Performance of soft-output equalization and convolutional coding over frequency-selective fading radio channels

PIMRC '94 D 2.1 209 PERFORMANCE OF SOFT-OUTPUT EQUALIZATION AND CONVOLUTIONAL CODING OVER FREQUENCY-SELECTIVE FADING RADIO CHANNELS An onio Valdo inos, An onio Na as, An oni Gelonch, Fe nando J. Casade all Depa men o Signal Theo y and Communica ions E.T.S. Ingenie os de Telecomunicaci6n Uni e sidad Poli Ccnica de Ca aluiia Apdo. 30002,08080 Ba celona, SPAIN e-mail. [email p o ec ed] Tel. 34 3 401 59 48 Fax. 34 3 401 72 00 Abs ac : This pape p esen s an analysis o so -ou pu equaliza ion and codi ica ion echniques applied o 4 and 16-QAM TDMA adio sys ems o equency selec i e ading channels. In pa icula , Typical U ban (TU) and Hilly Te ain (HT) en i onmen s ha e been conside ed. The use o he so in o ma ion p o ided by he equalize enhances he sys em pe o mance conside ably. Speci ically, an imp o emen o mo e han 4 dB can be achie ed in ela ion o ha d decoding echniques. The necessi y o in oducing some in e lea ing in o de o des oy he channel memo y has also been s a ed. The ac ual in es iga ed equalize s ha e been a So -Ou pu Decision-Feedback equalize (SODFE) and a So - Decision M-Algo i hm (SDMA) join ly wi h con olu ional coding and bo h ideal and ini e in e lea ing. I. INTRODUCTION The g owing impo ance o wi eless digi al adio sys ems has led o he de elopmen o high-pe o mance echniques necessa y o compensa e o he se e e equency-selec i e ading in oduced by he channel. In o de o comba he In e symbol in e e ence caused by he mul ipa h p opaga ion, he use o equaliza ion echniques becomes manda o y. F om he poin o iew o sys em pe o mance, non-linea equalize s a e mo e e icien han linea ones since hey can compensa e o deepe in-band nulls due o selec i e ading. Speci ically, Decision-Feedback Equalize s (DFE) and he Maximum Likelihood Sequence Es ima ion (MLSE) and Maximum a Pos e io i (MAP) algo i hms can be conside ed [l]. I he channel memo y is oo long, he p obabilis ic equalize s, ha is MLSE and MAP, become imp ac ical due o hei compu a ional complexi y, which g ows exponen ially wi h he channel memo y. The e o e, simpli ied algo i hms ha e o be in oduced in spi e o a mode a e loss in bi e o a e (BER) pe o mance. The mos widely in oduced echniques a e he M-Algo i hm (MA), [2], and he SDMA, [3], which ha e p o ed o be app op ia e o eliable ope a ion wi h ela i ely low compu a ional cos . Howe e , he only use o equaliza ion echniques does no usually p o ide good enough pe o mance o ope a e in p ac ical sys ems and some coding and in e lea ing which des oys he channel memo y a e equi ed. On he o he hand, he decode usually ope a es on he ha d decisions made by he demodula o , which leads o an in o ma ion and, consequen ly, o a pe o mance loss. This d awback can be ci cum en ed by making use o he addi ional in o ma ion con ained in he unquan ized samples gi en by he demodula o . In his pape bo h DFE and SDMA echniques ha e been in es iga ed join ly wi h con olu ional coding and ideal and ini e in e lea ing in wo ealis ic en i onmen s, namely Typical U ban (TU) and Hilly Te ain (HT). The chosen modula ion schemes ha e been M-QAM pa e ns because hey a e spec um e icien and so, app op ia e o en i onmen s whe e a high densi y o a ic is gene a ed. In pa icula , 4 and 16-QAM modula ion schemes ha e been conside ed. Pe o mance esul s, in e ms o bi e o a e alues, ob ained by means o compu e simula ion a e p esen ed. II. SYSTEM DESCRIPTION The block diag am o he simula ed ansmission sys em is shown in ig. 1. The ou pu sequence om he sou ce is p o ec ed by a con olu ional code and passed o