GA Based Sensing of Sparse Multipath Channels with Superimposed Training Sequence

Transcription

1 ELEKRONIKA IR ELEKROECHNIKA, ISSN 39-5, VOL., NO., 6 GA Basd Snsing of Spars Multipath Channls with Supriposd raining Squnc Syd Junaid Nawaz, Moazza I. iwana, Mohaad N. Patwary, Noor M. Khan 3, Mohsin I. iwana 4, Abdul Hasb 5 Dpartnt of Elctrical Enginring, COMSAS Institut of Inforation chnology, Faculty of Coputing Enginring and Scincs, Staffordshir Univrsity, Stok-on-rnt, Unitd Kingdo 3 Ac Cntr for Rsarch in Wirlss Counications, Mohaad Ali Jinnah Univrsity, 4 Dpartnt of Elctrical Enginring, National Univrsity of Scinc and chnology, 5 Dpartnt of Elctrical Enginring, Institut of Spac chnology, junaidnawaz@i.org Abstract his papr proposs an iprovd Gntic Algoriths (GA) basd spars ultipath channls stiation tchniqu with Supriposd raining (S) squncs. A nonrando and priodic training squnc is proposd to b addd arithtically on th inforation squnc for nrgy fficint channl stiation within th futur gnration of wirlss rcivrs. his liinats th nd of sparat ovrhad ti/frquncy slots for training squnc. h rsults of th proposd tchniqu ar copard with th tchniqus in th xisting litratur -th notabl first ordr statistics basd channl stiation tchniqu with S. h noralizd channl an-squar rror (NCMSE) and bit-rror-rat (BER) ar chosn as prforanc asurs for th siulation basd analysis. It is stablishd that th proposd tchniqu prfors bttr in trs of th accuracy of stiatd channl; subsquntly th quality of srvic (QoS), whil rtriving inforation squnc at th rcivr. With rspct to its coparabl countrpart, th proposd GA basd sch dlivrs an iprovnt of about db in NCMSE at db SNR and a gain of about db in SNR at - BER, for th population siz st at twic th lngth of channl. It is also donstratd that, this achivnt in prforanc iprovnt can furthr b nhancd at th cost of coputational powr by incrasing th population siz. Indx rs Channl stiation, supriposd training, channl. I. INRODUCION gntic algoriths, On of th ajor probls that liits th high spd data transission through a wirlss channl is th Intr Sybol Intrfrnc (ISI) []. ISI is causd by th ti disprsion inducd du to ultipath propagation phnona. h prforanc and fficincy of channl stiation and qualization tchniqus is of vital iportanc in dsigning advancd counication quipnt to itigat th channl distortions. h channl stiation tchniqus ar Manuscript rcivd May, 5; accptd 8 Novbr, traditionally classifid as: training-basd and blind. In th training squnc basd approachs, th rcivr stiats th channl by xploiting th availabl training and its corrsponding rcivd squncs. Basd on th bhaviour of channl s slctivity in frquncy and ti doains, th known training squnc is ithr transittd frquntly ovr th ddicatd ti slots (across ovr th ntir frquncy slots), or transittd ovr th ddicatd frquncy slots (across ovr th ntir ti slots). his ddicatd allocation of ti/frquncy slots for th training squnc is an ovrhad on th spctral fficincy, spcifically for th cas of highly slctiv wirlss fading channls. Blind channl stiation tchniqus avoid this ovrhad by not using an xplicitly known training squncs. Instad, th channl is stiatd by xploiting th statistical proprtis of inforation squnc known at th rcivr. Howvr, such blind stiation tchniqus also ipos crtain shortcoings, lik, nd of long inforation squncs and coplx signal procssing tchniqus lading to slow convrgnc rat [], [3]. hrfor, with th purpos to furthr nhanc th spctral fficincy, various supriposd training (S) squnc basd stiation tchniqus hav bn proposd in th litratur [3] [7]. Hr, instad of using xplicit ti/frquncy slots for training squnc, a low-powr priodic training squnc is arithtically addd ovr th inforation squnc. his not only iprovs th spctral fficintly but also ffctivly tracks th ti and frquncy slctivity in th counication channl. Ipuls rspons of wirlss counication channls is ncountrd as spars in various physical propagation scnarios whr xist only a fw largly sparatd (in dlay) doinant propagation paths,.g., aronautical counications, undr-watr acoustic counications, high-frquncy radio counication systs whr th doinant wavs arriv rflctd fro th ionosphr, and

