Outage Performance for Two-Way Relaying with CoChannel Interference and Channel Estimation Error

Transcription

1 Journal o Communcatons Vol. No. Dcmbr 5 Outag rormanc or Two-Way layng wth CoChannl Intrrnc and Channl stmaton rror Jnhong Fan and Chaow Yuan School o Inormaton and Communcaton ngnrng Bng Unvrsty o osts and Tlcommuncatons Bng 876 Chna Collg o lctronc Inormaton ngnrng North Chna Unvrsty o Tchnology Bng 44 Chna mal: qh9@63.com Abstract In ths papr w consdr th ag prormanc o a two-way dcod-and-orward rlayng ntwork n th prsnc o multpl strong ntrrrs at th sourc/dstnaton trmnals and channl stmaton rrors. W dn th sgnalto-nos ratos and sgnal-to-ntrrnc ratos and thn us thm to drv closd-orm prssons or th ag probablty o th systm undr th symmtrcal and asymmtrcal cass that th rcvd powrs at th rlay rom both trmnals ar th sam and drnt. Our analyss shows that th stnc o th channl stmaton rrors and th ntrrrs acts th ag prormanc. Smulaton rsults dmonstrat that our analytcal rsults ar n cllnt agrmnt wth th Mont Carlo smulatons. trado n AF and DF MIMO two-way rlayng ntwork was tackld n [9] []. Th two-way rlayng ntwork wth cogntv spctrum sharng protocols was nvstgatd n []. Othr actv aras spun rom th concpt o rlayng nclud rlay slcton [] [3] dstrbutd bam-ormng [4] [5] codng [6] [7] and multusr two-way rlayng ntwork [8]. Th twoway rlayng tchnology was combnd wth small cll [9] [] tchnology. Th co-channl ntrrnc s nvtabl n wrlss communcatons so prormanc analyss o on-way rlay ntwork has turnd th ocus to ntrrnc-lmtd channls []-[3]. On-way rlayng systm wth nosy rlay and ntrrnc-lmtd dstnaton was amnd and th closd-orm ag probablts wr drvd or both DF and AF protocols []. On-way rlayng systm wth multpl ntrrrs ovr aylgh adng channls was studd n []. Th act ag probablty o th DF on-way rlayng systm wth unqual-powr ntrrrs usng opportunstc rlay slcton was provdd n [3]. Th DF two-way rlayng ntwork wth co-channl ntrrncs was nvstgatd n [4] [5]. Th systms achvabl rat was drvd n [4]. A tght appromat prsson o th avrag symbol rror rat was drvd n closd-orm n [5]. Th ntrrnc lmts wr consdrd n cogntv mtoclls systm [6]. On th othr hand or th DF rlayng ntwork most o th work on prormanc analyss has bn carrd undr th assumpton o prct channl stat normaton (CSI at both rlay and nods. In practc howvr t s mpossbl or th rlay and nods to obtan prct knowldg o CSI du to mprct channl stmaton algorthms th Dopplr sht or nos on th plot sgnals. As such th authors n [7]-[9] took th channl stmaton rror nto consdraton. Th ag prormanc o DF basd opportunstc coopratv communcatons wth channl stmaton rrors was nvstgatd n [7]. Th symbol rror rat and powr allocaton or DF rlayng wth channl stmaton rror was analyzd n [8]. In papr [9] th prormanc o DF coopratv dvrsty ntworks wth mprct channl stmaton and co-channl ntrrnc was analyzd. Th prormanc o a DF two-way rlayng ntwork wth multpl ntrrrs and channl stmaton Ind Trms Two-way rlayng ag probablty dcodand-orward channl stmaton rror co-channl ntrrnc I. INTODUCTION layng tchnologs can mprov through and ncras communcaton rang. Thy hav mrgd as an ctv mans or plotng spatal dvrsty. Two-way rlayng has rcvd consdrabl ntrst ovr th last yars du to ts advantag o ovrcomng th hal-dupl loss n on-way rlay channls []. Untl now th prormanc analyss and drnt transmsson schms or Amply-and-Forward (AF and Dcod and Forward (DF two-way rlayng ntwork hav bn wll nvstgatd n th ltratur. Th rat prormanc o two-way rlayng ntwork has