Performance of joint diversity and equalization techniques in M -QAM indoor radio systems

PERFORMANCE OF JOINT DIVERSITY AND EQUALIZATION TECHNIQUES IN M-QAM INDOOR RADIO SYSTEMS Fe nando J. CASADEVALL Depa amen de Teo ia del Senyal i Comunicacions Uni e si a Poli kcnica de Ca alunya Apdo. 30002.08080 Ba celona, SPAIN In his pape we analyze he pe o mances o he join di e si y and equaliza ion echniques in an indoo adio en i onmen . 4, 16 and 64 QAM modula ion a e conside ed. The sys em pe o mances a e desc ibed in e ms o he Ou age P obabili y. The esul s show ha a sys em wi hou p o ec ion has e y limi ed pe o mances. When he channel in oduces low le el o dis o ion, he di e si y echnique p oduces be e pe o mances han he equalize echnique, bu i he channel in oduces a high deg ee o in e symbol in e e ence, hen he equalize echniques a e sligh ly be e han he di e si y echniques. Mo eo e , he join equaliza ion and di e si y echniques a e e y e ec i e ools o comba he deg ading e ec in oduced by he indoo channel. Imp o emen in he sys em pe o mances , wi h espec o a sys em wi hou any p o ec ion, anging om 10 o 100 ha e been ob ained. We will shown ha he sys em pe o mances emain almos unchanged o alues o he co ela ion coe icien be ween di e si y b anches lowe han 0.6 ,0.7 app oxima ely. E en hough some pa ial analysis abou his subjec ha e been ca ied ou .[l],[2], o example aking in o accoun speci ic bi a es, pa icula p opaga ion condi ions ando asymp o ic app oaches o he equalize beha io , in OUT knowledge, he e is no ye a gene al analysis o indoo adio channels ha p o ides a global cha ac e iza ion o he beha io o he di e si y and equaliza ion echniques wo king join ly when M-QAM modula ions a e conside ed. In his pape . we assess he pe o mances o M-QAM indoo adio sys ems ha use join di e si y and equaliza ion echniques. 4-QAM, 16-QAM and 64-QAM ha e been conside ed. The in luences on he sys em pe o mances o a ious sys em and channel pa ame e s, like he shape and .m.s. delay sp ead o he Powe Delay P o ile ha cha ac e ize he p opaga ion condi ions, he equalize s uc u e (linea and non-liiea ) as well as he numbe o aps e c... ha e been aken in o accoun . The sys em pe o mances a e desc ibed in e ms o bo h a e aged Bi E o Ra e an Ou age P obabili y. INTRODUCTION TRANSMISSION MODEL The use o adio in indoo da a communica ions is an a ac i e p oposi ion because i gi es o al mobili y o he inc easing numbe o e minal equipmen s in la ge buildings. Howe e , indoo adio sys ems a e a ec ed by equency selec i e ading caused by he mul ipa h ime delay sp ead ha p oduces in e symbol in e e ence (ISI). hus esul ing in an i educible bi e o a e @ER) and imposing an upjw limi on he da a symbol a e. In o de o comba his si ua ion di e si y echniques and o adap i e channel equalize s could be used. Di e si y echniques a e e icien when low o medium bi a e ansmission sys em a e conside ed because in hese cases he signal ading can be assumed o be non-selec i e. Howe e , o sys ems ope a ing a high bi a e, whe e he selec i e ading na u e caused by he mul ipa h p opaga ion in oduces ISI, he di e si y echniques a en’ sui able because hey can’ cope wi h he abo e men ioned ISI. On he o he hand, he equaliza ion echniques, ha a e able o compensa e he IS1 in oduced by he mul ipa h p opaga ion, ha e limi ed pe o mances due o he luc ua ions on he signal o noise a io p oduced by he Rayleigh na u e o he p opaga ion. Then, in o de o inc ease he sys em pe o mances i could be con enien o conside he beha io o he join di e si y and equaliza ion echniques. 