2 ELEKRONIKA IR ELEKROECHNIKA, ISSN 39-5, VOL., NO., 6 trrstrial high-dfinition tlvision broadcasting systs, tc. A S squnc basd tchniqu by Jitndra t al. [3] utilizs th first-ordr statistics of training and inforation squncs to stiat th channl. h proposd work ais at nhancing th prforanc of th channl stiation sch prsntd in [3] by using Gntic Algoriths (GAs), spcifically for th cas of spars ultipath channls. GAs ar volutionary coputing tchniqus that hav bn usd in various diffrnt filds to solv th coplx optiization probls [8]. GAs ar fficint stochastic sarch basd tchniqus that vry fficintly and quickly attain nar optial solution in larg solution spacs. GAs odl th biological procsss of volution, crossovr, and utation rpatdly in ordr to optiiz a highly coplx cost function [8]. h gradint fr natur of GA (with sufficint chroosos) ak th vry robust against gtting stuck in th local optiu solutions. GAs hav also bn ployd, for solving th channl stiation probl, in th litratur [8] [3]. Howvr, no GA basd channl stiation tchniqu with S squnc xist in th litratur which also xploits th availabl prior knowldg of channl s sparsity for accurat stiation of channl. [ ], squnc is dfind as c c c c N whr β scals th training squnc to aintain a crtain powr ratio btwn training and inforation squncs. h varianc of inforation and training squnc is dnotd by s and c, rspctivly. h training squnc is supriposd (arithtically addd) ovr th inforation squnc; th transittd squnc is thus dfind as x s c [ x x x N ]. his supriposd squnc is transittd ovr a ti-invariant and ultipath [ ]. frquncy-slctiv channl, h h h hl h ultipath propagation channl is dfind as L h hl l, () l whr hl and l is th gain and dlay of propagation path. Path dlay is takn as intgr ultipl of a sybol duration.. th l is th Kronckr dlta function. h channl s ipuls rspons is odlld as spars with only K Non-Zro (NZ) taps (such that K L ) at th positions, PNZ [ p p p ] K hl, l PNZ,, othrwis. () h nrgy of channl ipuls rspons vctor is odlld noralizd as h (whr. dnots nor ). h squnc rcivd at rcivd is dnotd by y y y y N [ s ] which is obtaind as y Xh n Sh Ch v, (3) Fig.. Syst odl with proposd GA basd channl stiator and qualizr for frquncy-slctiv spars ultipath channls. his papr proposs a GA basd channl stiation tchniqu for ti-invariant spars ultipath channls with S squnc. Sc. II prsnts th considrd syst odl and proposd GA basd stiation and qualization tchniqu. h obtaind siulation rsults ar prsntd in Sc. III, along with a coprhnsiv prforanc analysis. Finally, th proposd work is concludd in Sc. IV. II. CONSIDERED SYSEM MODEL h syst odl of considrd counication syst with GA basd channl stiator is illustratd in Fig.. h inforation and training squncs ar shown by b and c, rspctivly. h inforation squnc is takn as zro an BPSK odulatd inforation squnc dfind as, s [ s s s N ], whr th suprscript rprsnts transpos of th vctor. A known priodic training whr X, S and C ar [N L] convolutional oplitz atrics obtaind fro transittd squnc x, inforation squnc s, and known training squnc c, rspctivly. v [ v v v N ] is th asurnt nois odlld as whit and zro an Gaussian distributd with varianc. v A. First Ordr Statistics Basd Channl Estiators In this sction, th drivation of first ordr statistics basd channl stiators with supriposd pilot squnc proposd in [3], [4], and Error! Rfrnc sourc not found. ar prsntd. h inforation and nois squncs ar assud zro an, thrfor, aftr taking xpctation (i..,. y n, fro th contribution E ) of rcivd signal of non-rando priodic training squnc with priod P, w gt L Ey n hl c n l. (4) l By substituting th known priodic pilot squnc, 88

