Downlink beamforming in cellular mobile communications

DOWNLINK BEAMFORMING FOR CELLULAR MOBILE COMMUNICATIONS IN FREQUENCY SELECTIVE CHANNELS Ja ie R. Fonollosai, Jason Goldbe g1 and G egio i Vdzquez uni e si a Poli kcnica de Ca alunya Depa amen de Teo ia del Senyal i Comunicacions STel A i Uni e si y Dep . o Elec ical Enginee ing-Sys ems -G an Capi i. s/n, Campus No d, Mod. D-5 08034 Ba celona, Spain. { ono,g ego i}@gps. sc.upc.es ABSTRACT A echnique o downlink ansmission beam o me design in cellula mobile communica ions sys ems using an an- enna a ay a he bases a ion is p esen ed. The me hod is based on es ima ion o an unde lying spa ial dis ibu- ion associa ed wi h each sou ce’s spa ial downlink channel. The algo i hm is “blind” in he sense ha i depends only on uplink spa ial channel s a is ics, equi ing no mobile- o- bases a ion eedback in he design p ocedu e. The assumed unde lying spa ial dis ibu ion models a e gene al enough o be used in a wide a ie y o mobile communica ions sce- na ios (e.g., u al, u ban, sub-u ban, indoo ). 1. INTRODUCTION Expec ed demand o mobile communica ions se ices is such ha he use o spa ial di e si y o u he imp o e spec al e iciency has ecen ly ecei ed conside able a en- ion [1]-[3]. Speci ically, he use o an enna a ays in com- bina ion wi h signal p ocessing algo i hms a he bases- a ion o e he possibili y o exploi ing spa ial di e si y p esen in he scena io o inc ease sys em capaci y. In p in- ciple, hese capaci y enhancemen s a egies can be imple- men ed in bo h uplink (mobile- o-bases a ion) and down- link (bases a ion- o-mobile) communica ion. Speci ically, a se o weigh s is applied o he an enna a ay so as o educe ecei ed ( ansmi ed) co-channel in e e ence in he uplink (downlink). The choice o weigh s is a unc ion o he “spa- ial channel” o med be ween each co-channel mobile and each an enna elemen . In he uplink, a aining sequence can be used o design he weigh s acco ding o a leas mean squa ed e o (LMSE) c i e ion as in [l]. This app oach, known as “op imum combining,” is applicable in a wide a ie y o mobile com- munica ion scena ios: indoo , u ban, and sub-u ban and u al. Gene ally, downlink weigh design is mo e compli- ca ed. This is especially ue in F equency Di ision Duplex (FDD) sys ems whe e uplink and downlink communica ion ake place a di e en equencies. Thus, only i changes in he spa ial channel a e small o e he ime om s a o he uplink ame o he end o he downlink ame and o e he uplink-downlink equency di e ence, will he downlink This wo k was pa ially suppo ed by he Eu opean Com- mission unde ACTS, P ojec : AC020 TSUNAMI (11), he Na- ional Plan o Spain, CICYT, TIC95-1022-C05-01, TIC96-0500- C10-01, he Gene ali a de Ca alunya, CIRIT, 1996SGR-00096, and he Fulb igh Commission. The TSUNAMI (11) conso - ium is o med by he ollowing o ganiza ions: ERA Technology, Mo o ola ECID, O ange PCS, Robe Bosch, F ance Telecom CNET, CASA, Uni e si y o B is ol, Aalbo g Uni e si y, Uni- e si a Poli hcnica de Ca alunya and Wi eless Sys ems In e na- ional. J. Goldbe g was wi h UPC. 0-7803-3944-4/97/$10.00 0 1997 IEEE 197 Tel A i 69978, Is ael. jason@eng. au.ac.il and uplink channel be app oxima ely he same. Only hen can he uplink an enna weigh s be used in he downlink. In p ac ice (especially iin FDD), uplink and downlink channel di e ences a e o en so la ge ha he uplink weigh s canno be used di ec ly in he downlink. In his pape , we add ess his p oblem by p esen - ing a echnique o downlink ansmission beam o me de- sign which is especially app op ia e o FDD sys ems such as GSM-900, DCS-1800 and PCS-1900 in which he e- cei e pe o ms channel iden i ica ion ollowed by MLSE. Unlike [3], he me hod is use ul o cases whe e