UE Centric Coordinated Beamforming in Multi-cell MU-MIMO Systems

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1 UE Centrc Coordnted Bemformng n Mult-cell MU-MIMO Systems Jlng L Yngxue L InterDgtl Communctons LLC Melvlle NY USA e-ml: jlng.l@nterdgtl.com yngxue.l@nterdgtl.com Astrct User Equpment (UE) centrc coordnted emformng (CBF) s n enlng technology n mult-cell MU-MIMO systems. It s of gret mportnce to know the suggested coopertng set se for CBF nd the correspondng performnce. In ths pper novel jont spce-tme-frequency proportonlly fr scheduler for CBF s proposed to provde trdeoff etween the verge system performnce nd UE frness. The mpct of the coopertng set se on system performnce s predcted through the nlyss of smplfed system nd then confrmed through numercl results of the whole system usng the proposed scheduler. Keywords-Coordnted Bemformng; 3GPP LTE-A; MIMO Systems; Schedulng I. INTRODUCTION In cellulr system wth multple cells mny chllenges such s multpth fdng cell edge nterference scrce spectrum exst. In prtculr when the frequency reuse fctor of the system s 1 the cells re shrng the sme tme nd sme frequency nd. The queston s to How should the se sttons (.e. enhnced Node B s (enbs)) mlly shre the rdo resource n downlnk? s ever present. In the studes relted to 3GPP Long Term Evoluton-Advnced (LTE-A) Coordnted Multpont (CoMP) [1] coordnted emformng (CBF) technques hve een rought up s n enlng technology to nswer ths queston. In CBF enbs coordnte ther trnsmssons to mtgte the nter-cell nterference. Ths cn e done ether n network centrc wy (.e. the choce of enbs n coordnton s sed on the network structure) or n (User Equpment) UE centrc wy (.e. the choce of enbs n coordnton s UE dependent). Here we only consder the UE centrc CBF (clled CBF for short). Ech UE hs coopertng set the enbs of whch re nvolved n coordnted schedulng nd emformng for the UE. The coopertng set se (numer of enbs n the set) s the sme for ll UEs. As the coopertng set se ncreses the system performnce my e mproved. But the ddtonl mount of nformton exchnge nd schedulng complexty ncrese sgnfcntly. Furthermore due to the cellulr structure only lmted numer of nterferng enbs contrute to the domnnt nterference to ech UE. The wek nterferng enbs nvolvement n the CBF does not rng sgnfcnt gn ut sustntlly ncreses the overhed nd complexty nd I-T Lu Deprtment of Electrcl nd Computer Engneerng Polytechnc Insttute of New York Unversty Melvlle NY USA e-ml: tlu@poly.edu thus s not desrle. Therefore t s of gret mportnce to know the suggested se of the coopertng set for CBF n such mult-cell mult-user multple-nput nd multple-output (MU-MIMO) system nd the correspondng performnce. Ths queston cn e nswered from dfferent spects. The suggested se of the coopertng set cn e mum n mxmng the system performnce (e.g. spectrl effcency) mntnng frness mong UEs or reducng overhed nd complexty etc. The queston ws only prtlly ddressed n few prevous works. Ref. [2] looked t the spectrl effcency mprovement of dfferent coopertng set ses n downlnk mult-cell sngle user (SU) MIMO system whle the overhed s kept to mnmum (ssumng mplct CSI feedck). On the other hnd [3] tred to fnd the mxmum coopertng set se n downlnk mult-cell system whle keepng the system complexty t n cceptle level nd lower lod n ckhul nd uplnk. To the est of our knowledge there s no pulshed work studyng the suggested coopertng set se n mult-cell MU-MIMO systems from the spects of oth mxmng the verge system performnce nd cpturng the sustntl performnce mprovement of the mjorty of the UEs especlly cell edge UEs. In ths pper we try to fnd the coopertng set se tht cheves the desred performnce nd complexty trdeoff n mult-cell MU-MIMO systems y oth mxmng the system performnce nd cpturng the performnce mprovement of the mjorty of the UEs especlly cell edge UEs. Full nd perfect CSI s ssumed vlle t ech UE. And the nformton fed ck nd fed forwrd etween UEs nd enbs s ssumed through ero-dely nd error free lnks. A novel jont spce-tme-frequency proportonlly fr (STF- PF) scheduler for CBF s proposed for performnce evluton. The mpct of the coopertng set se on system performnce s predcted through the nlyss of smplfed system nd then confrmed through numercl results of the whole system usng the jont STF-PF scheduler. We fnd tht the coopertng set se etween 4 nd 6 cheves resonly good performnce nd complexty trdeoff. The rest of the pper s orgned s follows: The system model s presented n Secton II. In Secton III the jont STF- PF scheduler for CBF s proposed. The mpct of the coopertng set se on system performnce s predcted through nlyss of smplfed system n Secton IV nd vldted through numercl results n Secton V. We conclude wth Secton VI.