an in e lea e wi h some ini e span and dep h. The in e lea ed sequence is M-QAM modula ed and ansmi ed o he channel a e being passed h ough he ansmi e il e , hT( ), which is a oo - aised cosine il e wi h a oll-o ac o equal o 0.5. The e o e, he lowpass @ IEEE 210 D 2.1 PIMRC '94 Figu e 1. Lowpass equi alen model o he ansmission sys em. equi alen M-QAM signal ansmi ed o he channel can be exp essed as: m x( ) = a,hJ -kT) + jb,. hJ -kT) (l) k=- whe e {ak} and {b,} a e independen da a sequences o du a ion T o he in-phase and quad a u e channels espec i ely. They a e selec ed om he se {&1,&3, ...,k(M"2-l)} wi h M=4 o 4-QAM and M=16 o 16-QAM. A he ecei e a ma ched il e H,(Q is inco po a ed, hen: h,( ) = F-'[H,(R] 3 h;(- ) (2) whe e + deno es he conjuga e, F1 is he in e se Fou ie ans o m and hl( ) is he equi alen impulse esponse p io o he ma ched il e : (3) The e o e, he global impulse esponse esul s: (4) h( ) = hJ )*hc( )*h,( ) = h,( )*h;(- ) = h+(- ) Le us no ice as he ecei e il e is ma ched no only o he oo - aised cosine ansmi ing il e bu also o he en i e impulse esponse hl( ), which is a ec ed by he channel impulse esponse a ia ions, and hus needs o be con inually upda ed. I could be implemen ed in acco dance wi h a FIR s uc u e om he es ima ed impulse esponse. In his s udy, a ideal channel es ima ion is assumed and, so, he ideal ma ched il e is always a ailable. The unc ion h,( ) models he channel beha io ha in oduces selec i e ading in he adio link. The channel is assumed o be wide-sense s a iona y unco ela ed sca e ing (WSSUS) and i is ep esen ed by a unique co ela ion unc ion e e ed o as he Powe Delay P o ile, P( ), and gi en by: The mul ipa h phenomenon can be desc ibed in e ms o ime delays and hei associa ed powe alues. No Dopple shi s ha e been conside ed. The models adop ed co espond o hose p oposed by COST-207, [4], o desc ibe ypical u ban (non-hilly) and hilly e ain en i onmen s and is based on ep esen ing he channel by a ini e numbe o aps, each one de e mined by i s ime delay and a e age powe . The ampli ude o each ap is Rayleigh dis ibu ed. This models is desc ibed by a con inuous powe delay p o ile and app oxima ed h ough a disc e e numbe o aps, [4]. A he ou pu o he channel model, AWGN wi h a double-sided powe spec al densi y NJ2 is added. The signal a he ma ched il e ou pu is exp essed as: - ( ) = [ ak. h R( -kT) -bk. h '( -kT)] + k -m - + jc [bk.hR( -kT) +ak.h'{ -kT)] +nx( )+j ny( ) (6) k-a whe e wi h * he con olu ion ope a o . G is a gain ac o ha ensu es a cons an a e age powe a he demodula o inpu . I is in oduced in o de o conside he p esence o au oma ic gain con ol (AGC) and is only necessa y o 16-QAM pa e ns since in 4-QAM we ha e ze o-c ossing decision bounda ies. A e he ma ched il e , we ha e conside ed wo possible b anches co esponding o he SDMA and SODFE equalize s. Fo he i s one, he global impulse esponse p io he SDMA equalize is equi ed o be h(k) PIMRC '94 D 2.1 21 1 = 0 o k<O and so, a whi ening il e (WF) is necessa y. This il e has been cons uc ed as a DFE o wa d il e whose aps a e adjus ed ollowing he minimum mean- squa e e o (MMSE) echnique because e en hough ideally he WF shoud be adjus ed by means o he ze o o zing c i e ion [5], una oidably he numbe o aps is ini e and, he e o e, he esidual IS1 e ec is no negligible. Fu he mo e, he SDMA mus wo k wi h a ini e impulse esponse leng h, and so h(k) = 0 o k>L. We should ake a alue o L high enough o conside all he signi ican IS1 componen s, bu no so high ha he compu a ional complexi y becomes un easonable. The de ailed SDMA algo i hm can be ound in [3]. On he o he hand, a DFE s uc u e wi h symbol pe iod (T) spacing be