Performance of adaptive bayesian equalizers in outdoor environments

PERFORMANCE OF ADAPTIVE BAYESIAN EQUALIZERS IN OUTDOOR ENVIRONMENTS Jos6 Luis VALENZUELA, Fe nando CASADEVALL Depa amen de Teo ia del Senyal i Comunicacions E.T.S.E.B Uni e si a Poli kcnica de Ca alunya E-Mail: [email p o ec ed] Apdo. 30002,08080 Ba celona, SPAIN Tel. +34 3 401 59 48 FAX. Abs ac -Ou doo communica ions a e a ec ed by mul ipa h p opaga ion ha imposes an uppe limi on he sys em da a a e and es ic s possible applica ions. In o de o o e come he deg ading e ec in oduced by he channel, con en ional equalize s implemen ed wi h digi al il e s ha e been adi ionally used. In his pape a new app oach based on neu al ne wo ks is conside ed. In pa icula , he beha io o he adap i e Bayesian equalize implemen ed by means o Radial Basis unc ions applied o he channel equaliza ion o adio ou doo en i onmen s has been analyzed. The me hod used o ain he equalize coe icien s is based on a channel esponse es ima ion. We compa e he esul s ob ained wi h h ee channel es ima ion me hods: The leas sum o squa e e o s (LSSE) channel es ima ion algo i hm, ecu si e leas squa e (IUS) algo i hm employed only o ob ain one channel es ima ion and, inally, he RLS algo i hm used o es ima e he channel e e y decided symbol o he whole ame. I. INTRODUCTION Reliable da a ansmission in mobile digi al communica ion sys ems o en equi es he use o channel equaliza ion in o de o compensa e o he in e symbol in e e ence (ISI) induced by he mul ipa h p opaga ion. T adi ionally, decision- eedback equalize s (DFE) implemen ed wi h FIR il e s and maximum likelihood es ima ion (MLSE) ha e been employed o his pu pose. Equalize design o hi d gene a ion mobile sys ems and, in pa icula , sys ems ha use an ad anced TDMA mobile access o Uni e sal Mobile Telecommunica ion Sys em (UMTS), mus o e come p oblems ha a e much mo e complex han hose encoun e ed in he ac ual second gene a ion. MLSE equaliza ion is op imum in he sense ha i ob ains he bes pe o mance by de ec ing he en i e ansmi ed sequence ha minimizes he squa ed e o . Howe e , i s high complexi y makes i useless in many p ac ical implemen a ions. Mo eo e , i has been p o ed ha MLSE equaliza ion has impo an deg ada ion o ime- a ying channels [ 11. Symbol-decision equalize s ha e been commonly implemen ed wi h DFE s uc u es based on he linea il e +34 3 401 72 00 app oach. These s uc u es a e simple han MLSE despi e a ce ain pe o mance loss in a s a ic en i onmen . The op imal solu ion o he symbol-decision equalize s equi es nonlinea bounds ha can be de i ed adop ing a Bayesian app oach, also known as he maximum a pos e io i (MAP) equalize . The Bayesian could be implemen ed wi h o wi hou a decision- eedback s uc u e. I has been shown epea edly ha eedback s uc u es pe o m be e han no- eedback s uc u es. Recen ly, he applica ion o some new equaliza ion s uc u es such as Mul ilaye Pe cep on (MLP) and Radial Basis Func ion (RBF) ha e been in o de o implemen he nonlinea bounds. The equalize s implemen ed wi h MLP s uc u es could achie e nonlinea decision bounds, al hough he algo i hms, such as he backp opaga ion algo i hm, used o each he ne coe icien s need a g ea numbe o samples [2] and an immense compu a ional e o and his makes hem imp ope o equalizing mobile en i onmen s. On he o he hand, RBF s uc u es ha e been p esen ed in ecen pape s as e ec i e equalize s in s a ic channels wi h wo main algo i hms o upda ing he coe icien s. The clus e ing app oach [3] iden i ies hese coe icien s using a clus e ing algo i hm. This algo i hm is compu a ionally e y simple and e ec i e o nonlinea channel dis o ion. Howe e , as he backp opaga ion algo i hm o MLP, i needs a la ge amoun o aining samples. The second app oach es ima es he channel model and calcula es he RBF coe