2 Nottons re s follows. All oldfce letters ndcte vectors (lower cse) or mtrces (upper cse). A A -1 tr(a) E(A) stnd for the conjugte trnspose nverse trce nd expectton of A respectvely. (A) j denotes the j th element of S S x x S nd x S. A. For two sets S nd S II. SYSTEM MODEL In ths pper we consder downlnk frequency dvson duplexng (FDD) system wth N c hexgon cell stes. Ech hexgon cell ste conssts of 3 sectors nd so there re N s = 3N c sectors. An enb equpped wth N t trnsmt ntenns nd N UE UEs ech equpped wth N r receve ntenns re locted n ech sector. Ech UE s ssocted to one servng enb from whch t receves the strongest sgnl. All enbs trnsmt n the sme frequency nd. The frequency nd conssts of N RB frequency resource locks (RBs) dstruted nto N SB sunds. The se of su-nds depends on system ndwdth s specfed n [4]. We ssume full uffer trffc model so tht ll rdo resources re occuped ll the tme. Multple UEs shrng rdo resources through proportonlly fr scheduler. The schedulng decson s mde every trnsmsson tme ntervl (TTI) nd the mnmum schedulng unt s su-nd. Multple UEs my e selected to receve dt n the sme sund from the sme enb. One UE my e scheduled to receve dt n multple su-nds. When multple su-nds re ssgned to UE the precoders for the UE my vry from su-nd to su-nd ut the modulton codng scheme (MCS) remns the sme cross ll su-nds ssgned to the UE.. The receved sgnl (vector) t the th UE ssocted to the c th enb n the n th TTI nd m th RB s n m n m n m n m n m n m n m c c c jc j j j d d c jd y H F s H F s where the N r N t n m n m n m n m d jd j H F s n nm jd c jd (1) H nd N t N nm j F re the chnnel nd precoder from the d th enb to the j th UE the N j 1 s nm s the dt vector ntended for the j th UE the N r 1 n nm s the nose vector t the th UE N j s the numer of dt strems ntended for the j th UE Ω d s the set of the ndces of the scheduled UEs t the d th enb nd Ψ s the set of enb ndces n the whole system. It s ssumed tht n m n m j j N j E s s I for ll j. And the precoders re suject to the per-enb power constrnt n m n m F jd jd Ptx d jd F. In (1) the four terms represent the desred sgnl nter-user nterference from the servng enb nter-cell nterference from other enbs nd nose respectvely. In ths pper we consder N t = 4 nd N r = 2. In ny sund nd TTI t ech enb one of the followng three schedulng scenros s chosen sed on certn crteron: () Rnk-1 SU-MIMO: One UE wth one dt strem s scheduled; () Rnk-2 SU-MIMO: One UE wth two dt strems s j scheduled; () MU-MIMO: Two UEs ech wth one dt strem re scheduled. A. The Setup of the Non-CoMP Scheme In Non-CoMP the desred nd nterferng chnnels re ssumed perfectly known t ech UE. Assumng rndom emformng t nterferng enbs ech UE estmtes the receved nterference nd nose covrnce mtrx n ech RB. The receved nterference nd nose covrnce mtrx t the th UE ssocted to the c th enb n the n th TTI nd m th RB s n m n m n m n m n m d d rnd d d rnd d R H F H F E n n m n m n d rnd nm where F s the rndomly generted precoder for the d th enb ssumed y the th UE nd s the set of ndces of the nm enbs not consdered n the clculton of R. In Non- CoMP = {c}. The desred chnnels nd the estmted receved nterference nd nose covrnce mtrces n m n m c N RB H R re ssumed perfectly fed ck from ech m1 UE to ts servng enb. Schedulng s done t ech enb ndependent from tht of the other enbs. It s lso ssumed tht ech scheduled UE knows the precoder nd MCS for ts dt nd the precoder for the co-scheduled UE (f ny) through perfect feedck from ts servng