228 Figu e 1 shows he low-pass equi alen model o he ansmission sys em. The ansmi ed signal can be o mula ed as: - S( )= (a,+jb,).& -kT) =E d,.& - m, k--- - km -- whe e [ ak), [ b) a e da a sequences o du a ion T o he in-phase and quad a u e channels. They a e kl, 3, .... k(M”-I) wi h M=4 o 4-QAM, M=16 o 16-QAM,andM=64 o 64-QAM. Mo eo e , ak and 4, a e independen andom a iables. The o e all il e ing ans e unc ion H-,-( ).H,( ) is a aised-cosine ype wi h a oll-o ac o equal o 0.5. The il e ing is spli equally be ween he ansmi e and he ecei e . 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( ),[3]. A measu e o he wid h o P( ) is he oo mean-squa e delay sp ead, T. F om he Powe Delay P o ile unc ion , a sample o he channel impulse CH2944-7/91/0000/0228 $1 .OO 0 1991 IEEE -__ - -~ esponse can be cons uc ed by he ollowing o mula : whe e kj and hgn,i a e ze o mean gaussian andom a iables wi h a iance P(n. ,,)/;! and ,, is he ime be ween samples. The numbe o samples, L, needed o ep esen he indoo mobile channel in an accu a e o m, depends on he shape o he Powe Delay P o ile, P( ). and on i s ms delay sp ead. Measu emen s om many di e en buildmgs,[4],[5], allow us o conside ha he mos common shape o he Powe Delay P o ile is he one-side exponen ial p o ile, gi en by: In he analyzed cases i is su icien o conside ed a ime du a ion o he one-side exponen ial p o ile app oxima ely equal o 14. and ,,=~J2. The ecei ed signal l( ) ( esp. ,( )) can be exp essed by: m j( )= [a,.h” -~~)-b,.hl( -k~)l + k--m m +j [bk.hF( -KT) +u,.h ( -KT)] + k--- + n,W+j ny( ) whe e, in gene al wi h i=1,2 . F’ deno es he in e se con olu ion ope a o , and G; is a Fou ie ans o m, * is he gain ac o in oduced o conside ed he p esence o au oma ic gin con ol (AGC). We ha e aken in o accoun a ca ie eco e y ci cui ha minimizes he ou pu mean squa e e o .[6]. Assuming ha he bandwid h o he ca ie eco e y ci cui is much highe han he ading a e, i could be conside ed ha he ca ie phase can be acked as i he global impulse esponse, h,( ). is ime-in a ian . As we ocus on he e ec s o he delay sp ead, he phase ji e on he eco e ed ca ie caused by he gaussian noise will no be aken in o accoun . The op imum sampling ins an is ob ained om a classical squa ing iming eco e y loop,[7]. Two baseband equalize s uc u es a e analyzed. Linea and Non-Linea equalize s bo h wi h baud pe iod T spacing be ween s ages. In all he cases, he minimum mean- 229 squa e e o (MMSE) echnique has been adop ed o calcula e he ap alues. RESULTS We ha e examined he e ec i eness o he join adap i e equaliza ion and di e si y echniques in igh ing he mul ipa h and ading in oduced by he indoo adio channel. The objec i e is o de e mine he da a a e limi a ion o indoo communica ion sys ems. The c i e ium used o e alua e he sys em quali y is he ou age.p obabili y, de ined as : P,=P Ob.(P,>lo- ) whe e P, is he e o p obabili y and y is a cons an ha we ha e aken equal o 2 o 6. To compu e he e o p obabili y in eg al we ha e conside ed he LEVI’s me hodJ81. In igu es 2 and 3 we show he e olu ion o he ou age p obabili y, agains he no malized delay sp ead o he Powe Delay P o ile, . /T. We can see ha a sys em wi hou any p o ec ion has a e y limi ed pe o mances since o . /T > 0.1 he ou age p obabili y is g ea e han 0.1 (10%). Mo eo e . o smalle alues o . /T, he ou age p obabili y goes o an asymp o ic alue (ma ked by he le e A on he igu es) ha is g ea e han 0,Ol (1%). I is impo an o emphasize ha his alue shows