3 ELEKRONIKA IR ELEKROECHNIKA, ISSN 39-5, VOL., NO., 6 j n l c n l c, in (4) w gt whr d P whr / P P j { ( )} n E y n d, can b obtaind as givn blow (5) L j l d hl c, l (6) P j / n c P c n and. A an-squar consistnt stiat of d can b found as ˆ N j n d y n. N n (7) h stiat dˆ approachs to d as N approachs to. Vctor rprsntation ˆ ˆ ˆ ˆ d [ d d dp ] is givn as whr C is a P L u c C j j dˆ C h, (8) atrix obtaind as: P c cp j j Lu P L u, whr Lu is th uppr bound on channl lngth, such that Lu L. h last-squars stiat of th channl proposd in [3] can thus b obtaind fro th odl in (8) as (9) SIJ arg in d ˆ C. h () h his stiat can also b obtaind as ˆ h SIJ C d, () whr th suprscript rprsnts Moor-Pnros psudoinvrs. h contribution of supriposd inforation squnc and additiv asurnt nois lads to an rror in th stiat dˆ of d, i.., dˆ d. h stiation rror substituting y n in (7), givn as blow can b ralizd by N L N l N n l N n h s n l z j n n. () his inhrnt stiation rror lads to an iprcis stiat of th channl. Morovr, for th cas of spars ultipath channls, this stiation thod do not xploit th availabl prior knowldg of channl s sparsity, thus fails to corrctly stiat th zro valud channl taps. hrfor, an xtnsion of this thod is proposd in [4] for th cas of spars ultipath channls, which propos th following solution to obtain th channl s stiat arg in ˆ SICCS h C h d, (3) h subjct to whr. dnots nor. h convx progra Dantzig Slctor (DS) has bn castd to optiiz th stiat in (3). his thod prfors bttrs than () for th cass of spars ultipath channls [4]. Anothr xtnsion of th odl in (8) is prsntd in Error! Rfrnc sourc not found., which uss atching pursuit algorith to nhanc th stiat by calculating th positions of non-zro channl taps. B. GA Basd Channl Estiator h first ordr statistics basd channl stiation tchniqus, ntiond abov, do not copnsat for inhrnt stiation rror ξ. his rsults in an inaccurat channl stiat. Evolutionary sarch tchniqu of GAs, has bn sn as a potntial candidat to provid proising solutions to various challnging probls of stiation and qualization of wirlss channls. his sction prsnts a GA assistd channl stiator by xtnding th first ordr statistics basd stiator in [3] for th cas of spars ultipath channl. It xploits th availabl a priori knowldg of channl s sparsity and introducs a copnsation paratr for th stiation of rror vctor ξ in th objctiv function. h GA stochastically sarchs for a solution in th ntir solution spac that iniizs th following objctiv function arg in h GA h subjct to C h h dˆ,, (4) whr th paratr should b st in proportion to agnitud of rror, i.., ξ. Sinc, th channl is spars, thrfor iniization of objctiv function for its nor is considrd []. h GA holds a population of individual chroosos. GA initiat th sarch for th optial solution with an initial population h at th gnration g. h initial population h is gnratd using th first ordr stiator in (), aftr its thrsholding to nsur that it is a ˆK spars vctor. h population h i, corrsponding to gi, volvs succssivly fro th prvious population hi by ploying gntic oprators of slction, 89

