to aylegh adng, one can obtan x F xexp. (7) Substtutng (6) and (7) nto (), one can obtan the closed-orm expresson o F x as t v, exp, (8) F x x C Fnally, by pluggng (8) nto (), ater some algebrac manpulatons, the GF o can be approxmately calculated as t v,, exp s s C s x dx t v s C, U, ; s (9),, where U(a, b; x) denotes the conluent hypergeometrc uncton [4]. In dervng (9), we have appled [4, equaton..6.9]. Furthermore, usng (8) and (9) nto (6), one can readly obtan the approxmate expresson o r (s), gvng t v s r s C, s s, U, ; s. (), 4. Average Symbol Error ate The ASE o wreless communcaton systems wth varous modulaton ormants over adng channels can be expressed as [5] b Ps a d sn () where a, b and are the modulaton specc constants. However, to the best o our knowledge, due to the ntegral, the closed-orm soluton s mathematcally unavalable by drectly employng the above ormula. To overcome ths, we provde an approxmate yet accurate alternatve method to evaluate the ASE. For the case o -ary phase-sht keyng (-PSK) modulaton sgnal, we have sn P PSK d sn sn d sn sn d sn L L ()

4 ADIOENGINEEING, VOL., NO. 4, DECEBE 4 7 By usng the denton o GF, L can be calculated as xsn L exp xdxd sn exp sn x 4xsn exp 4 x dx 4 4 sn sn. () In dervng (), we have appled the ollowng approxmaton [6] x 4 sn 6 Smlarly, wth the help o dentty [6] exp d exp x exp x. (4) x exp d sn 4 expxexp L can be approxmately obtaned as x sn xsn L exp xdxd sn exp xsn 4 xsn exp xdx sn (5) sn 4 sn. (6) 4 sn Furthermore, the approxmate ASE expresson or -PSK modulaton sgnal can be wrtten as P sn 4 sn PSK sn sn. (7) In a smlar manner, the ASEs o -ary Pulse Ampltude odulaton (-PA) sgnals can be calculated as P PA d sn x exp sn x dxd 4 exp x exp x xdx 4. (8) 6 As or -ary Quadrature Ampltude odulaton (-QA) sgnals, t can be consdered as two ndependent -PA sgnals wth ts ASE beng expressed as 4 P QA d sn L 4 sn 4 d. (9) Followng a smlar manner to derve (), L can be obtaned as 4 L. () In addton, by applyng an approxmate expresson [], we have L4 6 L4 6. () Thereore, an approxmate expresson o calculated as P can be QA 4 P QA 6 6. () 5. Numercal esults In ths secton, we conrm the valdty o the derved analytcal results through comparson wth onte Carlo smulatons, and nvestgate the mpacts o the drect lnk and CCIs on the perormance o the consdered cooperatve relay network. Here we assume that s corrupted by CCIs wth the SNs denoted as I,, I,.6 and I,.8. In all the plots, we dene, I, I,

5 8 IN LIN, HENG WEI, JIAN OUYANG, KANG AN, CAN YUAN, ANALYSIS OF A DUAL-HOP COOPEATIVE ELAY NETWOK and I, where the cases o no drect lnk, and no ntererences are denoted as db and db. Fg., Fg. and Fg. 4 show, respectvely, the ASE versus γ n terms o QPSK, 8PA and 6QA modulaton or derent η. As we see, snce the approxmate method s used to calculate the GF o the output SIN n (), there exst a lttle devaton at low SN, the good match between the analytcal results and the onte Carlo experments n general can stll be obtaned. The scenaros conrm the valdty o the derved analytcal expressons.. In addton, t can also be ound that the ASE perormance s mproved wth the ncrease o drect S-D lnk strength. Ths s because the drect lnk can enhance the output SIN. ρ =,,, db ASE ASE η =,,,, db Fg.. ASE versus average SN or QPSK wth N = and ρ = db Fg. 5. ASE versus average SN or QPSK wth N = and η = db. ASE η =,,,, db ASE ρ =,,, db Fg.. ASE versus average SN or 8PA wth N = and ρ = db Fg. 6. ASE versus average SN or 8PA wth N = and η = db. ASE η =,,,, db ASE ρ =,,, db Fg. 4. ASE versus average SN or 6QA wth N = and ρ = db Fg. 7. ASE versus average SN or 6QA wth N = and η = db.