mobile- o- bases a ion eedback in he downlink beam o me design p ocedu e is undesi able o no possible. The app oach is simila in spi i o ha p esen ed in [Z] whe ein maximum likelihood es ima es o a Gaussian pa ame e iza ion o he spa ial densi y o he use s a e employed. This echnique ex ends he wo k o [4, [5] o accommoda e equency selec- i e ading channels. The me hod in his pape uses a leas squa es es ima o o pa ame e s o a mo e gene al Fou ie based densi ies simila o ha used in [6] in he con ex o a ay senso noise modelling. This esul s in a compu a- ionally e icien algo i hm which is app op ia e o a wide a ie y o en i onmen al scena ios. 2. CELLULAR NETWORK STRUCTURE Conside a ne wo k ci clus e s each con aining C adjacen hexagonal cells. The cell adius is deno ed as R. Each cell is u he di ided in o Q sec o s o wid h A = 2x/Q. An enna a ays (one pe cell sec o ) in conjunc ion wi h app op ia e signal p ocessing echniques can inc ease sys- em capaci y by (i) educing he channel e-use dis ance D by using ewe cells ]pe clus e and/o (ii) by pe mi ing mul iple co-channel use s wi hin a sec o . In his con ex , we ocus on he p oblem o designing he downlink ans- mission beam o me o enhance downlink sys em capaci y in he di icul ye common si ua ion whe e he downlink channel canno be es ima ed. 3. DATA A:ND CHANNEL MODELS The modula ion scheme employed o bo h he up and downlink ansmission is assumed o be linea o app op i- a ely modelled as such. Addi ionally, he ime dispe sion in oduced by he channel is assumed bounded by L symbol in e als. Conside a cell sec o wi h an a ay o M elemen s. Fo some gi en uplink slo and some gi en uplink ca ie e- quency, u, le N, deno e he numbe o ecei ed desi ed signals-o -in e es (SOI’s) due o he co-channel mobiles wi h uplink ca ie equency, ,,, loca ed in he sec o se - iced by he a ay in ques ion. Also, le N; deno e he num- be o ecei ed in e e ing signals-no -o -in e es (SNOI’s) due o co-channel mobiles a he same uplink ca ie e- quency, loca ed in o he sec o s. Le N = N, + N; deno e he o al numbe o ecei ed signals. The wideband a ay snapsho a e ma ched il e ing and synch onous sampling, jiu(m) = [yuT(m),.-,y,T(m+L. - 1)IT Y,(’) = [Yu1(%.-,Yu,(~)IT (1) whe e {yu, (Z)}g=l is he ou pu co esponding o each sen- so and (.)T deno es ma ix/ ec o anspose, can be mod- eIed as: ji,(m) = Au(m)su(m) + BIL s (m) + &(m) (2) The ML x N ma ix Au(m) con ains he ime a y- ing ML dimensional wideband spa ial signa u e ec o s, {SUk (m)) =] desc ibing he wideband uplink channels o med be ween each o he co-channel mobiles and he M an enna elemen s a ca ie equency u, T T %Uk (m) = [auk (m, o), . . . , awk (m, L - l)IT (3) and auL(m,Z) is he channel esponse o he k h use a ime (m + Z)T due o a symbol a ime mT. The N di- mensional ec o s,(m) con ains he symbols {sYk (n~)}kN,~ ansmi ed by he N co-channel mobiles a ca ie e- quency , and ime ins an mT. The con ibu ion o all o he symbols o ji,(m) is deno ed by he ec o yu s (m). The e o e, he wideband spa ial signa u e A, (m) models he ime dispe sion in oduced by he channel o symbols ansmi ed a ime ins an mT only, and no he ISI. The ec o o addi i e senso noise is deno ed as iiu(m). Analogously, conside he same uplink co-channel use s now ecei ing he bases a ion ansmission du ing he co - esponding downlink slo a ca ie equency d. We can g oup he ecei ed SO1 and SNOI signals in o an N dimen- sional use downlink “snapsho ” ec o , &(m): whe e Ad(m), Ed(m), and nd(m) a e espec i ely, he spa- ial signa u e ma ix, he an enna elemen ansmission ec- o o L symbols, and he addi i e Gaussian noise ec o a he mobiles. The ML x N ma ix &(m) con ains he ime a y- ing M L dimensional wideband signa u e signa u e ec o s, {adk (m)} ==, desc