Semi Blind Channel Estimation with Training-Based Pilot in AF Two- Way Relaying Networks

Transcription

1 Intrnational Journal of Currnt Enginring and chnology E-ISSN , P-ISSN INPRESSCO, All Rights Rsrvd Availabl at Rsarch Articl Smi Blind Channl Estimation with raining-basd Pilot in AF wo- Way Rlaying Ntwors Hmant Gavasar * and Sandp Kumar Agrawal Dpt. of ECE Dpartmnt, RGPV Univrsity, Rustamji Institut of chnology BSF Acadmy anpur, Gwalior, M.P, India Accptd 0 Jan 07, Availabl onlin 30 Jan 07, Vol.7, No. (Fb 07) Abstract -way rlaying ntwors ar dsign for bandwidth fficint us of th availabl spctrum, sinc it allow for data xchang btwn two usrs with th involvmnt of an intrmdiat rlay nod. Du to suprposition of signals in th rlay nod, th rcivd signal at th usr trminals is affctd by multipl paramtrs li channl gains, timing offsts, and carrir frquncy offsts which nd to b stimat and compnsat. Our proposd smi-blind stimator is basd on th Gaussian maximum lilihood critrion which trats that data symbols as Gaussian-distributd nuisanc paramtrs. o assist in th stimation of th individual channls, w adopt a suprimposd training stratgy at th rlay. W hav dsign th pilot vctors of th trminals and th rlay to optimiz th stimation prformanc. Morovr it w compar th smi-blind and pilot-basd Cramr-Rao bounds (CRBs) to us as prformanc bnchmars. W us simulation rsult to show that th proposd mthod provids improvmnt in stimation accuracy ovr th convntional pilot-basd stimation and it approachs th smi-blind CRB as SNR incrass & th simulation rsults shows that th prformanc of th proposd stimators is rlatd to th drivd CRLBs at modrat to high SNR. It is also shows that th ovrall BER prformanc of th AF WRN is clos to a WRN. Kywords: Man squar Error(MSE),Cramr-Rao lowr bounds (CRLB), Bit-rror Rat(BER) Gaussian maximum lilihood critrion, Amplify and Forward (AF).. Introduction Rlaying is th y tchnology to rlat th communication btwn two usr trminals, spcially whn thr ar larg distancs btwn thm (B. Ranov and A. Wittnbn Fb. 007). Unidirctional or on-way rlaying supports in communication from a sourc to a dstination usr and has bn studid in th litratur (B. Ranov and A. Wittnbn Fb. 007). On th othr hand, in two-way rlaying ntwors (WRNs), th flow of information is bidirctional and th two usrs xchang data simultanously with th rlation of an intrmdiat rlay nod (S. Abdallah and I. N. Psaromiligos(Jul. 0). h comparison with on-way half-duplx rlaying, bidirctional rlaying is a spctrally mor fficint rlaying protocol (S. Abdallah and I. N. Psaromiligos(Jul. 0). Both amplify-and-forward and dcod-and-forward protocols hav bn dsignd for WRNs. If comparison to th DF protocol & AF protocol is widly adoptd, as it rquirs minimal procssing at th rlay nod (F. Gao, R. Zhang, and Y. Liang,Oct. 009).h two phas communications in AF WRNs, th two usrs firstly transmit data to th rlay nod than rlay *Corrsponding author Hmant Gavasar is a PG Studnt and Sandp Kumar Agrawal is woring as Profssor broadcasts its rciv signal to both usrs in th scond in phas th two usrs signals at th rlay nod undr diffrnt propagation paths and may not b alignd in tim and frquncy. h suprimposd signal broadcastd from th rlay nod is affctd by multipl impairmnts xampls ar channl gains, timing offsts & CFO. h stimation and compnsation algorithms hav bn applid to countr ths impaird in unidirctional rlaying ntwors (F. Gao, R. Zhang, and Y. Liang,Nov. 009), (G. Wang, F. Gao, Y. C. Wu, and C. llambura, Fb. 0.) th proposd algorithms cannot b dirctly applid to WRNs du to diffrncs btwn th two systm modls. In WRNs Fig., ach usr can xploit th nowldg of th slf transmittd signal during Phas in ordr to dtct th signal from th othr usr during Phas. h blind (G. Wang, F. Gao, Z. X., and C. llambura, 00) & smi-blind (G. Wang, F. Gao, W. Chn, and C. llambura, Aug. 0) mthods hav bn proposd for channl stimation only in AF WRNs. A particl filtring basd mthod for stimating channl and timing offst is usd in (X. Liao, L. Fan, and F. Gao, 00). In training basd mthods, which ar mor for practical implmntation (E. d Carvalho and D.. Sloc, Apr. 004.), channl stimation (F. Gao, R. Zhang, and Y. Liang,Oct. 009), (.