ween s ages has also been in es iga ed. The MMSE echnique has also been adop ed o calcula e he ap alues. In his case, he so ou pu is ob ained om he unquan ized signal. Bo h equalize s deli e so decisions o each symbol and, om hem, he espec i e bi me ics a e calcula ed [3][6]. Finally, a e de- in e lea ing, hese me ics a e ed o he decode o exploi he so in o ma ion. In o de o compa e so e sus ha d-decision pe o mance, we ha e also conside ed he ou pu sequence om he quan ize which is ed di ec ly o he de-in e lea e . III. RESULTS The pe o mance o so -ou pu equaliza ion and con olu ional coding echniques in ou doo adio channels ha e been in es iga ed using he bi e o a e (BER) as quali y c i e ion. The signal- o noise a io is gi en by: Ell No SNR = - + 1OlogM whe e E, is he a e age bi ene gy and M=4 and M=16 o 4 and 16-QAM espec i ely. We ha e conside ed bi a e alues o 1 Mbi ls and 200 Kbi /s o TU and HT en i onmen s since hey lead o he same no malized delay sp ead de ined as he p oduc z.R,,, whe e Rb is he bi a e and z is he oo mean-squa e delay sp ead, which is a mesu e o he wid h o he Powe Delay P o ile and is equal o 1 ps o TU and 5 ps o HT in he analyzed models[4]. The numbe o aps o he SODFE has been chosen 6 o he o wa d and 5 o he eedback il e s. Fo he SDMA equalize a channel memo y leng h L=6 l@ 10-' 10-2 gj 10-3 10-4 10-5 10" 1 4 7 10 13 16 EWNo CdBl Figu e 2. BER e sus E;JN,.TU and 4-QAM. has been conside ed. Va ious echniques ha e been compa ed. In pa icula , ha d-decision e sus so -decision has been in es iga ed. In ig.:! he e olu ion o he BER as a unc ion o E,& o 4-QAM and TU en i onmen s is depic ed. A con olu ional code wi h a e =3/4 and cons ain leng h o K=2 is used o p o ec he sou ce da a. We can obse e ha he e is no app eciable di e ence be ween he SODFE and SDMA s uc u es, no mo e han 0.5 dB, al hough he la e is always slig hly be e . Howe e , he pe o mance imp o emen ob ained when in oducing decoding echniques is e y impo an , pa icula ly when So me ics a e conside ed. Fo a BER o lo2 So me ics o e an imp o emen o 3 dB wi h e e ence o ha d decoding and 4.5 dB wi h e e ence o no coding. Fo inc easing alues o E& we can no ice ha he di e ence be ween bo h so and ha d decoding echniques a ies slowly and is o abou 3 dB o and 4 dB o In con as , he ela i e deg ada ion i no coding is conside ed inc eases o highe E&, alues. Fo a BER o his deg ada ion is 7.5 dB and o could be 10.5 dB wi h e e ence o So me ics. A simila compa ison can be ca ied ou om he obse a ion o ig.3, which ep esen s he BER e olu ion o HT en i onmen s and 4-QAM modula ion schemes. In his case, o achie e a BER o he di e ence be ween so and ha d decoding is abou 4 dB. I mus be bo n in mind ha he delay sp ead in oduced by he channel in HT en i onmen s is i e imes g ea e han TU channels, and so, al hough igu es 2 and 3 p esen simila BER alues o equal E, / No, in he la e he bi a e is i e 212 D 2.1 PIMRC '94 108 10-1 18-2 10-3 1 0-4 18-5 10-6 _. 1 4 7 io 13 16 Eb/No CdBl Figu e 3. BER e sus E,,/NW HT and 4-QAM. imes lowe . Fig. 4 shows he sys em pe o mance o 16- QAM and TU en i onmen s. In his case he di e ence be ween SODFE and SDMA is sligh ly highe , bu ne e mo e han 1 dB. F om his igu e we can no ice ha he beha io is simila o ha o 4-QAM sys ems, bu i is clea ha he E,/N, alue needed o gua an ee a ce ain alue o BER is conside ably highe . Ac ually, a 16-QAM sys em needs app oxima ely 6 dB mo e han 4-QAM o achie e he same pe o mance. The e o e, highe le el modula ion schemes a e use ul o inc ease he spec al e iciency, bu no he maximum bi a e eached by he sys em due o i s highe sensi i i y o IS1 e ec s. Fig.5 p esen s