enb. So t s le to recover ts dt strem v mnmum men squre error (MMSE) decoder nd decode ts messge. The MMSE decoder t the th UE ssocted to the c th enb n the n th TTI nd m th RB s 1 n m n m n m n m c c c c G H F M n m n m n m n m n m n m c d jd d jd d jd nm c M H F H F R (2) (3). where the frst term n M represents the covrnce mtrx of ts own sgnl nd co-scheduled sgnl. B. The Setup of the CBF Scheme The setup of the CBF scheme s smlr to tht of the Non- CoMP scheme n the chnnel estmton nd feedck mechnsm. Ther dfferences re the followng. For ech UE there s coopertng set of se conssts of the enbs contrutng to the strongest sgnls to the UE. The UE s coopertng set ncludes t lest ts servng enb. Whle ech nterferng enb n the UE s coopertng set tres to mxme the performnce n ts own sector t lso ttempts to mtgte nterference to the UE n the su-nds the UE s scheduled. To cheve ths ech UE estmtes the receved nterference nd nose covrnce mtrces excludng the contruton from enbs wthn ts coopertng set. The UE lso mesures the downlnk chnnels response etween tself nd ll enbs wthn ts coopertng set. Here we redefne n (2) s the set of enb ndces n the coopertng set of the th UE (whch s comptle wth the defnton n Non-CoMP). The set desred nd nterferng chnnels n the coopertng set nd the The work ws sponsored y InterDgtl Communctons LLC.

3 estmted receved nterference nd nose covrnce mtrces n m n m d d NRB H R re ssumed fed ck perfectly m1 from the UE to ts servng enb. The servng enb shres the nterferng chnnels nm d N RB H wth the d th enb d m1 through ero-dely nd error free ckhul lnk. The d th enb wll mtgte the nterference to the th UE n the su-nds the th UE s scheduled. Note tht Non-CoMP cn e vewed s specl cse of CBF when = 1. III. JOINT STF-PF SCHEDULER FOR CBF A scheduler s n ntellgent component whch determnes how the network resources (n the spce tme nd frequency domns) re to e llocted to serve dfferent UEs. In ths secton novel jont STF-PF scheduler for CBF s proposed for the mult-cell MU-MIMO systems. Recll tht n CBF the enbs cn coordnte to mtgte the mutul nterference to coscheduled UEs. Also the system performnce evluton s two-fold: spectrl effcences (relted to throughputs) nd performnce mprovement for UEs (relted to frness). Therefore the STF-PF CBF scheduler hs multple tsks. The nterference mtgton s delt wth n the precoder desgn n su-secton B nd the trdeoff etween mxmng throughput nd mntnng UE frness s mnged y the PF crteron [5] n the schedulng s descred n su-secton A. A. Jont STF-PF Schedulng Frmework The schedulng frmework defnes the procedure of schedulng n the tme nd frequency domns (.e. n TTI s nd n su-nds) nd UE selecton (n the spce domn). The precoder desgn n the spce domn wll e descred n the next su-secton. In the jont STF desgn multple vrles depend on ech other: The UE selecton nd precoder desgn t dfferent enbs re coupled; the wdend MCS for ech scheduled UE depends on the UE selecton nd precoder desgn t the enbs nd the su-nd MCS selecton of the UE n ll su-nds. An exhustve serch over ll vrles to yeld the mum schedulng decson would result n hgh complexty for resonle sed network. To smplfy the desgn our des re s follows: Frstly the schedulng (UE selecton precoder desgn nd su-nd MCS selecton) s done on per su-nd ss. After the schedulng s done the wdend MCS s determned for ech scheduled UE sed on ts su-nd MCSs. Secondly n ech su-nd n tertve UE selecton procedure s used. The schedulng t ech enb s updted tertvely sed on tht of the