-H. Pham, Y.-C. Liang, H. Garg, and A. 09 Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07)

2 Hmant Gavasar t al Smi Blind Channl Estimation with raining-basd Pilot in AF wo-way Rlaying Ntwors Nallanathan,00) or joint channl and CFO stimation (G. Wang, F. Gao, and C. llambura,00) has bn considrd in th litratur. h bst of author s nowldg, stimation and dcoding schm for WRNs in th prsnc of channl gains, timing offsts, and CFO is still an opn rsarch problm. In this papr, a complt synchronization approach, i.., joint stimation and compnsation of channl gains, timing offsts, and CFO for AF WRNs is proposd. h rcption of mixd in signals broadcastd from rlay nod, th usr nods first jointly stimat th impairmnts using nown training signals and th proposd ML algorithm or diffrntial volution basd stimators ( S. Zhang, F. Gao, and C. Pi,Sp. 0). Subsquntly, th usrs mploy th proposd minimum man-squar rror rcivr in combination with th stimatd impairmnts to dcod th rcivd signal. h contributions of this papr can b summarizd as follows: W dsign a systm modl for having synchronization and st th channl paramtrs in AF WRN. W assign Cramr-Rao lowr bounds for joint stimation of multipl impairmnts at th usr nods for WRN. hs bounds can b applid to hav th prformanc of synchronization and channl stimation in AF WRN ntwors. W driv an ML basd stimator for joint stimation of multipl impairmnts. A DE basd algorithm is dsignd for an altrnat of ML stimator to rduc th complxity with synchroniz in AF WRNs. Simulation rsults show that th man squar rror prformancs of both ML and DE stimators ar clos to th CRLB at modrat to-high S/N ratios. W hav an MMSE rcivr for compnsating th impairmnts and dtcting th signal from th opposing usr. h simulations ar carrid out to masur th stimatd MSE and BER prformancs of th proposd transcivr structur. hs rsults show that BER prformanc of an AF WRN can b improvd in th prsnc of practical synchronization rrors. In fact, th application of th driv transcivr rsults in an ovrall ntwor fficincy which is vry clos to th idal ntwor basd on th assumption of nowldg of synchronization and channl paramtrs. Fig. Systm Modl for AF two-way rlay ntwor Notation: Suprscripts (.), (.) *, and (.) H dnots th transpos, th conjugat, and th conjugat transpos oprators, rspctivly. X {.} dnots th xpctation oprator with rspct to th variabl x. h oprator xˆ rprsnts th stimatd valu of x. {.} & {.} dnot th ral and imaginary parts of a complx quantity. CN (, ) dnots th complx Gaussian distributions with man µ and varianc. Boldfac small lttrs, x and boldfac capital lttrs, X ar usd for vctors matrics, rspctivly. [X] x;y rprsnts th ntry in row x and column y of X. I X dnots X X idntity matrix, ǁxǁ rprsnts th ɭ norm of a vctor x, and diag(x) is usd to dnot a diagonal matrix, whr its diagonal lmnts ar givn by th vctor x.. Systm Modl W considr a half-duplx AF WRN with two usr trminals, and, and a rlay nod, R, as shown in Fig..All nods ar quippd with a singl omnidirctional antnna. h channl gain, timing offst, and carrir frquncy offst btwn th th usr trminal and th rlay nod ar dnotd by h, and, rspctivly, for =,, whr th suprscripts, (.) [sr] and (.) [rs], ar usd for th paramtrs from usr