4 ELEKRONIKA IR ELEKROECHNIKA, ISSN 39-5, VOL., NO., 6 crossovr, and utation. First th chroosos of hi ar valuatd and sortd basd upon th objctiv function in (4). In th slction procss, bttr prforing chroosos ar slctd basd upon stochastic unifor sapling thod. Slctd chrooso with lowst scor passs off as it is to th nxt gnration. Whil th raining slctd chroosos ithr undrgo crossovr or utation to gnrat h i. In crossovr, pairs of chroosos ar randoly cobind to produc nw chroosos, whil utation involvs aking rando changs to individual chroosos. Mutation also avoids pratur convrgnc to a suboptial solution. Now, GA rplacs h i with h i. h procss continus itrativly, till GA trinats at th pr-st axiu liit on gnrations or if th avrag chang in objctiv function s fitnss valu at succssiv gnrations is lss than a pr-st valu. Finally, th individual chroosos corrsponding to th lowst valu of objctiv function togthr is th dtrind stiat of th spars ultipath channl C. Equalizr ĥ GA. A linar qualizr followd by a hard dcision appr is usd to obtain stiat of th inforation squnc ŝ, as illustratd in Fig.. h sybol dnots convolution opration. h qualizr is fd with th rgulatd rcivd squnc y, which is obtaind aftr roving th contribution of pilot squnc c, givn as undr NCMSE is dfind as undr L L hl hl hl l l NCMSE ˆ. (9) h NCME and BER prforanc of th syst is asurd against Signal-to-Nois-Ratio (SNR). h SNR is dfind as th ratio btwn powr of inforation squnc and asurnt additiv nois, SNR s / v. a) b) Fig.. Prforanc Coparison of Proposd GA basd chniqu with tchniqus by Jitndra t al. in [6] and SI-CCS Nawaz t al. in [3]: a) NCMSE vs SNR; b) BER vs SNR. (N = 6, Mont = runs, L =, K = 3, P = 5, γ =, and β =.7). y y Ch ˆ. (5) h block rprsntation of th obtaind stiat of inforation squnc ŝ is givn as blow s H v (6) ˆ ˆ s R ˆ ˆ s H H R R y, whr Rs s I, R v ˆ v I, and Ĥ is a [N N] oplitz atrix structurd as shown blow ˆ ˆ ˆ h h hl ˆ ˆ ˆ ˆ h h hl H, (7) Estiat of nois powr ˆ v ˆv is obtaind as, ( ) ˆ ˆ y y h h, N ( ) ˆ y y h, othrwis. N D. Prforanc Mtrics (8) Noralizd Channl Man Squar Error (NCMSE) and Bit Error Rat (BER) ar usd as prforanc trics. h a) b) Fig. 3. NCMSE prforanc of proposd GA basd tchniqu: a) Effct of population siz γ on NCMSE w.r.t. SNR; b) Effct of channl s sparsity on NCMSE w.r.t. SNR. (N = 6, Mont = runs, L =, K = 3, P = 5, γ =, and β =.7) III. RESULS AND DISCUSSION his sction prsnts an analysis on th rsults obtaind fro prford coputr siulations for NCMSE and BER prforanc of proposd GA basd tchniqu. A frquncyslctiv and ti-invariant spars channl is gnratd for siulations. Indpndnt ralization of channl is gnratd for ach Mont Carlo run for a crtain fixd sparsity K/L. Position of non-zro taps of channl ar takn fro unifor distribution and path gains of non-zro channl taps ar takn fro zro an Gaussian distribution with sa varianc for ach tap. Prforanc coparison of proposd GA basd tchniqu with first ordr statistics basd tchniqus in [3] and [4] is prsntd in Fig., for NCMSE and BER against SNR in (a) and (b), rspctivly. h 9

5 ELEKRONIKA IR ELEKROECHNIKA, ISSN 39-5, VOL., NO., 6 channl lngth and aount of non-zro taps ar takn as L = and K = 3, rspctivly. h powr ratio btwn pilot and inforation squncs is st to.8. h priodic pilot squnc with priod P = 5 is takn sa as takn [3] by for th siulations, which is c : P,,,,,,,,,,,,,,. It is clarly vidnt that th proposd GA basd tchniqu prfors significantly bttr than th tchniqus in [3] and [4] for th cas of spars ultipath channl. his iprovnt is bcaus of th iprovd stiation objctiv function in our proposd sch by considring a copnsation for stiation rror introducd by addd inforation squnc. h proposd sch provids an iprovnt of about db in NCMSE at db SNR, this iprovnt furthr incrass by an incras in SNR, which is clarly vidnt in Fig. (a). It can b witnssd in Fig. (b) that a prforanc gain of about db in SNR can b achivd by proposd GA basd tchniqu for BER of -. h siz of population is st for th graphs plottd in Fig.. In ordr to donstrat th ffct of population siz on th prforanc of proposd sch, th NCME against SNR is plottd in Fig. 3(a). It can b witnssd that th prforanc of GA stiator