ibing he wideband downlink channels o med be ween he an enna elemen s and he mobiles, No e ha in his case he signal ecei ed by he mobiles is modeled a ime ins an mT only and hus he spa ial signa u e ma ix Ad(m) models he IS1 in oduced by he downlink channel. Le us conside one o he co-channel use s, use IC, in he gi en uplink and downlink slo s and model i s co e- sponding uplink and downlink channels. This use ’s uplink spa ial signa u e a ime (m + Z)T and o symbols ans- mi ed a ime ins an mT can be w i en as a weigh ed a e age o poin sou ce signa u es: auk (m, 1) = (el il)!hk (0, ‘I u2 m)d0 (7) I€@ I‘ (8) ,,(el u)= [I, e~2n u$ sin e.. . edM-l)2n u$ sin e 7, whe e (61 u) is he s anda d a - ield, na ow band poin sou ce s ee ing ec o associa ed wi h he uni o m linea a ay (ULA), 6 is he angle o incidence (wi h espec o he a ay b oadside), z is he in e elemen an enna spacing, c is he p opaga ion speed and gYk (0, Zl ,, m) is a “spa io- empo al weigh ing unc ion.” The in e al o e which in- eg a ion is ca ied ou , 0 is he a ay’s angula co e age in e al and will depend on he di ec ionali y o he an enna elemen s (which, in u n, is la gely de e mined by he cell sec o iza ion scheme employed.) In gene al, he uplink weigh ing unc ion o he k h use , guk (0, Zl Y, m) can be w i en as: whe e Lk(m) is a ze o mean log-no mally dis ib- u ed shadowing e m wi h E( lOlogLk(m)l) = 0 and ~ ,-, E([1010gLk(m)32) = 0: o he kih use . The pa h loss e m is deno ed as ,/” whe e Dk(m) and .” ~ I y a e he dis ance be wee; he k h use and he bases- a ion (no malized by he cell adius, R), and he pa h loss exponen , espec i ely. The uni a iance Rayleigh dis ibu ed gain unc ion and he uni o mly dis- ibu ed phase unc ion a e deno ed as ,Buk (6, Zl Y, m) and auk (6, I1 u, m), espec i ely. Thei p oduc mod- els he as ading componen o he channel. Las ly, p:, (6, Zlm) is he non-nega i e “spa io- empo al densi y unc ion” associa ed wi h use k, In p ac ice, he ay gain and phase unc ions can be ex- pec ed o change a mo e apidly wi h sou ce mo emen han he spa io- empo al densi y unc ion. The weigh ing unc ion guk(O, ll u,m) will be a ze o mean andom unc ion o angle condi ioned on equency and ime and o co ela ion: whe e S(.) and d(.) deno e he Di ac and K oneke del a unc ions, and i has been ecognized ha he channel a one angle o delay o a i al is unco ela ed wi h ha a o he angles o delays o a i al. Analogously, he wideband downlink spa ial signa u e ec o o use k a ime ins an mT o symbols ansmi - ed a ime ins an (m - Z)T can be exp essed as: (0l d)gdk (0, ll d, m)d0 (12) 198 4. DOWNLINK OPTIMUM COMBINING ela ion ma ix pai : {~[d",] R;: 1: The pe o mance o a Maximum-likelihood sequence es i- ma ion (MLSE) ecei e like he ones employed in mos digi al mobiles oday is basically d i en by he signal o noise a io a i s inpu , excep o some pe o mance loss due o ISI. [7]. The e o e, in he downlink beam o me de- sign we will no be conce ned wi h channel equaliza ion, bu only wi h in e e ence a enua ion. Consequen ly, he goal is ha o designing a se o N, M-dimensional weigh ec o s {wd, } Zl which when weigh ed by he (assumed uni powe ) ansmi ed SO1 sig- nals, gi e ise o: %zk(m)yd(m) zdk(m), k E {1,"',N3i} %zk(m)yd(m)%o, k E{N,+1,"',N} k=l whe e (-)* deno es complex conjuga ion and sd(m) is gi en by (5). The signal zdk(m) ep esen s he desi ed signal o use k con aining symbol Sdk(m) plus IS1 which will be handled by he MLSE ecei e . Each weigh ec o can be designed such ha he o- al associa ed in e e ence powe is minimized subjec o a desi ed mobile ecei ed powe cons ain : N q=l,q#k L-1 Rdp = Rdq [m] = ad, (m, z)ag (m, l) (16) k0 whe e R[dl and R$: a e espec i ely he downlink signal and in e g ence co ela ion