icien s. The main ad an ages o his me hod a e he sho aining sequences needed and he possibili y o employing adap i e channel es ima o s ha allow he esul s ob ained wi h a non-adap i e algo i hm o be ou pe o med. In his pape we p esen he esul s ob ained wi h he RBF s uc u es in a ime- a ying channel, using di e en channel es ima o s, and compa e hem wi h he esul s ob ained using a con en ional decision- eedback equalize . The sys em pe o mance is e alua ed by means o he bi e o a e (BER) as a unc ion o he signal- o-noise a io (SNR) and he no malized delay sp ead [4] o se e al mobile speeds. 0-7803-3659-3/97 $1 0.00 01 997 IEEE 2143 11. TRANSMISSION MODEL Fig. 1 shows he low-pass equi alen model o he ansmission sys em. DECEM Fig. 1 Low-pass ansmission model. means o he Powe Delay P o ile, he numbe o disc e e coe icien s, he delay coe icien and he Rayleigh dis ibu ed ampli ude o each ap, a ying acco ding o a Dopple spec um. In his channel model h ee Dopple spec um classes a e conside ed. The ecei ed and sampled signal a he inpu o he equalize can be o mula ed as: whe e nknT,,,) is a complex Gaussian andom unco ela ed p ocess wi h a iance equal o 0: and h[(n-k)T] is he sampled esponse o he channel model gi en by: In gene al he ansmi ed baseband QAM signal can be o mula ed as: whe e {ad, {bJ a e independen da a sequences o he in- phase and quad a u e channel. These da a sequences ake hei alues om he se kl, k3,..,k(M1”-1) wi h M=4 o 4-QAM. The o e all il e ing ans e unc ion Hd’=H#)HR( 3 is a aised-cosine ype wi h a oll-o ac o , p equal o 0.5, which is equally spli be ween he ansmi e and he ecei e . The unc ion HJ ) models he channel beha io ha in oduces selec i e ading in he adio link. The ecei ed signal can be exp essed as: ki-m whe e nk ) is he Gaussian il e ed noise added by he channel and h( ) is he o e all impulse esponse gi en by: whe e being l he in e se Fou ie ans o m ope a o , p he oll-o ac o o he aised-cosine unc ion and Tis he symbol pe iod. In his pape , we ha e conside ed an ou doo non- s a ic channel model based on COST-207 documen [5,6]. In pa icula we ha e used he model denomina ed Typical U ban en i onmen . This documen cha ac e izes he channel by whe e is he delay o he channel ap i de ined in COST 207 documen , (h,+jh,,) is he ins an aneous complex ampli ude o he ap i whose mean powe and ime a ia ion a e also de ined in COST 207 documen and being wi h y=(l-k) (7) IJI. BAYESIAN DECISION-FEEDBACK EQUALIZER The MAP equalize eaches he op imum pe o mance in a symbol-decision sys em based on a p obabilis ic decision algo i hm. Fo a ini e sampled linea impulse esponse h(kT), he ecei ed symbols wi hou noise a e: 1=p Fo an inpu sequence wi h leng h equal o N, he algo i hm decides he symbol wi h highe p obabili y: I is clea ha o a modula ion wi h M symbols he e a e ML possible s a es, wi h L=p+q+l. Then, when he decided symbol co esponds o he cen al impulse esponse sample, he possible s a es a ins an k a e: 21 44 The Bayes heo em could be applied o equa ion (1 1) gi ing he ollowing exp ession: whe e SZ, is he se ha encompasses all ML s a es and R(dJ is he se o s a es when he symbol k is dk. Then, each e m o equa ion (13) could be ac o ized as: wi h and Fig. 2 Radial Basis Func ion ne . Compa ing his se o equa ions wi h he RBF s uc u e shown in Fig. 2, i is clea ha by calcula ing he cen e s (ci) o each node as he noiseless es ima ed ecei ed signal, he ne could pe o m as a MAP algo i hm. ~ 2145 IV. CHANNEL ESTIMATORS In his pape we ha e e alua ed h ee kinds o channel es ima o s. Fi s , we ha e used he LSSE algo i hm. This algo i hm is simila o he es ima o used in he GSM sys em based on a co ela ion p ocedu e wi h a aining sequence and has been chosen o he Uni e sal Mobile Telecommunica ion Sys em (UMTS) [7,8]. The main cha ac