other enbs. Before gettng nto the schedulng procedure we mke few defntons. For the th UE defne r (n) s the estmted nstntneous dt rte n the th su-nd nd the n th TTI nd R ( n) s the verge sum throughput efore the n th TTI (the summton s done over ll RBs). Intlly R (1) 1 for ll. Also defne g (n) s the ndctor of UE selecton of the th UE n the n th TTI nd th su-nd. If g (n) = 1 t s selected; otherwse t s not selected. The jont STF-PF schedulng procedure cn then e descred s follows: Step 1: For the th su-nd n the n th TTI consder the schedulng t the c th enb n the x th terton. Bsed on the tenttve UE selecton nd precoders t other enbs consder the k th ( xk ) possle UE group c (consstng of 1 or 2 UEs dependng on ech scenro defned n Secton II). ( xk ) Step 2: For c perform precoder desgn nd su-nd MCS selecton for the UEs nd clculte the enb-wde sum PF metrc n n r (see remrk 1). ( xk ) c R ( xk ) Step 3: Repet Steps 1 to 2 for ech UE group c k = 12. (The numer of UE groups depends on the numer of UEs ssocted to the c th enb.) Select the mum UE group ( x) whch mxmes the enb-wde sum PF metrc.e. c ( x) c rg mx k n r. (4) ( xk ) c R n Step 4: Repet Steps 1 to 3 for ech enb c n the x th terton. Step 5: Repet Steps 1 to 4 for ech terton untl the UE ( x) ( x1) selecton converges (.e. c c for ll c ) or untl x > N ter where N ter s the mxmum numer of tertons (see remrk 3). The fnl UE selecton s denoted s. Set g (n) = 1 for ll c ; nd g (n) = c c for ll c. Step 6: Repet Steps 1 to 5 for ech su-nd = 1 N SB. Step 7: For ech scheduled UE determne the wdend MCS sed on the su-nd MCSs (see remrk 2). Step 8: Updte the verge sum throughput of ech scheduled UE fter trnsmsson: N 1 SB n 1 R n 1= g nr n R n (5) n 1 n where r n denotes the ctul dt rte for the th UE n the th su-nd nd the n th TTI. Step 9: Repet Steps 1 to 8 for ech TTI n = 12. Remrk 1: Regrdng the sum PF metrc frstly nd re the prmeters n the PF metrc r n R n. In 3GPP LTE they re generlly consdered close to 1. We choose = = 1. Secondly the PF metrc s good to cheve mult-user dversty nd mntn frness n SU systems. We consder ts strghtforwrd extenson to MU systems y usng the enb-wde sum PF metrc n (4). Note tht wth the tertve UE selecton procedure the system-wde UE n r selecton prolem d rg mx d xk d ( xk ) d R n s solved y solvng the enb-wde prolem n (4) for ll enbs

4 tertvely. Lstly {r (n)} re determned y the UE selecton nd precoder desgn t the enbs nd the su-nd MCS selecton of the th UE n the th su-nd (descred n susecton B). For smplcty ts dependence on the terton ndex x nd UE group ndex k s omtted n the notton. Remrk 2: One wdend MCS for ech scheduled UE s selected sed on the su-nd MCSs. Ths s done sed on n emprcl guess. The trget rte s estmted s r n 1.1 r n1 1.1 n / r n (6) where r n NSB NSB = g n r n g n nd 1 1 n 2 = NSB NSB g n r n r n g n 1. 1 The wdend MCS s chosen s the MCS provdng the lrgest rte not exceedng r (n). Remrk 3: The frmework works for rtrry. In CBF the numer of tertons requred for convergence of the UE selecton depends on. In generl the lrger the more tertons my e requred. The convergence my not e gurnteed though. To prevent lrge performnce degrdton we choose N ter = 1. (When N ter = 1 the UE selecton converges n t lest 85% of the reltons for ech we re nterested n.) Note tht n Non-CoMP N ter = 1. B. Precoder Desgn nd Su-nd MCS Selecton In scenro () MU-MIMO rnk-1 precoders re used. On the other hnd n SU-MIMO the pproprte rnk nd precoder re chosen to mxme the enb-wde