bn tnsvly studd n rcnt yars. Th achvabl rat rgons or hal-dupl two-way rlayng ntwork wr studs n [] [3]. Latr n [4] th act ag probablts or a thr-nod twoway rlayng ntwork usng AF and DF schms wr prsntd and an adaptv AF/DF schm was proposd to achv th optmal ag prormanc. Th multplnput multpl-put (MIMO two-way rlayng ntwork was consdrd n [5]-[8]. Th papr [8] showd that th capacty scals lnarly wth th numbr o antnnas at th sourc nods and logarthmcally wth th numbr o rlay nods. cntly th optmal dvrsty-multplng Manuscrpt rcvd Aprl 8 5; rvsd Dcmbr 4 5. Ths work was supportd by Natonal Natural Scnc Foundaton o Chna undr grant Scntc sarch Common rogram o Bng Muncpal Commsson o ducaton undr grant No.598. Corrspondng author mal: qh9@63.com. do:.7/cm Journal o Communcatons 963

2 Journal o Communcatons Vol. No. Dcmbr 5 rror s analyzd n th ltratur and ths problm rprsnts th man ocus o ths papr. Ths papr s organzd as ollows. Th systm modl s dscrbd n Scton. In Scton 3 w nvstgat th ag probablty o th DF two-way rlayng systm wth channl stmaton rror and multpl ntrrrs. In Scton 4 som numrcal rsults ar gvn to vry our analyss. Fnally Scton 5 concluds th papr. Notatons-w dnot {B} as th probablty o a random vnt B whl {B} rturns th pctd valu o th nput random varabl or vnt. FB( and B( ar rspctvly th cumulatv dnsty uncton and th probablty dnsty uncton o B. transmt N y h s( n whr {s( }N ar th ntrrnc sgnals. Th channls btwn th ntrrrs and S ar {h }. Thy ar ndpndnt aylgh wth { h } I { s( } and I { s( }. Th channl stmaton s basd on tranng squncs (plots and a partcular plot powr rsult n a crtan lvl o channl stmaton rror varanc [7]. Th actual and th stmatd channls can b modld as ˆ (4 ˆ (5 whr and ar th stmatd channl cocnts and and dnot th channl stmaton rrors. Lt { } { } a paramtr whch rlcts S th accuracy o channl stmaton. Snc s assumd to b ndpndnt o and s assumd to b Fg.. Th two-way rlayng systm modl wth co-channl ntrrnc ndpndnt o and a ar compl Gaussan random varabls wth varancs { ˆ } and In th rst tm slot S and S snd thr mssags and to and has th ollowng rcvd sgnal: { ˆ }. ( W dn th ollowng sgnal-to-nos ratos (SN: SN at rom S: whr n s th compl Gaussan nos wth zro man and varanc o. It s assumd that α and α ar ndpndnt quas-statc aylgh channls wth ` { } and { }. W also dnot th 5 Journal o Communcatons adng or... N. Morovr w also assum {g } and {h } to b quas-statc channls. Furthrmor w assum that th nlunc o ntrrnc at S and S ar domnant and thror that th ct o n and n ar nglctd. Th transmt powr s gvn by { }. Th ntrrnc powr at S and S s (b Th scond tm slot y n (3 S ( ndpndnt aylgh dstrbutd wth { g } or... N. Th rcvd sgnal by S s h... hn { } whr th contrbuton rom N ntrrnc sgnals {s( }N s consdrd. Th channls btwn th ntrrrs and S ar {g }. Thy ar assumd to b (a Th rst tm slot S S by g... g N and N n S y g s( n Th two-way rlayng systm modl wth co-channl ntrrnc s shown n Fg. whr two mobl trmnals S and S at th dgs o two drnt clls chang mssag wth th ad o a rlay nod assumng that th drct path btwn thm s brokn. Th sourc nods S and S ar at th cll-dgs and sur rom ntrrnc rom othr mobl/rlay nods n adacnt clls whl th rlay nod s r rom ntrrnc. W assum that ntrrnc s th domnatng actor lmtng th prormanc. Th noss at S and S wll b gnord whlst s nos-lmtd. Th orward and backward channls ar rcprocal wth α dnotng th channl btwn S and and α dnotng th channl btwn S and. W assum that S S and ar quppd wth on antnna only. Th DF protocol s usd at th rlay. Th DF two-way rlayng stratgy conssts o two qual tm slots. at and { } rspctvly. In th scond tm slot both and ar dcodd succssully th rlay combnd th dcodd symbols usng physcal layr ntwork codng obtans and broadcasts t to S and S [3]. Thror atr two tm slots S obtans II. SYSTM MODL S powr SN at rom S: 964 ˆ (6