e is ic o his algo i hm is he low compu a ional cos equi ed o es ima e he impulse esponse. Howe e , his algo i hm canno be implemen ed in an adap i e o m. The second simula ed sys em uses he classical RLS in o de o calcula e he impulse esponse. When he es ima ed esponse is ob ained a he end o he aining sequence, he algo i hm is s opped. This algo i hm needs sho e aining sequences han he LSSE algo i hm. I only needs 2N-I whe e N is he leng h o he es ima ed impulse esponse [9], bu i has a highe compu a ional cos . This algo i hm is mo e app op ia e han he leas mean squa e (LMS) algo i hm because o he low- ime con e gence achie ed wi h LMS which p oduces a loss o acking in as a ying channels [4]. We ha e also e alua ed he sys em pe o mance u ilizing he same IUS algo i hm bu using he decided symbol when he aining sequence is inished. This echnique compensa es o he ime a ia ion e ec s o he mobile channel. In he i s and second sys ems, he equalize coe icien s a e calcula ed when he aining sequence is inished and he equalize keeps hese coe icien s o he whole in o ma ion ame. Howe e , he hi d sys em needs o calcula e he coe icien s e e y i e a ion. Finally we ha e conside ed a ame wi h 20 aining symbols and IO0 in o ma ion symbols when he LSSE es ima o is employed, and IO aining symbols and 110 in o ma ion symbols when he IUS es ima o is used. V. RESULTS We ha e examined he e ec i eness o he RBF used as an equalize in igh ing he mul ipa h and ading in oduced by he adio channel. The c i e ion used o e alua e he sys em quali y is he bi e o a e, Pe, e sus he signal- o-noise a io and he no malized delay sp ead. The equalize s ha e he ollowing cha ac e is ics: he RBF ne has been implemen ed wi h 3 inpu signal nodes and 3 eedback-decided symbol nodes. The con en ional DFE has he same s uc u e in o de o ha e he same in o ma ion in each equalize . The equalize coe icien s a e calcula ed om an es ima ed impulse esponse o 5 aps. The en i onmen modeled is a ypical u ban channel wi h 12 aps and 1 mic osecond o delay sp ead [5,6]. 10-2 cc LL m 10-3 0.01 0.1 1 TRb Fig. 3. B.E.R. e sus no malized delay sp ead in a s a ic en i onmen . In Fig. 3, we show he e olu ion o he mean alue o he bi -e o p obabili y agains he no malized delay sp ead alue, Tb, Tb being he bi pe iod, 20 dB o signal- o-noise a io, and a s a ic en i onmen . In he igu e, he esul s ob ained o bo h equalize s, RBF and con en ional DFE, a e compa ed. Thei coe icien s ha e been calcula ed aking he LSSE algo i hm and IUS algo i hm as channel es ima o s. I could be no iced ha equalize s ained wi h he LSSE algo i hm ha e a pe o mance loss o all he alues o he no malized delay sp ead. I is also shown ha i he delay sp ead is highe han 0.2, he RBF pe o mance is be e han he con en ional DFE. These esul s seem o be easonable, since a RBF s uc u e is able o c ea e mo e complica ed decision egions in his case as hey a e needed. 10-2 w m 10-3 10-1 5 10 15 20 25 30 35 SNR (dB1 Fig. 4. B.E.R. e sus SNR in a low dispe si e and s a ic en i onmen . In Figs. 4 and 5 we show he e olu ion o he BER e sus he signal- o-noise a io conside ing a null equency Dopple . In hese g aphics, he e ec i eness o he RLS algo i hm compa ed o he LSSE algo i hm is shown. I could be no iced ha a gain o 2 dB up o a SNR o 25 dB o a no malized delay sp ead equal o 0.02 is ob ained. The sys em wi h he RLS algo i hm also has a gain o abou 1 o 2 dB o a no malized delay sp ead equal o 1.0. On he o he hand, i is shown ha he RBF equalize is be e han a con en ional DFE o a no malized delay sp ead equal o 1.0, ob aining a gain app oxima ely o 1 dB. iO-1 ..... ..... 2-. ........... .-.; ............ -L.. . i1 ' &. . 