sum PF metrc n (4). The rnk-1 precoder (n scenro ()) nd rnk-2 precoder (n scenro ()) re desgned ccordng to the followng crteron. To mtgte nterference whle mxmng throughput the precoder desgns of ll scheduled UEs re coupled. To sgnfcntly reduce the complexty we choose the mxmum sgnl-to-lekge-rto (SLR) precoder (not consderng the nose n the mxmum sgnl-to-lekge-nose-rto (SLNR) precoder n [6]). F n n n tr c c c n F A F c n n n n n n F c trf c Fc Pc tr F c Bc Fc rg mx n n m n m c c c ms A H H n n m n m c jc jc d ( xk ) jd j ms n c B H H where rnk-1 or rnk-2 F s the precoder for the th UE n the th su-nd nd n th TTI nd S s the set of ndces of the RBs n the th su-nd. P c = P tx f there s one UE n the UE group nd P c = P tx /2 f there re two UEs n the UE group. n For smplcty the dependence of F c on the terton ndex x nd UE group ndex k s omtted n the notton. In (7) oth the lekge to co-scheduled UEs n other cells nd tht to the other UE served y the sme enb re consdered. The closed (7) c n form soluton of F s gven n [6]. When only one UE s consdered n the UE group nd when the current enb s not n the coopertng sets of ny coscheduled UEs t other enbs sngulr vlue decomposton n (SVD) sed precoder s used nsted. F s proportonl to the frst few domnnt egenvectors of n c F s ccordng to the rnk consdered. c n c A nd the rnk of The sgnl-to-nterference-nose-rto (SINR) of the l th dt strem of the th UE n the m th RB nd n th TTI s estmted s n m n n m n c c c c ll H F H F nm SINRl (8) n m n n m n n m d jd d jd H F H F R d ( xk ) j d ll where m S. The su-nd MCS s selected sed on the exponentl effectve SINR mppng (EESM) [7]. The nstntneous rte r (n) s determned y the su-nd MCS. IV. PERFORMANCE IMPACT OF COOPERATING SET SIZE In ths secton we nlye the mpct of the coopertng set se on system performnce. Becuse of the rndomness of the UE loctons nd complcted schedulng process the theoretcl nlyss for the whole system s complcted nd ntrctle. We eleve tht the CBF s most enefcl when the domnnt nterference (contruted from lmted numer of enbs) s mtgted through coordntng schedulng nd emformng. Therefore we consder reltve smple cse sed on whch the mpct of the coopertng set se on system performnce of the whole system cn e predcted. In ths smple cse we consder L downlnk sngle-crrer su-systems n n solted spce (wthout outsde nterference). The su-systems hve mutul nterference though. Ech su-system hs n enb equpped wth N t trnsmt ntenns nd two UEs ech equpped wth N r receve ntenns. At ech UE the nterferng sgnls re ssumed s strong s the desred sgnls. Recll from Secton II one of the schedulng scenros of () rnk-1 SU-MIMO () rnk-2 SU- MIMO nd () MU-MIMO my hppen. To smplfy the nlyss we frst ssume the schedulng scenros cross the whole network re the sme. In the frst step for ech scenro we determne the mxmum L so tht ech ctve UE cn recover ts own dt nterference free. Ths s equvlent to fndng the mxmum degrees of freedom (DoF) n the system wthout symol extenson [89]. Scenros () nd () re equvlent to n L-user nterference MIMO chnnel [1] denoted s (N t N r d) L wth d degrees of freedom per user where d=1 n () nd d=2 n (). As n [1] L stsfes N t + N r (L + 1)d. Therefore when N t = 4 nd N r = 2 L = 5 n () s chevle v nterference lgnment nd L = 2 n () s chevle v ero-forcng/lock dgonlton. For scenro () lterntvely we consder system (N t 2N r d) L whose performnce s the upper ound of (). In ths system L stsfes N t + 2N t (L + 1)d. Therefore when N t = 4 nd N r = 2 L 3 n ().