6 ADIOENGINEEING, VOL., NO. 4, DECEBE 4 9 Fg. 5, Fg. 6 and Fg. 7 depct the ASEs o QPSK, 8PA and 6QA modulatons aganst SN or varous ρ. As we expect, at mddle and hgh SN regmes, a well agreement between the analytcal results and onte Carlo experments s observed. Furthermore, t can also be seen that the ASEs o the network decreases wth the ncrease o ρ. Ths s because when ρ s ncreased, the CCIs are degraded, resultng n the ncrease o output nstantaneous SN at the destnaton. 6. Conclusons In ths paper, a dual-hop AF cooperatve relay network has been nvestgated n the presence o S-D drect lnk and multple CCIs at the relay. In partcular, we have derved the new analytcal expressons or the GF o the output SIN as well as the ASE o the system. Furthermore, we have also provded numercal results to demonstrate the valdty o the theoretcal analyss, and examned the eects o drect lnk and ntererence on the consdered AF relay network. It should be ponted out the extenson o the presented method to the more complex networks, such as more than one nodes havng mult-antenna and/or multple relays are exploted to amply the sgnals, s our urther work. Acknowledgements Ths work s supported by the Natonal Natural Scence Foundaton o Chna (6755), the Natural Scence Foundaton o Jangsu Provnce (BK68), and the Open esearch Fund o Natonal oble Communcatons esearch Laboratory n Southeast Unversty (D5). eerences [] KAKITANI,., BANTE, G., SOUZA,. Energy ecency analyss o a two-dmensonal cooperatve wreless sensor network wth relay selecton. adoengneerng,, vol., no., p. 549 to 557. [] FAN, Z. J., GUO, D. X., ZHANG, B. N. Outage probablty and power allocaton or two-way DF relay networks wth relay selecton. adoengneerng,, vol., no., p [] LI,., LIN,., YU, Q., ZHU, W.-P., DONG, L. Optmal beamormer desgn or two hop IO AF relay networks over aylegh adng channels. IEEE Journal on Selected Areas n Communcatons,, vol., no. 8, p [4] OUYANG, J., LIN,., ZHUANG, Y. Perormance analyss o cooperatve relay networks over asymmetrc adng channels. Electroncs Letters,, vol. 48, no., p.7 7. [5] LI,., AN, K., OUYANG, J., WEI, H., et al. Eect o eedback delay on dual-hop xed gan relay networks over mxed adng channels. Transactons on Emergng Telecommuncatons Technologes, 4, vol. 5, no., p [6] SUAWEEA, H. A., HAI, K. G., NALLANATHAN, A. Perormance analyss o two hop amply-and-orward systems wth ntererence at the relay. IEEE Communcatons Letters,, vol. 4, no. 8, p [7] TIGUI, I., AFFES, S., STEPHENNE, A. On the ergodc capacty o amply-and-orward relay channels wth ntererence n Nakagam-m adng. IEEE Transactons on Communcatons,, vol. 6, no. 8, p [8] AN, K., LIN,., OUYANG, J., WEI, H. Beamormng n dualhop AF relayng wth mperect CSI and co-channel ntererence. Wreless Personal Communcaton, 4, vol. 78, no., p. 87 to 97. [9] PHAN, H., DUONG, T. Q., ELKASHLAN,., ZEPENICK, H.- J. Beamormng amply-and-orward relay networks wth eedback delay and ntererence. IEEE Sgnal Processng Letters,, vol. 9, no., p [] AN, K., LIN,., OUYANG, J., WEI, H. Perormance analyss o beamormng n two-hop AF relay networks wth antenna correlaton and ntererence. AEU-Internatonal Journal o Electroncs and Communcatons, 4, vol. 68, no. 7, p [] DING, H., HE, C., JIANG, L.