he beha io o he sys em pe o mances when a la ading channel is conside ed. I he di e si y echnique is conside ed we can see ha o high alues o he a io . /T he sys em pe o mances a e only sligh ly be e han he ob ained o a sys em wi hou p o ec ion, bu when smalle alues a e aken in o accoun he alues o he ou age p obabili y con e ge on he alue o a la ading channel. On he o he hand, o small alues o he no malized delay sp ead, he sys em pe o mances inc ease by a ac o o en app oxima ely. In conclusion. he di e si y echnique could be used in an e ec i e way i a la channels o channels wi h low dis o ion a e conside ed. When join equalize and di e si y echniques a e aken in o accoun , he pe o mance o he sys em inc eases quickly. Fo a BER o 1W2 and a linea equalize o 5 aps in each b anch (ma ked as 2+2 in he igu e) he sys em is able o gua an ee an ou age p obabili y lowe han 0.001 (0.1%) o alues o he no malized delay sp ead smalle han 0.8. Howe e i a BER o is conside ed he sys em is no able o gi e an ou age p obabili y lowe han 0.01 (1%). In o de o ob ain an ou age p obabili y lowe han lo3 o bo h BER alues o lo-’ and lo6 a highe signal o noise a io mus be conside ed. In pa icula we ha e chosen a signal o noise a io o 30 dB. Figu es 4 and 5 show he sys em pe o mances in his case. Conside ing a non-linea equalize wi h 3 aps (1 ap in he non-linea pa ) and o a BER equal o lo2 he ou age p obabili y is lowe han (0.01%) o alues o T/T< 0.5 . I is impo an o emphasize ha , when join equaliza ion and di e si y echniques a e conside ed, he sys em pe o mances a e be e han he ob ained o a la ading channel o alues o . /T anging om 0.01 o 0.5 . This could be explained because he sys em uses he mul ipa h as a addi ional edundan channels o inc ease he di e si y gain. Howe e , o la ge alues o T/T he induced in e symbol in e e ence .due o he mul ipa h, inc eases conside ably and he equalize can no cope comple ely wi h i , and as he esul he sys em pe o mances deg ades quickly. Fo a BER o an ou age p obabili y smalle han 10” could be ob ained o alues o T/T lowe han 0.3 . I could also be no iced ha o g ea alues o T/T he sys em pe o mances a e limi ed by he in enymbol in e e ence due o he limi ed numbe o equalize aps (3 aps a e only conside ed in each b anch). Fo highe alues o he ~ l a io, be e sys em pe o mances could be ob ained inc easing he numbe o aps. Figu es 6 and 7 show he sys em pe o mances when 16 QAM modula ion is conside ed. Again a signal o noise a io o 30 dB is aken in o accoun . The beha io o he linea and non linea equalize is shown conside ing 3 and 5 aps in each di e si y b anch (ma ked in he igu e by 1+1 and 2+2 espec i ely). Fo a BER o lo-’ a linea equalize could gua an ee an ou age p obabili y lowe han 0.01 (1%) o alues o ~ l< 0.3 i 3 aps a e aken in o accoun , and ~ l< 0.5 when 5 aps a e used. An ou age p obabili y lowe han could only be gua an eed o ~ l~0.1. Howe e i a nonlinea equalize wi h 5 aps (ma ked by 2+2) is conside ed he ou age p obabili y could be lowe han i ~ l<0.55 and lowe han lo-’ i T/T< 0.7. Fo a BER o a non linea equalize wi h 5 aps is necessa y in o de o ob ain an ou age p obabili y lowe han lo-’ o ~/T<0.4 Finally, igu es 8 and 9 show he sys em pe o mances when 64 QAM modula ion is conside ed. In his case a signal o noise a io o 40 dB is aken in o accoun . Again, he beha io o he linea and non linea equalize conside ing 3 and 5 aps in each di e si y b anch (ma ked in he igu e by 1+1 and 2+2 espec i ely) is also analyzed. Fo a BER o lo-’ a linea