3 Journal o Communcatons Vol. No. Dcmbr 5 ˆ whr (7 p(d p(d C ( C ( C ( C ( p( ] [ Th sum-sn at : MAC ˆ ˆ (8 N AN ( I N ( I Ik k k W also dn th sgnal-to-ntrrnc ratos: Sgnal-to-ntrrnc rato at S: ˆ g N B N ( I N ( I Il (9 l l ˆ h ( N N whr g g I and h h I. In ths scton w nvstgat th ag probablty or th two-way rlayng ntwork. Frstly w assum that all th transmt sgnals to b Gaussan varabls and dnot th transmsson rats rom S to S and rom S to S by and rspctvly. Accordng to th rat rgon or th two-way rlayng ntwork n [3] an ag vnt actly occurrd whn C ( N C ( C ( I B C ( I (3 C ( C ( N N I wth ( ( ( ( C ( C (. C ( C ( roo: S Appnd. IV. NUMBICAL SULS I Hr w prsnt th numrcal rsults to valdat th analytcal rsults o th ag probablty. Fg. shows th ag probablty o DF two-way rlayng ntwork wth channl stmaton rrors and multpl ntrrrs or... Th ntrrnc powr s dnotd S and S.. I I and I I th ag probablty s gvn by ( ( N ( N by squncs I [ I( ] and I [ I( ].... I... I In th smulatons w st th transmsson rats by N N I I d ( ( N N I I ( ( N N I I d + ( ( N N I I ( 5 Journal o Communcatons I A unqual powr.. and. Our man rsults s gvn n th ollowng concluson. Concluson: I th ntrrrs hav dssmlar powr at I C ( N mn{ log( log( } or ( mn{ log( log( } or log( MAC W assum that th ntrrrs at S or S ar o I d III. OUTAG OBABILITY ANALYSIS d I Sgnal-to-ntrrnc rato at S: =. =.8 and th powr o nos by. W st th numbr o th ntrrrs by N=N=N=3 and w st th dstnct ntrrnc powrs as an arthmtc squnc whch s s=s= [ ]. In th asymmtrcal cas w assum ==3dB =3dB.8.7 ; In th symmtrcal cas w assum.7. Th comparson or th ag probablty btwn th analytcal rsults q. ( and th smulaton rsults s shown n Fg.. It s clarly obsrvd that th analytcal rsults q. ( match th act rsults prctly. As pctd th ct o channl stmaton rrors also can b asly obsrvd. 965

4 Journal o Communcatons Vol. No. Dcmbr 5 In Fg. 3 w prsnt th ag probablty prormanc o th DF two-way rlayng ntwork or drnt numbrs o ntrrrs. Hr w assum.. Whn th numbr o th ntrrrs s N=N=N=3 th ntrrnc powr s s=s= [ ]; Whn th numbr o th ntrrrs s N=N=N=4 th ntrrnc powr s s=s=[ ]. Th stnc o drnt numbrs o ntrrrs acts th ag prormanc sgncantly. ANDIX OOF W dn th uncton C ( wth. Thn ( s rcast as { C ( or C ( or C ( (4 or C ( or MAC C (} whr / or. Thror th ag probablty s gvn by -. Outag robablty undr asymmtrcal and symmtrcal cass. sults show that our analyss s vry clos to th act valus. { C ( or C ( or C ( -. (5 or C ( or C (} whr Analyss or asymmtrcal casrror s. Smulaton or asymmtrcal casrror s. Analyss or asymmtrcal casrror s. Smulaton or asymmtrcal casrror s. Analyss or symmtrcal casrror s. Smulaton or symmtrcal casrror s. Analyss or symmtrcal casrror s. Smulaton or symmtrcal casrror s. ˆ ( g ( ˆ h ( ( A db From (5 w s that s actd by th cumulatv dnsty unctons (CDFs o and Fg.. Outag probablty o DF two-way rlayng systm wth drnt. It s asly drvd that C( C( C( (6 -. Thror w obtan th prssons o or drnt cass: ( { C ( or C ( or C (} -. Outag robablty -.3 Smulaton or asymmtrcal casn=4 Analyss or symmtrcal casn=3 Smulaton or symmtrcal casn=3 Analyss or symmtrcal casn=4 Smulaton or symmtrcal casn= A (db C ( C ( C ( C ( C ( (8 (3 { C ( or C ( } C ( C ( (9 (4 { C ( Fg. 3. Outag probablty o DF two-way rlayng systm or drnt numbrs o co-channl ntrrrs or C ( or C (} ( C ( C ( C ( C ( C( V. CONCLUSIONS (5 { C ( or C ( } In ths papr w analyzd th ag prormanc o a DF two-way rlayng ntwork wth channl stmaton rrors and co-channl ntrrnc. Frstly th sgnal-tonos ratos and sgnal-to-ntrrnc ratos o th systm was dnd. Scondly th prsson o th ag probablty was transormd to th uncton o multpl varabls and th cumulatv dnsty unctons and probablty dnsty unctons o th varabls wr gvn. At last by mployng th dstrbuton w drvd closorm prsson o th ag probablty o th systm 5 Journal o Communcatons (7 ( { C ( or C ( or C (} Analyss or asymmtrcal casn=3 Smulaton or asymmtrcal casn=3 Analyss or asymmtrcal casn=4 -.4 C ( C ( C ( C ( C ( ( (6 { C ( or C ( or C (} C ( C ( C ( C ( C ( C ( 966 (

5 Journal o Communcatons Vol. No. Dcmbr 5 { C( or C( } (7 C( C( C( C( C( C( C( (3 G ( C( C( (3 (3 (4 G ( C( C( (3 (5 G ( C( C( (33 and whr F ( F ( F ( ( ( d d (3 ( ( d d (4 d d (5 ( d ( d (6 ( d d (7 d d (7 ( d d ( F ( ( (4 ( dnot th CDFs and th probablty dnsty uncton (DFs or and rspctvly. Wth CDFs o and ar rspctvly gvn by - ( whr and whr ( th F (5 - ( ( F (6 rspctvly gvn by and th DFs o and ar ( (7 ( (8 Followng (7-(3 w hav ( G ( C( C( (9 ( G ( C( C( (3 whr and ( y s G ( C( C( (34 (6 (7 G ( C( C( (35 G ( y ( y (36 y G ( y p[ ( ] (37 C( p[ ( y] C( ( y p[ ( ] (38 ( C( y C( [ p( ] = whr Accordng to th dntons g ( ( h and th CDFs o ( ( g and ar gvn by whr and h. N I I th CDFs and DFs o N F ( A (39 N I I N F ( B (4 N N I I I A (4 N N B I I I (4 N N N ( I I I A 5 Journal o Communcatons 967

6 Journal o Communcatons Vol. No. Dcmbr 5 B N N N ( I l l l I I ( ( Substtutng (9-(35 (39-(4 nto (4 and smplyng th rsult gvs th dsrd rsult (. ACKNOWLDGMNT Ths rsarch was supportd by Natonal Natural Scnc Foundaton o Chna undr grant Scntc sarch Common rogram o Bng Muncpal Commsson o ducaton undr grant No.598. FNCS [] B. ankov and A. Wttnbn Spctral cnt protocols or hal-dupl adng rlay channls I Journal on Slctd Aras n Communcatons vol. 5 no. pp Fb. 7. [] S. Km. Mtran and V. Tarokh rormanc bounds or bdrctonal rlayng I Transactons on Inormaton Thory vol. 54 no. pp Nov. 8. [3] Y. Han S. H. Tng C. K. Ho and W. H. Chn rormanc bounds or two-way amply-and-orward rlayng I Transactons on Wrlss Communcaton vol. 8 pp Jan. 9. [4] Q. L S. Tng A. andharpand and Y. Han Adaptv two-way rlayng and ag analyss I Transactons on Wrlss Communcaton vol. 8 no. 6 pp Jun. 9. [5] H. J. Yang J. Chun and A. aulra Asymptotc capacty o th spatratd MIMO two-way rlay channl I Transactons on Inormaton Thory vol. 57 no. pp Nov.. [6].Wang and M.Tao Jont sourc and rlay prcodng dsgn or MIMO two-way rlayng basd on MS crtra I Transactons on Sgnal rocssng vol. 6 no. 3 pp Mar.. [7] M. Tao and. Wang Lnar prcodng or mult-par two-way MIMO rlay systms wth ma-mn arnss I Transactons on Sgnal rocssng vol. 6 no. pp Oct.. [8]. Vaz and. W. Halth Capacty scalng or MIMO two-way rlayng n roc. I Intrnatonal Symposum on Inormaton Thory Nc 7 pp [9]. Vaz and. W. Halth On th capacty and dvrstymultplng trado o th two-way rlay channl I Transactons on Inormaton Thory vol. 57 no. 7 pp Jul.. [] X. Ln M. Tao and Y. Xu Fnt-SN dvrsty-multplng trado o th two-way mult-antnna rlay adng channls n roc. I Global Communcaton Conrnc Mam FL pp. -5. [] Q. L S. H. Tng A. andharpand and Y. Han Cogntv spctrum sharng wth two-way rlayng systms I Transactons on Vhcular Tchnology vol. 