-G. Perormance analyss o xed gan IO relay systems n presence o co-channel ntererence. IEEE Communcatons Letters,, vol. 6, no. 7, p. 6. [] CUI, X. W., FENG, Z.. Lower capacty bound or IO correlated adng channels wth keyhole. IEEE Communcatons Letters, 4, vol. 8, p [] GADSHTEYN, I. S., YZHIK, I.. Table o Integrals, Seres, and Products. 7 th ed. Academc Press, 7. [4] PUDNIKOV, A. P., BYCHKOV, Y. A., AICHEV, O. I. Integrals and Seres. Vol., st ed. New York (USA): Gordon and Breach Scence Publshers, 986. [5] SION,. K., ALOUINI,. S. Dgtal Communcaton over Fadng Channels. nd ed. Wley, 5. [6] CKAY,.., ZANELLA, A., COLLINGS, I. B., et al. Error probablty and SIN analyss o optmum combnng n can adng. IEEE Transactons on Communcatons, 9, vol. 57, no., p About Authors... n LIN was born n Zheang Provnce, Chna, n 97. He receved the B.S. degree rom the Natonal Unversty o Deense Technology, the.s. degree rom Nanng Insttute o Communcaton Engneerng, and Ph.D. degree rom the Southeast Unversty n 99,, and 8, respectvely, all n Electrcal Engneerng. Hs current research nterests nclude wreless communcatons, array sgnal processng and antenna technology. He s the author or coauthor o more than 7 papers, and holds 4 patents. Dr. Ln s a ember o IEEE and Senor ember o Chnese Insttute o Electroncs (CIE). Heng WEI (correspondng author) was born n Jangsu Provnce, Chna, n 989. He receved the B.S. degree rom the College o Electronc and Inormaton Engneerng, Nanng Unversty o Aeronautcs and Astronautcs n. He s currently workng towards the.s. degree n Electronc Engneerng, rom the PLA Unversty o Scence and Technology. Hs research nterests are IO technque and wreless relay communcatons. Jan OUYANG was born n Jangsu Provnce, Chna, n 98. He receved the B.S.,.S. and Ph.D. degrees rom

7 4 IN LIN, HENG WEI, JIAN OUYANG, KANG AN, CAN YUAN, ANALYSIS OF A DUAL-HOP COOPEATIVE ELAY NETWOK the College o Computer Scence and Technology, Nanng Unversty o Aeronautcs and Astronautcs n 7,, and 4 respectvely. Snce July 4, he has been wth the Insttute o Sgnal Processng and Transmsson, Nanng Unversty o Posts and Telecommuncatons (NUPT). Hs current research nterests nclude wreless cooperatve networks. Kang AN was born n Xnang Uygur autonomous regon, Chna, n 989. He receved the B.S. degree rom the College o Electronc and Inormaton Engneerng, Nanng Unversty o Aeronautcs and Astronautcs n, and.s. degree n Electronc Engneerng, rom the College o Communcatons Engneerng, PLA Unversty o Scence and Technology n 4. He s currently workng towards the Ph.D. degree at the College o Communcatons Engneerng, PLA Unversty o Scence and Technology. Hs research nterests nclude hybrd satellte-terrestral network, cooperatve communcatons, cogntve rado and array sgnal processng. Can YUAN was born n Anhu Provnce, Chna, n 99. He receved the B.S. degree rom the College o Scence, Nanng Unversty o Aeronautcs and Astronautcs n. He s currently workng towards the.s. degree n Communcaton Engneerng at the College o Communcatons Engneerng, PLA Unversty o Scence and Technology. Hs research nterests are array sgnal processng and wreless cooperatve communcatons.