10-2 1 ........................... ..... m i 0-3 m4 5 IQ 15 20 25 30 SNR (dB) Fig. 5. B.E.R. e sus SNR in a high dispe si e and s a ic en i onmen . When we conside he Dopple e ec (Figu es 6 o 9), i could be no iced ha he sys em has a g ea loss o pe o mance, especially o low alues o he no malized delay sp ead. I is shown in Figu e 6 ha only when acking RLS is used, (in Figu es k. ls), does he bi e o descend o app oxima ely In hese igu es i could be no iced ha when he Dopple e ec is conside ed, he LSSE es ima o pe o ms be e han he no- acking RLS es ima o , (in Figu e no k. ls), o low alues o he no malized delay sp ead. 10-1 ' : 1 ..................... *. ...........-.....I- ............ ) u 10-7 I 5 IQ 15 20 25 30 SNR (dB) Fig. 6. B.E.R. e sus SNR in a low dispe si e en i onmen wi h 50Hz o Dopple . 2146 E : Fig. 7. B Dopple . 10" 10-2 10-3 .- 0.01 0.1 1 T Rb ..ER. e sus no malized delay sp ead wi h 10-1 10-2 ; aj w 10-3 1 n-4 50 Hz o .- 5 10 15 20 25 30 SNR (dB) Fig. 8. B.E.R. e sus SNR in a high dispe si e en i onmen wi h IOOHz o Dopple . Fig. 10-1 n .;! 10-2 m 10-3 0.01 0.1 1 T Rb 9. B.E.R. e sus delay sp ead wi h 100 Hz o ' Dopple . VI. CONCLUSIONS In his pape he pe o mance o he MAP algo i hm implemen ed wi h RBF using h ee es ima o s in a ypical u ban adio en i onmen ha e been analyzed and compa ed wi h a con en ional DFE. I has been shown ha he MAP algo i hm o e s e ec i eness o adap i e equaliza ion o he h ee analyzed channel es ima o s wi h espec o he con en ional DFE and ha i p o ides a iable solu ion o he p oblem o channel dis o ion in digi al communica ion sys ems. I has been shown ha his new echnique allows he signal- o-noise a io in high dispe si e channels o be educed mo e han 1 dB. On he o he hand, i has been p o ed ha he LSSE es ima o p oduces losses in pe o mance o low dispe si e s a ic channels. Howe e , i is mo e obus espec o he no- acking RLS algo i hm when he dopple e ec is aken in o accoun . This e ec is p oduced because he simula ed sys em wi h he LSSE es ima o has a longe aining sequence. When he no- acking RLS algo i hm has he same leng h o aining sequence, we ha e p o ed ha i has he same beha io as he LSSE algo i hm. Howe e , his does no p oduce he same e ec o acking RLS algo i hms. We hink ha in his pape he necessi y o using RLS acking echniques o compensa e he e ec s p oduced by ime- a ying dispe si e channels has been demons a ed. VII. ACKNOWLEDGMENTS The wo k desc ibed in his pape has been ca ied ou wi hin he CICYT TIC94-0870-C02-01 p ojec , in he amewo k o Na ional Plan o Spain. VIII. REFERENCES [1]S. Chen, S. McLaughlin, B. Mulg ew, P. M. G an , "Adap i e Bayesian Decision Feedback Equalize o Dispe si e Mobile Radio Channels", IEEE T ans. on Comm., ol. 43, no. 5, pp. 1937-1945, May 1995. [2]M. Peng, C. L. Nikias y J. G. P oakis, "Adap i e Equaliza ion wi h Neu al Ne wo ks: New Mul ilaye Pe cep on S uc u es and hei E alua ion", IEEE-ICASSP-92, ol. 2, San F ancisco, Ma ch 1992. [3]S. Chen, B. Mulg ew, P. M. G an , "A Clus e ing Technique o Digi al Communica ions Channel Equaliza ion using Radial Basis Func ion Ne wo ks", IEEE T ans. on Neu al Ne ., ol. 4, [4] J.G. P oakis, "Digi al Communica ions", 2nd ed. New Yo k, McG aw-Hill, 1982. [5] COST 207, "Digi al Land Mobile Radio Communica ions", Final Repo . O ice o O icial Pub. o he Eu opean Commun., Luxembou g, 1989. [6] R. W. Lo en z, "Co ec ions o COST 207 P oposals o Simula ion o Radio Channels", COST 231 TD (91) 26, Da ms ad , Feb ua y 1991. [7] S.N. C ozie , D.D. Falcone , S.A. Mahmoud, "Leas Sum o Squa ed E o s (LSSE) Channel Es ima ion", IEE P oc.-F o1.138,no. 4, pp. 371-378, Augus 1991. [SI A. U ie, M. S ee on, C. Mou o , "An Ad anced TDMA Mobile Access Sys em o UMTS' PIMRC 94, pp. 685-690, Sep . 94. The Hague. [9] J.G. P oakis, "Adap i e Equaliza ion o TDMA Digi al Mobile Radio", IEEE T ans. on Vehicula Tech., ol. 40, no. 2, pp. 333-341, May 1991. pp. 570-579. 2147