6 no. 3 pp Mar.. [] A. Bltsas A. Khst D.. d and A. Lppman A smpl coopratv dvrsty mthod basd on ntwork path slcton I Journal on Slctd Aras n Communcatons vol. 4 no. 3 pp Mar. 6. [3] T. J. Ochtrng and H. Boch Bdrctonal rgnratv haldupl rlayng usng rlay slcton I Transactons on Wrlss Communcaton vol. 7 no. 5 pp May 8. [4]. Dng W. H. Chn and K. K. Lung Dstrbutd bamormng and powr allocaton or coopratv ntworks I Transactons on Wrlss Communcaton vol. 7 no. 5 pp May 8 [5] G. hng K. K. Wong A. aulra and B. Ottrstn obust collaboratv-rlay bam-ormng I Transactons on Sgnal rocssng vol. 57 no. 8 pp Aug. 9. [6] Y. Jng and B. Hassb Dstrbutd spac-tm codng n wrlss rlay ntworks I Transactons on Wrlss Communcaton vol. 5 no. pp Dc. 6. [7] X. Y. Guo and X. G. Xa A dstrbutd spac-tm codng n asynchronous wrlss rlay ntworks I Transactons on Wrlss Communcaton vol. 7 no. 5 pp May 8. [8] M. Chn and A. Ynr Multusr two-way rlayng: Dtcton and ntrrnc managmnt stratgs I Transactons on Wrlss Communcaton vol. 8 no. 8 pp Aug. 9. [9] H. J. hang X. L. Chu W. Guo and S. Y. Wang Costnc o W-F and htrognous small cll ntworks sharng unlcnsd spctrum I Communcatons Magazn vol. 53 no. 3 pp Mar. 5. [] H. J. hang C. X. Jang X. L. Chu and X. B. Wang sourc allocaton or cogntv small cll ntworks: A coopratv barganng gam thortc approach I Transactons on Wrlss Communcatons 5. [] C. hong S. Jn and K. K. Wong Dual-hop systm wth nosy rlay and ntrrnc-lmtd dstnaton I Transacton on Communcatons vol. 58 no. 3 pp Mar.. [] D. L and J. H. L Outag probablty or dual-hop rlayng systms wth multpl ntrrrs ovr aylgh adng channls I Transactons on Vhcular Tchnology vol. 6 no. pp Jan. [3] J. B. Km and D. Km act and closd-orm ag probablty o opportunstc dcod-and-orward rlayng wth unqual-powr ntrrrs I Transacton on Wrlss Communcatons vol. 9 no. pp Dc.. [4] S. Hatamna S. Vahdan and M. Mohammad rormanc analyss o two-way dcod-and-orward rlayng n th prsnc o co-channl ntrrncs IT Communcaton vol. 8 no. 8 pp Aug. 4. [5] X. C. Xa D. M. hang K. Xu and Y. Y. Xu Intrrnclmtd two-way DF rlayng: Symbol-rror-rat analyss and comparson I Transacton on Vhcular Tchnology vol. 63 no. 7 pp [6] H. J. hang C. X. Jang X. T. Mao and H. H. Chn Intrrnc-lmtd rsourc optmzaton n cogntv mtoclls wth arnss and mprct spctrum snsng I Transactons on Vhcular Tchnology 5. [7] C. Q. Yang W. B. Wang and S. hao rormanc o dcod and orward opportunstc coopraton wth channl stmaton rrors n roc. I st Intrnatonal Symposum on rsonal Indoor and Mobl ado Communcatons pp [8] A. azav and M.. akravan Symbol rror rat analyss and powr allocaton or dcod and orward rlayng wth channl stmaton rror n roc. 9th Intrnatonal Conrnc on Tlcommuncatons pp. -6. [9] S. S. Ikk and S. Assa Impact o Imprct channl stmaton and co-channl ntrrnc on rgnratv coopratv ntworks I Wrlss Communcatons Lttrs vol. no. 5 pp Oct.. [3]. opovsk and H. Yomo hyscal ntwork codng n two-way wrlss rlay channls n roc. I Intrnatonal Conrnc on Communcatons 7 pp [3] W. Nam S. Y. Chung and Y. H. L Capacty bounds or twoway rlay channls n roc. I Intrnatonal urch Smnar on Communcatons urch 8 pp Journal o Communcatons 968

7 Journal o Communcatons Vol. No. Dcmbr 5 Jnhong Fan rcvd hr BS dgr rom Tayuan Unvrsty o Tchnology Chna n. Sh s currntly a h.d canddat wth School o Inormaton and Communcaton ngnrng Bng Unvrsty o osts and Tlcommuncatons Bng Chna. Hr rsarch ntrsts nclud coopratv usrs and rlay systms or wrlss communcaton and MIMO systms. 5 Journal o Communcatons 969