trminal to rlay nod and from rlay nod to usr trminal, rspctivly. h timing and carrir frquncy offsts ar modld as unnown dtrministic paramtrs ovr th fram lngth, which is similar to th approach adoptd in (E. d Carvalho and D.. Sloc,Apr. 004) and (B. Ranov and A. Wittnbn Fb. 007). Quasi-static and frquncy flat fading channls ar considrd, i.., th channl gains do not chang ovr th lngth of a fram but chang from fram to fram according to a complx Gaussian distribution, CN (0, ). h us of such channls is 0 Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07) h motivatd by th prior rsarch in this fild (S. Abdallah and I. N. Psaromiligos, Jul. 0), (.-H. Pham, Y.-C. Liang, H. Garg, and A. Nallanathan,00)].h transmission fram from ach usr is comprisd of training and data symbols. h xchang of data among th two usr trminals is compltd in two phass: ) During th first phas, th transmission fram, [t ; d ], is transmittd from th th usr, =, to an intrmdiat rlay nod, whr t and d dnot th th usr s training and data signal, rspctivly. his is illustratd in Fig.. h signal from th two usrs is suprimposd at th rlay nod. ) During th scond phas, th rlay nod amplifis th suprimposd signal and broadcasts it bac to th usrs. h usrs us th training part of th rcivd [P] signal, y, to jointly stimat th multipl impairmnts, i., channl gains, timing offsts, and carrir frquncy offsts. h ffct of ths impairmnts is compnsatd and th rcivd signal, [DP] y, is dcodd at th thusr s trminal. Not: that th suprscripts (.) [P] and (.) [DP] dnot th signals in training and data transmission priods,

3 Hmant Gavasar t al Smi Blind Channl Estimation with raining-basd Pilot in AF wo-way Rlaying Ntwors rspctivly and Fig. shows th transmittd frams at th first usr trminal,. A similar structur is followd for th scond usr trminal,. h rcivd signal at th rlay nod during th training priod, r [P] (t), is givn by j r h t L t( n) g( t n ) n( t) n0 whr th timing and carrir frquncy offsts, () [SR] [SR] and,ar normalizd by th symbol duration, L is th lngth of training signal t, g(t) stands for th root-raisd cosin puls function, and n(t) dnots zro-man complx additiv whit Gaussian nois (AWGN) at th rlay rcivr, i.., n( t) CN(0, ). o avoid amplifir saturation at th rlay, th rlay nod r P amplifis th rcivd signal,, with th powr constraint factor,, and broadcasts th h n amplifid signal to th usrs (F. Romr and M. Haardt, Nov. 00). h rcivd signal at th usr trminal,, during th training priod, y [P] (t) is givn by v j t y h r ( ) w( t), () whr w (t) dnots th zro-man complx AWGN at th rcivr of, i.. w( t) CN(0, w ) Substituting () into (), y [P] (t) is givn by v v [ j t j ( t y h ( h v j t h n( ) w( t), rs] ) L ) t( n) g( t n )) n0 (3) Not that unli, th dvlopd systm modl in (3) tas into account both th timing rrors, from usrs to th rlay nod,, = ;, and from rlay nod [SR] [ SR] bac to usr trminal,. h rcivd signal in y P (3),, is sampld with th sampling tim s = /Q and th sampld rcivd signal, y P ( i), is givn by y h Whr jv jv i/ Q i/ Q t n( i) w ( ) L t ( n) g( i n0 s n ) (4) jv h h is th combind channl gain from -R- and -R- for = and =,rspctivly, v v v is th sum of carrir frquncy offsts from -R- and -R- for = and =, rspctivly, v v bcaus sam oscillators ar usd during transmission from usr to th rlay nod and from rlay nod bac to usr, thus, v = v v =0, Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07) is th rsultant timing offst from -R- and -R- for = and =, rspctivly, Q is th sampling factor, n = 0,, L- and i = 0,,..LQ - ar usd to dnot -spacd and s spacd sampls, rspctivly, and n(i) has bn usd in plac of n(i s - ]), sinc n(t) dnots th AWGN and its statistics ar not affctd by tim dlays. Upon rcption of