5 sector verge spectrl effcency (/s/h) In the second step smlr to [11] y llowng nterference one more su-system (ech dt strem my hve lower dt rte though) my e supported f the system s prtlly loded s n () nd () ut not n (). In the lst step we extend to the whole system where ll three scenros my coexst n ny gven su-nd nd t ny gven TTI we mke the followng predcton: () CBF sgnfcntly mproves the system performnce when L 3 snce n ll three scenros cn eneft from CBF. () CBF stll provde mrgnl gns when 4 L 6 ecuse only scenros () nd () my eneft from CBF. V. NUMERICAL RESULTS A. Smulton Setup We consder N c = 19 N s = 57 N t = 4 N r = 2 N UE = 1 N RB = 5 nd N SB = 9. The wdend ndwdth s 1MH nd the ndwdth of ech RB s 18kH. There re 6 RBs n ech of the frst 8 su-nds nd there re 2 RBs n the lst sund. One TTI s.1 sec. The smulton s run for 1 drops ech conssts of 1 TTIs. In ech drop the UEs re rndomly dropped dfferent loctons n the sectors. The chnnel model s 3GPP Cse 3 (specfed n Tles A nd A n [1] nd n [12]). In ddton cross-polred 3D ntenns t enbs (ntenn confgurton E n Tle A.3.1 n [1]) re ssumed. Block fdng model s ssumed. Ech chnnel remns constnt n one TTI nd chnges from TTI to TTI. Hyrd utomtc repet request (HARQ) employng Chse Comnng s ssumed nd the mxmum numer of retrnsmssons s lmted to 4. To smplfy the smulton we only perform schedulng n the centrl hexgonl cell ste (3 sectors) mong 3 UEs. The nterference from the enbs n the wrpround cells s estmted. If wrpround enb s n UE s coopertng set ts nterference s stll tken nto ccount n the nterference nd nose covrnce mtrx n (2). The dfference s tht nsted of ssumng rndom precoder t the wrpround enb mxmum SLR precoder s ssumed. The mxmum SLR precoder s otned sed on rndomly generted desred chnnel n the wrpround cell nd the nterferng chnnel from the wrpround enb. C. Performnce Improvement for UEs (Relted to Frness) The performnce mprovement for UEs n prtculr the cell edge UEs s looked t n ths su-secton. The UEs hvng the 5~1% worst performnce re the cell edge UEs who receve wek desred sgnls nd strong nterference. The 5%- tle nd 1%-tle spectrl effcences of dfferent re presented n Tle I. The cumultve densty functon (CDF) of the UE spectrl effcency s plotted n Fg. 2. And tht for the cell edge UEs ( oom n vew of the CDF from ~.1) s plotted n Fg. 3. The percentge of the ncrement of UE spectrl effcences for over these for -1 s plotted versus the normled UE spectrl effcences for -1 (rnged from ~1) n Fg. 4. We hve the followng oservtons: Frstly the generl trend (except for the 1~4% worst performnce UEs s shown n Fgs. 3 nd 4) s tht s ncreses the UE spectrl effcences ncrese whle the UE spectrl effcency ncrement decreses especlly when 7. Secondly s n Fg. 2 the UE spectrl effcency ncrement (n /s/h) for the hgh performnce UEs s lrger thn tht for the low performnce UEs. Thrdly s n Fg. 4 the reltve UE spectrl effcency ncrement (.e. the ncrement percentge) for the mjorty of UEs s lrge when = 2 especlly for the UEs wth 2~4% normled spectrl effcency; t ecomes smller nd closer to unform for ll UEs s ncreses ( 4); s further ncreses ( > 6) t ecomes negtve for some hgh performnce UEs so s to provde cell edge UEs hgher gns thn the verge gn (whch s elow 2%). Lstly due to sttstcl vrton the curves n Fgs. 2 3 nd 4 re not smooth; s n Tle I nd Fgs. 3 nd 4 the spectrl effcency of ech cell edge UE my not ncrese monotonclly s ncreses. TABLE I. SPECTRAL EFFICIENCIES Sector verge spectrl effcency (/s/h) 5%-tle spectrl effcency (/s/h) 1%-tle spectrl effcency (/s/h) B. Averge Performnce The cell verge performnce s looked t n ths susecton. The sector verge spectrl effcences of dfferent re presented n Tle I. The sector verge spectrl effcences re lso plotted versus n Fg. 1. Note tht the = 1 scheme s the Non-CoMP scheme. We oserve the followng: Frstly the sector verge spectrl effcency ncreses s ncreses. Secondly the performnce gns of the CBF wth sectors n the coopertng set over the CBF wth - 1 sectors n the coopertng set re ove 7% when 2 3 round 2~7% when 4 6 nd elow 2% when 7. The gn s expected to vnsh s ncreses to certn pont. Ths grees wth our predcton nd physcl nsghts n Secton IV Fgure 1. Sector verge spectrl effcency vs..