equalize could gua an ee an ou age p obabili y lowe han 0.01 (1%) o alues o T/T < 0.2 i 3 aps a e aken in o accoun , and ~ k 0.5 when 5 aps a e used. I a nonlinea equalize wi h 5 aps (ma ked by 2+2) is conside ed he ou age p obabili y could be lowe han 10-3 i /T<O.4 and lowe han IO-’ i T/T< 0.55. a non linea equalize wi h 5 aps is necessa y in o de o ob ain an ou age p obabili y lowe han lo-’ o T/T4.4 Fo a BER o CORRELATED CHANNELS We ha e also conside ed he in luence on he sys em pe o mances o he impulse esponse co ela ion be ween bo h di e si y channels. Gi en a alue o he co ela ion coe icien ,p, de ied as: E[(X-X).(Y-Y)I = lsIY P= -, /E[(x-m’l.E[(Y-n’l /GG p =m mu=m,=02 XY XY wi h 02 he a iance, he wo complex impulse esponse o he sys em a e ob ained by means o he ollowing p du e: a- b.- C.- whe e X and Y a e ze o mean a iables and: 230 Two unco ela ed complex gaussian impulse esponse, h( ) and b( ), a e gene a ed, wi h : L h( )=c.x (h,+jhqn).8( -n n) bO)=c.h nil (b,+jbq,,).& -n n) n- 1 Fo each couple o andom a iables, h,,, and b, ( esp. bqn and b ) wo new co ela ed andom a iables a e ob ained using he ollowing exp essions: q? U, =U1 .hi, in=uZ1 .h, +uz2.bin U ¶n =ull.h, qn=uZ1 .h, +%.bqn wi h: mXY a21 =- J;;;; The impulse esponse o he wo new co ela ed channels a e ob ained as : In igu e 10 we show he e olu ion o he ou age p obabili y, o a BER o agains he co ela ion coe icien p o a 4-QAM modula ion and a signal o noise a io a I.F. o 20 dB. Th ee di e en a io l, ela ed o channels wi h small, medium and high le el o he in e symbol in e e ence, ha e been conside ed. F om he igu e we can conclude ha o co ela ion coe icien s, p. lowe han 0.7 he sys em pe o mances emain almos unchanged. Howe e when he co ela ion coe icien inc eases i s alue he sys em pe o mances deg ades quickly. Simila esul s we e ob ained o highe signal o noise a ios and high le el M-QAM modula ion: Fu he mo e, in each igu e we a e able o compa e he beha io o h ee di e en sys ems. The poin deno ed by A in he uppe cu e gi es he sys em pe o mance when an unp o ec ed sys em is conside ed. The eason is ha i we conside a sys em wi h only di e si y echnique when he co ela ion coe icien is equal o one, bo h di e si y channels ha e he same impulse esponse and as a esul he sys em pe o mances a e co esponding o an unp o ec ed sys em. O e he same cu e, he poin B indica es he sys em pe o mance when ideal di e si y echnique is conside ed. In a simila o m, on he lowe cu e we can dis inguish wo poin s. The poin deno ed by C ep esen s he sys em pe o mances when join equaliza ion and di e si y echniques a e conside ed. Finally he poin D deno es he sys em pe o mances o an equalized sys em, because as he co ela ion coe icien is equal o one bo h di e si y channels ha e he same impulse esponse and as a esul only he equaliza ion echnique becomes ope a i e. Compa ing he h ee igu es i can be concluded a.- When he impulse esponses p esen low le el o dis o ion wi h, e.g. o . / =0.05, he di e si y echnique p oduces be e pe o mances han he equalize echniques. b.- When he impulse esponses show a high deg ee o in e symbol in e e ence, e.g. o ~/T=0.5, he equalize echniques a e sligh ly be e han he di e si y echniques. c.- The imp o emen on he sys em pe o mances due o use join ly di e si y and equaliza ion echniques, wi h espec o an unp o ec ed sys em, anges be ween 10 o 100. CONCLUSIONS In his pape we ha e analyzed he pe o mances o he join di e si y and equaliza ion echniques in an indoo adio en i onmen . 