signal broadcastd from th rlay, it is assumd that th usrs first mploy coars fram synchronization to nsur that th suprimposd signals ar within on symbol duration from ach othr Eq. (4) can b writtn in vctor form as y Gt Gt h n w (5) Whr G is th LQ L matrix of th sampl of th puls shaping filtr such that [ G ] i, n [ rd] grrc( is n ), jv (0)/ ( )/ ([ N j v,......, LQ N diag ]) LQ LQ matrix, [rs] jv (0)/ ( )/ ([ N j v,......, LQ N diag ]) LQ LQ matrix, y diag [ y (0),......, y ( LQ )] t [ t (0),......, t( LQ )], w n [ n (0),......, n( LQ )] and [ w (0),......, w( LQ )]. is an is an h rcivd signal during th data transmission priod y [ DP ],can b similarly xprssd as (5), whr training t is rplacd by th data d =[d (0),.. d (L - )]. Not that as anticipatd, th data lngth L is diffrnt and largr than th training lngth L Without loss in gnrality,w driv th CRLB and stimators for joint stimation of channl gains, timing offsts, and CFO at th usr trminal.h systm modl in this part and th drivd CRLB, stimation, and dtction schms in ths sctions can b asily manipulatd to dtct d at th usr trminal. hs dtails ar not includd to avoid rptition. 3. Smi-Blind Channl Estimation W prsnt th proposd smi-blind channl stimation algorithm. For comparison purposs, w also considr fully pilot-basd stimation and driv th corrsponding Pilot-basd last-squars (LS) channl stimator.

4 MSE of LSE channl stimation for SNR= 5dB Hmant Gavasar t al Smi Blind Channl Estimation with raining-basd Pilot in AF wo-way Rlaying Ntwors A. th CRB for Pilot-basd Estimation his tchniqu combins th ffort of both pilotassistd stimation tchniqu and blind stimation tchniqus, whr th intrinsic information in th unnown data symbols and th nown pilot information ar usd for channl stimation. Using th sam numbr of pilot symbols, smi-blind stimation tchniqus prform bttr than pilot basd tchniqus. Smi-blind tchniqus solv th uncrtainty problm associatd with blind stimation using fw pilot symbols. Som litraturs hav invstigatd smi-blind stimation using th subspac mthod. According to (G. Wang, F. Gao, Z. X., and C. llambura, 00), thr is high computational complxity associatd with th subspac mthod. Also, in th study in (X. Liao, L. Fan, and F. Gao, 00), linar prdiction was usd to stimat th blind constraint whil th matrix A was stimatd using th last squar (LS) algorithm. h us of smi-blind channl stimation in singl input multipl output (SIMO) systms achivd good prformanc using th subspac mthod and it has a simpl structur (G. Wang, F. Gao, W. Chn, and C. llambura, Aug. 0) but its application in multipl inputs multipl output (MIMO) systm is not too succssful bcaus it can only stimat channl subjct to a polynomial matrix ambiguity (G. Wang, F. Gao, W. Chn, and C. llambura, Aug. 0). B. h CRB for Smi-blind Estimation Som othr litratur stat that stimations ar basd on scond-ordrd statistics of a long vctor, thrfor thr is nd for a larg numbr of OFDM symbols to stimat th corrlation matrix and this is not suitabl for fast tim-varying channls. According to th subspac mthod is not practical for gnral MIMO channl stimation. h subspac algorithm in is limitd to MIMO OFDM systms. It analyss th various smi blind channl stimation having th stimation on MIMO systms. Paralll data and training signal algorithm is dvlopd, bloc rcodd spac tim OFDM transmission is prsntd. h last squar stimator basd on nown pilot squnc is analyzd in and th statistical structur of th obsrvation is usd in th stimation. h first and scond ordr statistic is usd in to stimat th channl. 