6 UE spectrl effcency ncrement (%) CDF CDF =1 =2 =3 =4 =5 =6 =7 =8 = UE spectrl effcency (/s/h) Fgure 2. CDF of the UE spectrl effcency. =1 =2 =3 =4 =5 =6 =7 =8 = UE spectrl effcency (/s/h) Fgure 3. CDF of the UE spectrl effcency of the cell edge UEs ( CDF.1) =2 =4 =6 = normled UE spectrl effcency Fgure 4. Percentge of UE spectrl effcency ncrement. D. Suggested Se of the Coopertng Set Bsed on the ove oservtons to cpture the lrge verge performnce mprovement t s suggested tht 3 6; to cpture the sustntl performnce mprovement for the mjorty of the UEs especlly cell edge UEs t s suggested tht 4 (when the reltve ncrement (n percentge) s looked t). Also note tht the lrger the lrger the overhed nd the hgher complexty the system hs. For the performnce nd complexty trdeoff t s suggested tht 4 6. When 7 the overhed nd complexty ncrements re not worthy for the lttle verge performnce mprovement (<2%). VI. CONCLUSION In cellulr system wth frequency reuse fctor of 1 CBF llows the enbs to coordnte ther trnsmssons to mtgte nterference. An mportnt desgn spect s to determne the proper CBF coopertng set se nd predct ts correspondng performnce n mult-cell MU-MIMO systems. In ddton to mxmng the sector verge performnce nother desgn crteron s to cpture the sustntl performnce mprovement of the mjorty of the UEs especlly cell edge UEs. In ths pper novel jont STF-PF scheduler for CBF s proposed. The mpct of the coopertng set se on system performnce s nlyed sed on smplfed system nd vldted wth the numercl results. It s suggested tht the coopertng set se etween 4 nd 6 provdes the est performnce (n terms of oth mxmng sector verge performnce nd cpturng the sustntl performnce mprovement of the mjorty of the UEs especlly cell edge UEs) nd complexty trdeoff. ACKNOWLEDGMENT We would lke to thnk Hongsn Sheng Crl Wng Phlp Petrsk Ru Yng Dougls R. Cstor Gregory S. Sternerg Brn G. Kernn nd Roert A. DFo ll from InterDgtl Communctons LLC for ther helpful dscussons nd comments on the work. REFERENCES [1] 3GPP TR v9.. Further dvncements for E-UTRA physcl lyer spects (Relese 9) Mr. 21. [2] R Performnce Evluton of CoMP CS/CB Smsung Fe. 21. [3] R Selecton Threshold nd Mxmum Se of CoMP Coopertng Set CHTTL Aug. 29. [4] 3GPP TS v8.3. Physcl lyer procedures (Relese 8) My 28. [5] D. Tse Multuser Dversty n Wreless Networks Apr. 21 onlne vlle from [6] M. Sdek A. Trght nd A. H. Syed A lekge-sed precodng scheme for downlnk mult-user MIMO chnnels IEEE Trns. Wreless Communctons vol. 6 no. 5 pp My 27. [7] IEEE 82.16m-8/4r5 IEEE 82.16m Evluton Methodology Document (EMD). [8] K. Gomdm V. R. Cdme nd S. A. Jfr Approchng the Cpcty of Wreless Networks through Dstruted Interference Algnment n Proc. IEEE Glol Communctons Conference 28. [9] T. Gou nd S. A. Jfr Degrees of Freedom of the K User MIMO Interference Chnnel n Conf. Record Aslomr Conference on Sgnls Systems & Computers Oct. 28. [1] C. M. Yets S. A. Jfr nd A. H. Kyrn Feslty Condtons for Interference Algnment rxv: v1. [11] J. L E. Lu nd I-T. Lu Performnce Benchmrk for Network MIMO Systems: A Unfed Approch for MMSE Trnscever Desgn nd Performnce Anlyss n Proc. IEEE Glol Communctons Conference Dec. 21. [12] 3GPP TR v7.1. Physcl lyer spects for evolved Unversl Terrestrl Rdo Access (UTRA) (Relese 7) Sep. 26.