ma ices associa ed wi h he k h use , and (.) deno es he ma ix ace ope a ion. No e he cons ain in (16) equi es ha he ecei ed powe a he desi ed use equal he mean powe ecei ed by each an enna om his use in he uplink no malized by he mobile's ansmission powe Cuk. This ype o cons ain is p e e ed o an absolu e powe ype cons ain such as wXRY;w = 1 because he la e may place e y high a enua ion equi e- men s on he design o he downlink beam o me . Fo ex- ample, conside wo co-channel use s he no ms o whose uplink channel ec o s di e , say, by 30dB, due o pa h loss di e ences, e c. The cons ain wHR[dlw = 1 im- plies ha ansmission powe di ec ed owa d he weak use (by he ansmission beam o me o he weak use ) will be 30dB la ge han ha di ec ed owa d he s ong use (by he ansmission beam o me o he s ong use ). This in u n implies ha , in o de o achie e a downlink signal- o- in e e ence a io (SIR) o say, 1OdB a he s ong use , he beam o me o he weak use mus di ec a leas 40dB less ansmission powe owa d he s ong use ela i e o he weak use . On he o he hand, i he cons ain in (16) is used, hen o achie elodB SIR a he s ong use , he beam- o me o he weak use need only di ec a leas 1OdB less owa d he s ong use ela i e o he weak use . The solu ion is p opo ional o elmax1 he gene al- ized eigen ec o associa ed wi h he mammum gene alized eigen alue o he k h signal and in e e ence and noise co - d!, 5. ALTERNATIVE COMBINER DESIGN The downlink combine design p oposed in (16) equi es ull knowledge o he downlink channels associa ed wi h he use o in e es as well as all e ec ed in e e ed mobiles. O en in p ac ice, such in o ma ion will no be a ailable. In his sec ion we p opose an al e na i e downlink combine o such cases. The echnique is mos easily de i ed in he con ex o a Time Di ision Mul iple Access (TDMA) sys em wi h he ollowing assump ions: Fi s , o each use he uplink and subsequen downlink channels a e unco ela ed (in he sense ha hei andom weigh ing unc ions in (7) and (12) a e unco ela ed). Nex , a aining sequence o du a ion M is a ailable in uplink slo o each use . Such sequences a e inco po a ed in o exis ing sys em s anda ds. Also, he uplink channel o a use in a gi en ame is unco e- lu ed wi h he uplink channel o he same use in ano he ame. This will e y much be he case in equency hop- ping sys ems since he gain and phase ading unc ions o (9), ,&,(e, ll y, m) and auk (e, ll y, m) a e highly sensi i e o changes in he ca ie equency. Las ly, he unde ly- ing spa ial densi ies associa ed wi h he uplink and down- link channels, pz, (e, Zjm) and pi, (e, llm), o (9) and (13), espec i ely, a e assumed o change e y slowly wi h ime compa ed o he gain and phase ading unc ions. In pa ic- ula , we assume ha hese unde lying spa ial densi ies a e app oxima ely cons an o e se e al ames. This is eason- able since hese unc ions do no exhibi g ea luc ua ion in esponse o changes in he ca ie equency and/o "small" changes in he mobille posi ion. Mo eo e , i is assumed ha he unde lying uplink and downlink spa ial densi ies a e app oxima ely equal: Pi, (e, llm) = P:, (8, llm) (18) This is he in o ma ion which is assumed common o bo h he uplink and he downlink (in addi ion o he usually conside ed common log-no mal ading and pa h loss com- ponen s) and will o m he basis o he combine design p ocedu e desc ibed below. In such a case, a modi ied e sion o he op imum com- bine based on pa ame ic signal and in e e ence and noise co ela ion ma ices which a e a e aged o e he as ading e ms can be o mula ed. Le us de ine Rdk as he downlink co ela ion ma ix associa ed wi h he k h use which has been a e aged o e he as ading: Is1 L-1 1=0 whe e Ep,*[.] deno es expec a ion o e he as ading and Tk(e, I) = wp:, (6, llm). Based