4. Cramr-Rao Lowr Bound Whr Gt Gt is an LQ matrix,, and u h n w, basd on assumption and proposd systm modl, th rcivd signal vctor,, is a circularly symmtric complx Gaussian P y y P random variabl, CN(, ), with man and covarianc matrix.givn by = (7a) and { u, u H h n w u LQ } ( ) I I, (7b) LQ Rspctivly. o dtrmin th CRLB, w hav to first formulat th paramtr vctor of intrst. h usr has to stimat th channl gains α, timing offsts [, ], and th carrir frquncy offst v. hr is no nd to stimat v as this is found to b 0 as xplaind blow (4).As a rsult, th paramtr vctor of intrst,, is givn by,, v, (8) Finally, th CRLB for th stimation of is givn by th diagonal lmnts of th invrs of F. Not that th CRLB for channl stimation is th sum of th CRLBs for ral and imaginary parts of th channl stimation. 5. Simulation Rsult In this sction, w invstigat through simulations th prformanc of th proposd smi-blind algorithm and compar it to that of th pilot-basd LS stimator Nt =, Nr = Pilot Basd Estimat Pilot Basd CRB Smi Blind Estimat smi Blind CRB K In this sction, th CRLB for joint stimation of multipl impairmnts at ar drivd. h signal modl in (5) can b rwrittn as y P u (6) Fig.MSE prformanc of th smi-blind and pilotbasd (LS) stimators along with th corrsponding smi-blind and pilot-basd CRBs plottd vrsus K for th cass of Gaussian-distributd and QPSK-distributd data symbols Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07)

5 Bit rror rat (BER) MSE of LSE channl stimation MSE of LSE channl stimation Hmant Gavasar t al Smi Blind Channl Estimation with raining-basd Pilot in AF wo-way Rlaying Ntwors SNR [db] Fig.3MSE prformanc of th LS stimator and th smi-blind stimator vrsus SNR (L = 0, N = 3) for thr scnarios: ) optimal pilots (κ = 9,δ= 0), ) suboptimal pilots (κ = 9, δ = 5) and 3) randomly gnratd pilots Nt =, Nr = Smi Blind Estimat Random Pilots LSE Estimat Random Pilot Smi Blind Estimat (=9, Dlta= 0) LSE Estimat Optimal Pilot Smi Blind Estimat Optimal Pilot LSE Estimat (=9, Dlta= 0) Nt =, Nr = Pilot Basd Estimat Pilot Basd CRB Smi Blind Estimat(Gaussian) Smi Blind Estimat (QPSK) smi Blind CRB SNR [db] Fig.4MSE prformanc of th smi-blind and pilotbasd (LS) stimators along with th corrsponding smi-blind and pilot-basd CRBs plottd vrsus SNR for th cass of Gaussian-distibutd and QPSKdistributd data symbols th individual channls, w mployd suprimposd training at th rlay. In abov Fig, w hav a comparison btwn CRB basd tchniqus such tchniqus ar pilot basd stimation, pilot basd CRB, smi blind stimation and smi blind CRB. W found that SNR incras along with x-axis and MSE lvl dcrass along with y-axis and smi blind CRB tchniqu provids bttr rsult as compard to th othr CRB basd tchniqus. In abov Fig 3, w hav comparison in smi blind stimation random & optimal pilot, LSE stimation random & optimal pilot. In which smi blind stimat random pilot provid bttr rsult as compar to othr tchniqu. As w incras SNR along X-axis MSE gt rduc along Y-axis. In abov Fig 4, w hav compar pilot basd stimat & CRB, Smi blind stimat & CRB along by using Gaussian and QPSK modulation tchniqu. In which smi blind stimat provid bttr rsult as compar to othr tchniqu. As w incras SNR along X-axis MSE gt rduc along Y-axis. In abov Fig 5, Comparison btwn BER & SNR, In which bit rror rat gt rduc along Y-axis as w incras SNR along X-axis. h rsulting GML stimats wr obtaind numrically using th BFGS algorithm. W also drivd conditions for th optimality of th training pilots and providd xampls of pilot vctors that satisfy thm. As prformanc bnchmars, w drivd th smi-blind and pilot-basd CRBs. W usd simulation studis to compar th proposd smi-blind stimator to th convntional pilot-basd stimator and showd that th proposd stimator provids a substantial improvmnt in accuracy. h prformanc of th smi-blind algorithm closly approachs th drivd smi-blind CRB as SNR incrass. Finally, ths