4,16 and 64 QAM modula ion ha e been conside ed. F om he ob ained esul s we can conclude ha a sys em wi hou p o ec ion has e y limi ed pe o mances. When he channel in oduces low le el o dis o ion, he di e si y echnique p oduces be e pe o mances han he equalize echnique, bu i he channel in oduces a high deg ee o in e symbol in e e ence. hen he equalize echniques a e sligh ly be e han he di e si y echniques. On he o he hand he join equaliza ion and di e si y echniques a e e y e ec i e ools o comba he deg ading e ec in oduced by he indoo channel. Imp o emen in he sys em pe o mances , wi h espec o a sys em wi hou any p o ec ion, anging om 10 o 100 ha e been ob ained. Mo eo e he sys em pe o mances emain almos unchanged i he alue o he co ela ion coe icien be ween di e si y b anches is lowe han 0.6 ,0.7 app oxima ely. REFERENCES R.A. VALENZUELA, Pe o munce o ADap i e Equaliza ion o Indoo Radio Communica ions, IEEE T ans. on Communica ions, ol. COM-37, pp. 291-293, Ma ch 1989. T.A. SEXTON and KPAHLAVAN, Channel Modelling and Adap i e Equaliza ion o indoo Radio Channels, IEEE J. Selec ed A eas in Communica ions, Vol. SAC-7, pp. 114-121, Janua y 1989. J.C. PROMS, Digi al Communica ions, Mc C aw Hill, 1983. Chap e 7. D.M.J. DEVASIRVATHAM, Time Delay Sp ead Measu emen s 850 MHz Radio Wa es in Building En i onmen s, IEEE T ans. An ennas and P opaga ion, Vol. AP-34, pp. 1300-1305, No embe 1986. R.J.C. BULTlTUDE, A Compa ison o Indoo Radio P opaga ion Cha ac e is ics a 9IOMHz and 1.75 GHz, IEEE J. Selec ed A eas in Communica ions, Vol. SAC-I, pp. 20-30. Janua y 1989. S. MORIDI, H. SARI, Analysis o Decision-Feedback Ca ie Reco e y Loops wi h applica ions o 16 QAh4 Digi al Radio Sys ems, In e na ional Con e ence on Communica ions (ICC’83), 1983, pp. 671-675. N. AMITAY, L.J. GREENSTEIN. Mul ipa h Ou age Pe o mance o Digi al Radio Recei e s Using Fini e- aps Adap i e Equalize s, IEEE T ans. on Communica ions, Vol. COM-32, NQ 5. May 1984. A. LEVI, Fas E o Ra e E alua ion in he P esence o In e symbol In e e ence, IEEE T ans. on Communica ions, Vol. COM-33, NQ5, May 1985, pp. 479-481 AGREEMENTS This wo k has been inanced by Spain CICYT TIC880543. 231 k Figu e 1.- LOU PASS EQUIVALENT MOOEL OF THE TRANSMISSION SYSTEM N w m LL W * +-- - =! m M 4 0 LL (L W (3 4 0 5 Tau/ T Figu e 2.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. $-PAM, SNR=ZOdB, BER= lom2 1 N w m E W , .... , ,... , .... I Tau/T Figu e 4.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. 4-QAM. SNR=30dB, BER=10-2. CD w m =! m m LL W - 4 0 LL a W 4 0 5 Tau/T Figu e 3.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. 4-QAM, SNR=ZOdB, BER=10-6 Tau/T Figu e 5.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. 4-QAM, SNRJOdB, BER=10-6. 232 ...... 10' , Tau/T ..... ..... . . ,., I ............... ..... ..... . . ,., ..... -ul hau p o ecclon . -01 . L MIII[WR EO. 104 10-4 I Tau/T Figu e 6.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. 16-PAM, SNR=30dB, BER=1Om2 Figu e 7.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. 16-QAM, SNR=30dB, BER=10-6 I Tau/T I Figu e 8.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. &-PAM, SNR=40dB, BER=10-2 CORRELATION COEFFICIENT (a) - CD I W I, CI W + m ! > c m m U 0 E a W a Q c 3 0 10-1 109 Tau/T Figu e 9.- OUTAGE PROBABILITY VERSUS NORMALIZED DELAY SPREAD. &-PAM, SNR=40dB, BER=10-6. le. !@L&Pl Iau/T=E. 1 CORRELATION COEFFICIENT (b) CORRELATION COEFF [CIENT (C) Figu e 10.-OUTAGE PROBABILITY VERSUS CORRELATION COEFFICIENT. SNR=20 dB, 4-QAM, T/T = 0.05, 0.1, 0.01