he e ec o conside ing ini e ins ead o in ini e in e lea ing. We ha e ocused on TU en i onmen s, 4-QAM and So me ics. I no in e lea ing a all is in oduced, he deg ada ion due o he channel memo y is as high as 4 dB o BER = lo-*, 6 dB o BER=10-3 and 8 dB o BER=10-4. I a ini e in e lea ing dep h o 4 is conside ed, he deg ada ion is 2, 3 and 4 dB espec i ely o SDMA equaliza ion. In he case o SODFE an addi ional deg ada ion o 1 dB is e ealed. F om his igu e we can conclude ha some kind o in e lea ing is needed in o de o ake he mos ad an age om he so in o ma ion deli e ed by he equalize . O he wise he e ec o coding no only is no ad an ageous, bu may in oduce a highe pe o mance deg ada ion. 108 la-' 18-2 2 10-4 10-5 lad ... ... .II ... I.. I,. ... ... .II ... ... 4 6 8 18 12 14 16 18 20 EWNo CdBl Figu e 4. BER e sus E,,/N,.TU and 16-QAM. Finally, we ha e analyzed he e ec o a ying he code a e om = 314 o 213 and 112 when an in e le ing dep h o 4 is conside ed. The esul s a e p esen ed in ig. 6. I can be no iced ha passing om -314 o 2 3 an imp o emen o abou 2 dB is achie ed, and oughly 2.5 dB when passing om 213 o 112. This may no seem a g ea imp o emen aking in o accoun he inc easing bandwid h equi ed when dec eases. IV. CONCLUSIONS In his pape we ha e in es iga ed he pe o mance o equaliza ion and codi ica ion echniques applied o 4 and 16-QAM TDMA adio sys ems in wo ypical ou doo en i onmen s whe e he dispe si e na u e o he channel in oduces bo h in e symbol in e e ence and Rayleigh luc ua ions o he signal- o-noise a io. The use o equaliza ion echniques which p o ide so in o ma ion o he decode , namely SODFE and SDMA, has p o ed o be e y e ec i e and leads o BER alues conside ably lowe han hose achie ed by using he mo e con en ional ha d-decision echniques. Mo eo e , we ha e p esen ed a b ie compa ison be ween 4 and 16-QAM modula ion schemes. F om he esul s ob ained we can conclude ha he use o high-o de QAM pa e ns does no o e any ad an age in e ms o maximum bi a e achie able by he sys em, and i s use is only ad isable when a high spec al e iciency is equi ed. We ha e also s a ed he necessi y o in oducing some ini e in e lea ing, as high as he da a delay equi emen s make PIMRC '94 D 2.1 21 3 l@ 10-' 10-2 10-3 10-4 10-5 106 2 4 6 8 10 12 14 16 18 Eh/No CdBl Figu e 5. BER e sus WN,. TU and 4-QAM. possible, in o de o des oy he channel memo y, and we ha e e alua e he esul s o h ee di e en cases. Finally, he e ec o a ying he code a e, , has been analyzed, bu , ob iously, he adeo be ween BER and bandwid h has o be sol ed in each pa icula case. V. REFERENCES J.G. P oakis. "Adap i e Equaliza ion o TDMA Digi al Mobile Radio". IEEE T ans. on Vehic. Tech. Vol. 40. NO 2. May 1991. pp. 333-341. A. Baie and G. Hein ich. "Pe o mance o M- Algo i hm MLSE Equalize in F equency- Selec i e Fading Mobile Radio Channels". P oc. IEEE ICC'89, Bos on, MA, 1989, pp. 281-285. R. Mehlan and H. Mey . "So Ou pu M- Algo i hm Equalize and T ellis-Coded Modula ion o Mobile Radio Communica ions". P oc. 42nd IEEE Vehic. Technol. Con ., Den e , CO, 1992, pp. 586,591. COST 207: "Digi al Land Mobile Radio Communica ions". Final Repo . Published by he Commission o he Eu opean Communi ies.Luxembou g, 1989. pp. 135- 147. E.A. Lee and D.G. Messe schmi . "Digi al Communica ions". Kluwe Academic Publishe s. Y.J. Liu, M. Wallace and J.W. Ke chum. "A So -Ou pu Bidi ec ional Decision Feedback Equaliza ion Technique o TDMA Cellula 1988. pp. 345-346. l@ 10-' 10-2 10-3 10-4 10-5 1 A6 -- 2 4 6 8 10 12 14 16 EWNo CdBl Figu e 6. BER e sus E&.TU and 4-QAM. Radio". IEEE Jou nal on Selec ed A eas in Comm.. Vol 11. NO. 7. Sep embe 1993. pp. 1034-1045.