prformanc gains can b achivd at a rasonabl computational cost, which clarly stablishs th mrit and practicality of smi-blind channl stimation for AF WRNs. Rfrncs Conclusion SNR [db] Fig.5 Bit rror rat (BER) v/s SNR In this papr, w proposd a smi-blind channl stimator for OFDM-basd AF WRNs basd on th Gaussian ML approach. o assist in th stimation of B. Ranov and A. Wittnbn (Fb. 007),Spctral fficint protocols for halfduplx fading rlay channls,ieee J. Sl. Aras Commun., vol. 5, no., pp S. Abdallah and I. N. Psaromiligos(Jul. 0),Blind channl stimation for amplify-and-forward two-way rlay ntwors mploying M-PSK modulation,ieee rans. Signal Procss., vol. 60, no. 7, pp F. Gao, R. Zhang, and Y. Liang,( Oct. 009), Optimal channl stimation and training dsign for two-way rlay ntwors, IEEE rans. Commun.,vol. 57, no. 0, pp F. Romr and M. Haardt,( Nov. 00), nsor-basd channl stimation (ENCE) and itrativ rfinmnts for two-way rlaying with multipl antnnas and spatial rus, IEEE rans. Signal Procss., vol. 58, no., pp F. Gao, R. Zhang, and Y. Liang,( Nov. 009),Channl stimation for OFDM modulatd two-way rlay ntwors,ieee rans. Signal Procss., vol. 57, no., pp ,. G. Wang, F. Gao, Y. C. Wu, and C. llambura,( Fb. 0.), Joint CFO and channl stimation for OFDM-basd twoway rlay ntwors, IEEE rans. Wirlss Commun., vol. 0, no., pp Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07)

6 Hmant Gavasar t al Smi Blind Channl Estimation with raining-basd Pilot in AF wo-way Rlaying Ntwors G. Wang, F. Gao, Z. X., and C. llambura (00) Suprimposd training basd joint CFO and channl stimation for CP-OFDM modulatd two way rlay ntwors, EURASIP J. Wirlss Commun. and Ntwor., vol.00, ID= G. Wang, F. Gao, W. Chn, and C. llambura (Aug. 0) Channl stimation and training dsign for two-way rlay ntwors in tim-slctiv fading nvironmnts, IEEE rans. Wirlss Commun., vol. 0, no. 8, pp X. Liao, L. Fan, and F. Gao,( 00) Blind channl stimation for OFDM modulatd two-way rlay ntwor, in Proc. 00 IEEE Wirlss Comm.and Ntworing Conf. E. d Carvalho and D.. Sloc (Apr. 004.) Blind and smiblind FIR multichannl stimation: (global) idntifiability conditions, IEEE rans. Signal Procss., vol. 5, no. 4, pp , S. Abdallah and I. N. Psaromiligos (Jul. 0) Exact Cramr- Rao bounds for smi-blind channl stimation in amplifyand-forward two-way rlay ntwors mploying squar QAM modulation, ArXiv pr-print cs.i/ ,.-h. Pham, Y.-C. Liang, H. Garg, and A. Nallanathan (00) Joint channl stimation and data dtction for MIMO- OFDM two-way rlay ntwors, in Proc. 00 IEEE Global Comm. Conf. G. Wang, F. Gao, and C. llambura (00) Suprimposd pilot-basd joint CFO and channl stimation for CP-OFDM modulatd two-way rlay ntwors, in Proc. 00 IEEE Global Comm. Conf. S. Zhang, F. Gao, and C. Pi (Sp. 0) Optimal training dsign for individual channl stimation in two-way rlay ntwors,ieee rans. Signal Procss., vol. 60, no. 9, pp K. L, H. Sung, E. Par, and I. L (Dc. 00) Joint optimization for on and two-way MIMO af multipl-rlay systms, IEEE rans. Wirlss Commun., vol. 9, no., pp S. Abdallah and I. N. Psaromiligos (Jul. 0) Blind channl stimation for amplify-and-forward two-way rlay ntwors mploying M-PSK modulation, IEEE rans. Signal Procss., vol. 60, no. 7, pp F. Romr and M. Haardt,( Nov. 00) nsor-basd channl stimation (ENCE) and itrativ rfinmnts for two-way rlaying with multipl antnnas and spatial rus, IEEE rans. Signal Procss., vol. 58, no., pp ,. N. Mollr (Jan.008) On Schoonhag s algorithm and subquadratic intgr gcd computation, Mathmatics of Computation, vol. 77, pp ,. B. P. Singh and R. Singh (006) Elctronic dvics and intgratd circuits.parson Education India, Intrnational Journal of Currnt Enginring and chnology, Vol.7, No. (Fb 07)