on a e age co ela- ion ma ices o he o m in (19), we can e o mula e he cons ained minimum in e e ence powe c i e ion o (16) (based on in o ma ion ha canno be in e ed om he up link) as he ollowing cons ained minimum a e age in e - e ence powe c i e ion (based on in o ma ion ha can be Dk m) 199 in e ed om he uplink): n= 1 ,n# k The solu ion is gi en as: wi h ELY1 deno ing he “maximum” gene alized eigen ec- o o {Rdk,Rdk}. The downlink combine p oposed in (20) is o ced o enhance ecep ion o he use o in e es and a enua e he in e e e s on he basis o magni ude as a unc ion o angle and delay. The combine will a emp o inc ease he magni ude o i s spa ial esponse in hose di ec ions whe e he desi ed use is unde lying spa ial den- si y is la ge while ying o a enua e i in hose o he whe e he in e e e s spa ial densi y unc ions a e la ge. Pe o - mance will depend on he ex en o which he spa ial densi y unc ions o he use s o e lap. While he abo e app oach is clea ly sub-op imal, i makes he bes ou o a di icul si ua ion- ully exploi ing all in o ma ion abou he down- link channel ha can be ob ained om he uplink. -+SI --I4 6. IMPLEMENTATION We now explain how es ima es o he co esponding a e - age downlink signal and in e e ence co ela ion ma ices, $:: and Rdk , espec i ely, a e ob ained o use in he new p ocedu e. Since he uplink spa ial weigh ing co ela ion unc ion is de ined only o e he sec o , i can be ep e- sen ed by a Fou ie se ies expansion as i s p oposed in [6] o modelling noise s a is ics. The Fou ie se ies expan- sion o he spa ial weigh ing co ela ion unc ion o e he in e al 8 E [-Ala, A/2) can be w i en as: --i4 00 p=-00 - FA12 Now, since he co ela ion unc ion will o en be a qui e smoo h unc ion o angle, in p ac ice a unca ed e sion o (22) will usually be a su icien app oxima ion. P-1 Tk(8,l) ck(p,l)ejPQe, 8 E [-A/2,A/2) (24) The a e age uplink and downlink co ela ion ma ices can be app oxima ed as [6]: p=-P+1 L-1 P-1 2=0 p=-P+1 Thus, he p oblem o es ima ing he spa ial weigh ing co - ela ion unc ion om he uplink da a can be posed as he p oblem o es ima ing he coe icien s om he uplink da a. The spa ial signa u e es ima es a e ob ained by pos - mul iplying an uplink snapsho da a ma ix by he pseudoin e se o a known “ aining sequence signal ma ix,’’ like in [4]. The a e age uplink co ela ion ma ices can be es i- ma ed by a e aging he ou e p oduc o spa ial signa u e es ima es o a gi en use ob ained o e a numbe o p e i- ous ames. F-I L-1 (27) 1 - R,, = qe, (m, I). m=O l=O Ideally, equency hopping is pe o med o e a band su i- cien ly wide so as o deco ela e as ading om one ame o he nex , bu su icien ly na ow so as o p oduce negli- gible changes in he uplink s ee ing ec o (8) as a unc ion o equency. This u he implies ha he dependence o &’‘ on k can, in e ec , be elimina ed. whe e , is a “nominal” uplink ca ie equency. Now, e u ning o he es ima ion p oblem, one app oach is ha o a simple pa ame ic leas squa es i o he es- ima ed uplink co ela ion ma ix, which is e y e icien compu a ionally since many ope a ions can be compu ed o -line [4]. Once he Fou ie pa ame e s a e es ima ed, he associa ed pa ame ic downlink co ela ion ma ix es i- ma es a e simply o med using (26) and he weigh ec o is calcula ed using (21). 7. CONCLUSION A echnique o downlink ansmission beam o me design in cellula communica ions sys ems has been p esen ed. The algo i hm equi es no mobile- o-base s a ion eedback, is compu a ionally e icien , and is well sui ed o a wide a ie y o scena ios ypically ound in mobile communica- ions. De ails on algo i hm implemen a ion and esul s a e de e ed o a u u e jou nal publica ion. 8. REFERENCES [l] J.H. Win e s. 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