significantly iprovs with an incras in population siz up to L. By furthr incrasing byond L, furthr slight iprovnt in NCMSE prforanc can b achivd at th cost of coputational powr. h ipact of channl s sparsity on th prforanc of proposd GA basd sch is plottd in Fig. 3(b). h proposd tchniqu provids iprovnt in stiation of channls with high sparsity. An iprovnt of.4 db in NCMSE is obsrvd with an incras in channl s sparsity (K/L) by.. IV. CONCLUSIONS A GA basd channl stiation tchniqu for tiinvariant spars ultipath channls with S squncs has bn proposd. NCMSE and BER basd prforanc coparison of proposd tchniqu with so notabl S basd channl stiation tchniqu has bn prsntd. It has bn stablishd that th proposd tchniqu prfors bttr in trs of th accuracy of stiatd channl and stiatd inforation squnc. It has bn shown that th proposd tchniqu proiss an iprovnt of about db in NCMSE at db SNR and consquntly a gain of about db in SNR at - BER, whn copard to [3] with population siz st at twic th lngth of channl. Morovr, it has also bn stablishd that, this prforanc iprovnt can furthr b nhancd at th cost of coputational powr by an incras in th population siz. REFERENCES [] S. Brnard, Digital counications. NJ: Prntic Hall,. [] W. U. Bajwa, J. Haupt, A. M. Sayd, R. Nowak, Coprssd channl snsing: A nw approach to stiating spars ultipath channls, in Proc. IEEE, vol. 98, no. 6,, pp [Onlin]. Availabl: [3] J. K. ugnait, W. Luo, On channl stiation using supriposd training and first-ordr statistics, IEEE Coun. Lttrs, vol. 7, no. 9, pp , 3. [Onlin]. Availabl: [4] R. Carrasco-Alvarz, R. Parra-Michl, A. Orozco-Lugo, J. ugnait, i-varying channl stiation using two dinsional channl orthogonalization and supriposd training, IEEE rans. on Signal Procss., vol. 6, no. 8, pp ,. [Onlin]. Availabl: [5] L. H, Y.-C. Wu, S. Ma,.-S. Ng, H. Poor, Supriposd trainingbasd channl stiation and data dtction for OFDM aplify-andforward cooprativ systs undr high obility, IEEE rans. Signal Procss., vol. 6, no., pp ,. [Onlin]. Availabl: [6] A. Orozco-Lugo, M. Lara, D. McLrnon, Channl stiation using iplicit training, IEEE rans. Signal Procss., vol. 5, no., pp. 4 54, 4. [Onlin]. Availabl: SP [7] J. ugnait, X. Mng, On supriposd training for channl stiation: prforanc analysis, training powr allocation, and fra synchronization, IEEE rans. Signal Procss., vol. 54, no., pp , 6. [Onlin]. Availabl: SP [8] K. Yn, L. Hanzo, Gntic algorith assistd joint ultiusr sybol dtction and fading channl stiation for synchronous CDMA systs, IEEE J. on Sl. Aras in Coun., vol. 9, no. 6, pp ,. [Onlin]. Availabl: [9] H. Ali, A. Douct, D. I. Ashah, GSR: A nw gntic algorith for iproving sourc and channl stiats, IEEE rans. on Circuits and Sys., vol. 54, no. 5, pp , 7. [Onlin]. Availabl: [] G. Routraya, P. Kanungo, Gntic algorith basd RNN structur for Rayligh fading MIMO channl stiation, in Proc. Enginring, vol. 3,, pp [] K. Yn, L. Hanzo, Gntic-algorith-assistd ultiusr dtction in asynchronous CDMA counications, IEEE rans. on Vh. chnol., vol. 53, no. 5, pp. 43 4, 4. [] S. Chn, Y. Wu, Maxiu liklihood joint channl and data stiation using gntic algoriths, IEEE rans. on Signal Procss., vol. 46, no. 5, pp , 998. [Onlin]. Availabl: [3] M. Jiang, J. Akhtan, L. Hanzo, Itrativ joint channl stiation and ulti-usr dtction for ultipl-antnna aidd OFDM systs, IEEE rans. on Wirlss Coun., vol. 6, no. 8, pp , 7. [Onlin]. Availabl: [4] S. J. Nawaz, K. I. Ahd, M. N. Patwary, N. M. Khan, Supriposd training-basd coprssd snsing of spars ultipath channls, IE Counications, vol. 6, no. 8, pp ,. [Onlin]. Availabl: [5] Z. Jun-yi, M. Wi-xiao, J. Shi-lou, Spars undrwatr acoustic OFDM channl stiation basd on supriposd training, J. of Marin Scinc and Appl., vol. 8, no., pp. 65 7, 9. [Onlin]. Availabl: