SLNR-based User Scheduling in Multi-cell networks: from Multi-antenna to Large-Scale Antenna System

Transcription

1 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII LNR-based Use ceduling in Multi-cell netwos: fo Multi-antenna to Lage-cale Antenna yste Yancun Li, Guangxi Zu, ua Cen, Mino Jo 3 and Yingzuang Liu Depatent of Electonics and Infoation Engineeing, uazong Univesity of cience and Tecnology, Wuan, ubei Cina [e-ail: yancun, gxzu, liuyz@usteducn] College of Mateatics and Copute cience, Wuan Textile Univesity, Wuan, ubei Cina [e-ail : @qqco] 3 Depatent of Copute and Infoation cience, Koea Univesity, ejong, - Koea [e-ail: inojo@oeaac] *Coesponding auto: Mino Jo and ua Cen Received Octobe 9, 3; evised Decebe, 3; accepted Januay 4, 3; publised Febuay 9, 4 Abstact In tis pape, we investigate te pefoance of ignal to Leaage and Noise Radio (LNR) based use sceduling in uplin of ulti-cell wit lage-scale antenna syste Lage antenna aay is desied to ipove te pefoance in futue syste by poviding bette beafoing capability oweve, soe studies ave found tat te signal cannel is adened (becoes invaiant) wen te antenna nube goes exteely lage, wic iplies tat te signal cannel awae use sceduling ay ave no gain at all Wit te ateatic tool of ode statistics, we analyzed te signal and intefeence tes of LNR in a oogeneous ulticell netwo Te deived distibution function of signal and intefeence sows tat te leaage cannel s vaiance is uc oe influential tan te signal cannel s vaiance in lage-scale antenna egie o even toug te signal cannel is adened, te LNR-based sceduling can acieve eaable ultiuse divesity (MUD) gain due to te fluctuation of te uplin leaage cannel By poviding te final INR distibution, we veify tat te LNR-based sceduling can leveage MUD in a bette way tan te signal cannel based sceduling Te Monte Calo siulations sow tat te tougput gain of LNR-based sceduling ove signal cannel based sceduling is significant Keywods: Lage-scale antenna syste, ulti-cell, intefeence anageent, ultiuse divesity Tis eseac was suppoted by te National Reseac Foundation of Koea gant funded by te Koea govenent (MET) (No -48), te ino-koea Joint Reseac oject unde gant (No DFG5) and Natue cience Fund of ubei povince unde gant (No 3CFB39) ttp://dxdoiog/3837/tiis433

2 946 Yancun et al: LNR-based Use ceduling in Multi-cell netwo Intoduction Use sceduling as been widely adopted in te uplin of MIMO ulticell netwos to ipove syste tougput It can get significant ultiuse divesity gain if te vaying in cannel is lage and te cannel state is nown by scedule Te latest engineeing advances allow te ultiple antennas to be extended to exteely lage antenna aay in a pactical and affodable way[] Tis tecnology is naed lage-scale antenna syste (aa assive MIMO) Te lage nube of antennas is desied to ipove te pefoance in futue syste by poviding bette signal captue capability oweve, soe studies ave found tat te signal cannel is adened (becoes invaiant)[] wen te antenna nube goes exteely lage Moeove, te acquisition of cannel state infoation (CI) wic is te peequisite of sceduling becoes callenging since te cannel size is lage wile te esouces fo cannel taining is liited Tus, wete to scedule uses o not in assive MIMO is a subject of paticula inteest In tis wo, we investigate te pefoance of ignal to Leaage and Noise Ratio (LNR)-based sceduling wic is awae of te cannel condition in bot signal and leaage cannels in lage-scale antenna syste Recent wos sow tat accuate CI is available in assive MIMO syste, so te sceduling pefoance in ig CI accuacy egie is of paticula inteest Te pilot containation was consideed as a seious poble fo assive MIMO[3] Te inaccuate CI causes te adening in bot signal and intefeence cannel so tat te use sceduling gain vanises Recently, planty of eseaces sow tat accuate is acquiable fo assive MIMO [4] [5] [6] Tus, cannel awae use sceduling is viable fo assive MIMO syste Moeove, we notice tat, wen te sceduled use in ote cell is diffeent fo te use causes te pilot containation, te pecoding will be also un-coelated wit te intefeing cannel It also iplies tat te intefeence cannel will not be adened lie te signal cannel Motivated by nowing tat te intefeence powe flactuates significantly, we conside deploying use sceduling to educe te intefeence in ulticell assive MIMO systes Te use sceduling scees in [7] [8] exploit te uses cannel divesity on lage-scale to ipleent coopeative downlin assive-mimo tansission Tus, te intefeence can be tuned into signal oweve, te excanging of CIs aong cells faces nubes of callenges, eg delay, bacaul oveead (especially fo vey lage antenna syste) Tus, we ae inteested at te scee wic doesn t need coodination aong cells Te LNR-based sceduling can awae of te intefeence poduced by local-cell use witout assitance fo ote cells It can suppesse inte-cell intefeence oppotunistically wile boost signal [9] Te pefoance of LNR-based sceduling as been studied in taditional ulti-antenna syste In taditional ulti-antenna syste, te signal cannel fluactuates uc oe signicantly tan inteefeence cannel Ou ealy study sows it can povide significant tougput gain [] oweve, in assive MIMO syste, te cannel adening effect causes signal cannel fluactuate less significantly Wete te LNR-based sceduling could still povide pefoance gain as not yet nown In tis wo, we study te pefoance of use sceduling in ig CI accuacy egie Wen te ipact of intefeence on pilot is suppessed, te data eceiving will be less affected by te islead cannel estiation oweve, te intefeence on data becoes a non-negligible facto Unlie te signal cannel based sceduling scee wose gain

3 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII vanises in asssive MIMO, we find tat te LNR-based sceduling can still povide pofound pefoance gain even wen te signal cannel is adened Te ajo contibutions of tis pape ae as follows: ) By te ateatic tool of Ode tatistics, we analyzed te signal and intefeence tes in LNR of a oogeneous ulticell netwo Te way tat signal is enanced and intefeence is suppessed is illustated ) We find tat, fo lage-scale antenna syste, te leaage cannel s vaiance is uc oe influential tan te signal cannel s vaiance in lage-scale antenna egie based on te deived distibution function of signal and intefeence o, even toug te signal cannel is adened, te LNR-based sceduling can acieve eaable ultiuse divesity (MUD) gain due to te fluctuation of te leaage cannel 3) By poviding te eventual INR distibution, we veify tat te LNR-based sceduling can leveage MUD in a bette way tan te signal cannel based sceduling Te Monte Calo siulations sow tat te tougput gain of LNR-based sceduling ove signal cannel based sceduling is significant Tis pape is oganized as follows ection intoduces te syste odel, descibes MRC detecto and uplin ection 3 discusses te elationsip between CI accuacy and te fluctuation caacteistics in effective signal and intefeence cannels Afte discoveing te fluctuation in assive MIMO intefeence cannel of ulti-cell uplin, we povide a siple eview of LNR-based use sceduling, wic can effective exploiting te cannel fluctuation oppotunistically, in ection 4 In ection 5, te distibution of sceduled use s INR is deived And te effect of ultiuse divesity in intepeted Te Monte Calo siulation esults ae pesented in ection 6 And ection 7 concludes te pape We use following notations in te pape f and F X X is te obability Density Function (DF) and Cuulative Distibution Function (CDF) of a Rando Vaiable (RV), coespondingly yste Model We conside te uplin of a ulti-cell syste wit M Bs Denote te B in cell as B B is equipped wit N antennas Eac B seves K single-antenna uses Te uses ae identified by tei index in cell and cell index jointly, eg te t use in cell is denoted by U, Te B wit ultiple antennas can suppot oe tan one uplin data steas siultaneously Due to te lage antenna size, te inte-use intefeence is consideed as being tivial fo assive MIMO ince we ae paticulaly inteested at intecell intefeence, we assue a B seves one use on eac uplin esouce bloc fo te sae of siplicity and tactability We conside te popagation cannel wit lage-scale pat loss and sall-scale cannel fading Assue OFDM is deployed so tat eac subcaie can be consideed as flat fading Te lage-scale patloss powe gain of te cannel between B B and te use U n, is,, n M and K Fo te signal cannel between B B and its use, n, N U,, te sall scale fading coefficient vecto can be denoted by, C Fo te intefeing cannel between B B and any use fo ote cell, U n,, n, te sall

4 948 Yancun et al: LNR-based Use ceduling in Multi-cell netwo scale fading coefficient vecto can be denoted by Rayleig fading fo all cannels, ten te eleents in, g N, n, C We assue independent and g, n, n follow iid coplex Gaussian distibution CN, We assue tat all Bs and uses ae pefectly synconized and opeate in Tie Division Duplexing (TDD) ode wit univesal fequency euse o, te cannel as downlin-uplin ecipocity afte Tx-Rx adwaes ae calibated Denote te sceduled use of B B as Te signal tansitted by te sceduled use of B B is x, All use send signal wit unifo tansit powe UL E x, Te eceived signal at B B is te supeposition of te signal fo te sceduled uses in all cells, y x g x n (),,,,, n, n, n, n n, n nm, n Noise wee, te last te is te wite Gaussian Noise at B, n ~, IN CN We assue a siple single-use detecto wit linea filteing All intefeence is teated as noise Bot te Maxial Ratio Cobining (MRC) and te MME detecto ae coonly used in conventional MIMO systes oweve, due to exteely lage N, te atix invesion opeation in MME as ig coputational coplexity MRC eceive is consideed ee Fo te signal of B B s sceduled use, te output of MRC eceive is ˆ ˆ,, UL, so v y () ˆ wee, v,,, is te noalized MRC eceiving weigt vecto, is te estiated cannel vecto Ten, te uplin INR of B B can be epesented by,,,,,,, v, g n n, n, n nm, n Noise UL wee, is te noalized noise powe, / ince bot te signal and intefeence ave been pocessed by vecto v,, we ae inteested at te effective cannel tat te signal and intefeence popagate toug v,, is effective cannel fo signal wile v, g, n, n is te effective cannel fo intefeence Tey jointly deteines te acievable ate of tis tansission, log evaluated by te aveage tougput pe cell, E v (3) Te syste pefoance can be log ee, we assue te duation of te cannel easueent, feedbac and te sceduled tansission is uc less tan te coeent tie of te vaying cannel o, te cannel easueent/feedbac oveead can be oitted Te cannel can be seen as constant witin a sceduling peiod

5 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII 3 Relation between CI Accuacy and ignal/intefeence Cannel Caacteistics Te CI accuacy, and te coupling between use sceduling and pilot allocation, jointly deteines te caacteistics of effective signal and intefeence cannel In tis section, we sow tat in diffeent level of CI accuacy, te effective signal and intefeence cannel will pesent diffeent level of fluctuation Fute, we find te opputunistic use sceduling can elp decoelating te pecoding wit intefeence cannels, so tat te intefeence cannel as fluctuation independent of N To depict te CI accuacy in ulticell MIMO syste wit pilot containation, we begin wit exaination of te fundeantal cannel estiation pocess We assue MB acquies cannel state via uplin taining accoding to te cannel ecipocity in TDD ode J otogonal pilot sequences ae eused aong uses Denote te set of uses using j t pilot sequence in cell is j, Assue eac set as equal nube of uses, K,, J, Fo te case tat te nube of uses in cell is lage tan J te nube of pilot sequences ( K J ), pilot sequences will be eused witin a cell, j, Due to te pilot euse in intefeence cannel, te estiated signal cannel is containated by te intefeing cannels wic use te sae pilot sequences In te ost seious case, te estiated signal cannel is te supeposition of local signal cannel and intefeence cannel [5] And in ote cases, te pilot containation is alleviated[4] [6] Te signal and intefeence cannel can be sees as otognal to eac ote as N goes exteely lage (fo Lea in [5]),,, N u,,,, N g n l and g, n, l, u N Tus, geneally, te estiated signal cannel of use U, can be expessed as ˆ,,,,,,, u u,,, g, n, l υ n l, u \ nm l j,n wee,,, signal cannel j, inta-cell containation intecell containation and,,, u ae te scala pojection of,, n, l, on,, u, and g, n, l, espectively ince te vecto,, u, and g, n, l ae not noalized, te above scala pojection of a on b sall be calculated by coefficients,, ˆ a b b (4) Te and,,, u ae deteined by te pefoance of,, n, l deployed pilot tansission design and cannel estiation scees jointly υ, is te esidual pat wic can be calculated by υ ˆ,,,,,,,, u u,,, g n l, n, l u j, \ nm l j,n Note tat wen N is sall,,, u, and g, n, l ae not stictly otogonal wit eac

6 95 Yancun et al: LNR-based Use ceduling in Multi-cell netwo ˆ ote, and tat (4) is not a stict otogonal decoposition of vecto,, so υ, is wealy coelated wit,, u, and g, n, l Ten, we conside te data eceving wit te estiated CI Cobining () and (), we can ewiten te eceived signal in fo of ˆ ˆ ˆ g n,,,, n, n,,,, x,,,, ˆ x n n n n nm, n ˆ ˆ,,, ignal Intefeence (5) Fist, we conside te signal te of above equation Fo (4), we can now te coponent ˆ,, in te signal te as ˆ,,,,,,,, u, u, u j, \ (6), g, n, l, n, l, υ,, nm l j,n, is uncoelated wit u, and g, n, l And esidual te υ, is neglectable Te pilot containation s ipact on te signal te can be evaluated by,,,, u,, n, l u j, \ nm l j,n If,, is uc lage tan, wic eans te pilot containation is sevee, te pecoding vecto v ˆ ˆ can t atc te signal cannel,,, In tis case (CI, Accuacy level I in Table ), te gain of effective signal cannel will fluctuate Despite fluctuation exists in level I, tis is case is not desiable at all due to te loss of ulti-antenna beafoing gain o, tis case will be avoided in pactical syste Wen te facto, is significant,,, is doinant in (6) o te signal cannel becoes adened wen N goes lage (CI Accuacy level II and III in Table ) Ten, we conside te intefeence te in (5) Te coponent g,, n, n in intefeence te as ˆ g g,, n, n,,, n, n,,, u, g u, n, n u \ nm l j,n j, g g υ g ˆ,, n, l, n, l, n, n,, n, n Obviously, u, u, is uncoelated wit g, n, n o, te ipact of inta-cell pilot containation can be neglected Wen te caacteistics wic exist in ealistic popogation cannels ae not exploited at all, te signal cannel and intefeence cannel ae indistinguisable [5] In suc case,,

7 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma 4 95 Copyigt c 4 KII, and, ae copaable and te pilot containation is seious Te wo in [5] assues all uses eusing te sae pilot sequence ae sceduled siultaneously Te te g, n, n in ˆ, causes te adening in intefeence cannel (CI accuacy level II in Table ) Obviously, tee is also adening in intefeence cannel fo te CI accuacy level I Table Relation between CI Accuacy and ignal/intefeence Cannel Caacteistics in assive MIMO yste CI Accuacy Level I II III aaetes in estiated cannels, Effective ignal Cannel Effective Intefeence Cannel Fluctuating adened,, and, ae copaable adened adened,, adened Fluctuating, Recent wos sow tat, by exploiting te cannel statistical featue in ealistic envionent, te sopisticated pilot sequence assignent [4] and pilot stage allocation scee [5] can estiate te signal cannel quite accuately Te siulation in sows tat te ean squae eo of te estiation, t E ˆ,, ˆ,,, can be exteely sall and te estiation esult even appoaces te intefeence-fee case We denote it as te accuacy level III in Table A pilot sequence allocation scee as been poposed in [4] wic sows tat te containation facto is sall and appoaces (,,coespondingly) In tis CI accuacy level, te coelation between ˆ, and g, n, n is sall and te intefeence cannel becoe fluctuating Moeove, we find tat te intefeence cannels ae no longe adened wen ulti-use sceduling is deployed Assuing te sceduled use in cell using te j t pilot sequence, j, and all use as equal sceduling opputunities Te pilot containation is ost daaging wen n jn, as in [5] Te eceiving vecto will patial atc te diection wee te intefeence coes fo In fact, te pobability of tis event is sall, n K J Te case tat te use using ote pilot seqeunce in cell j, n j, n n is oe pobable, j, n j, n n K K J Te intefeing cannel g, n, l fo cell n is uncoelated wit te cannel wic causes te pilot containation g, n, n o te intefeence cannels ae no longe adened wen N goes lage Te sceduling pefoance in CI accuacy level III as not yet been studied by any existing papes In late of tis wo, we conside te CI accuacy level III and exploit te cannel caacteistics to acieve tougput gain

8 95 Yancun et al: LNR-based Use ceduling in Multi-cell netwo 4 Exploiting Cannel Fluctuation in MIMO Multi-cell yste In tis section, we study ow LNR-based sceduling elps boosting te INR in ulticell syste ince te LNR-based use sceduling in uplin affects te INR distibution in indiect way, to obtain of distibution of te esulting INR, we sall fist now te distibutions of sceduled use s signal and intefeence wic ae associated wit te axial LNR And tese distibutions ely on te distibution of axial LNR wic is affected by te nube of candidate uses o we deive te distibution of te sceduled use s LNR, signal, intefeence and INR, one by one Te LNR-based scedule as te benefit of exploiting te fluctuation in bot signal and intefeence cannels [] Te LNR of use U, is,, v,,, n,, vn, ngn,, nm, n (7) Te LNR awae scedule can pic te use wit igest LNR, ag ax, (8) K Te LNR-based sceduling gain elies on te sall scale cannel fluctuation in (7) To siplify te notation and ease te analysis, we define te sall-scale powe gain of effective cannel fo bot signal and intefeence cannel Te sall-scale powe gain of effective signal cannel of use, U is s v N, wee N,,, ~ stands fo te ci-squaed distibution wit N degees of feedo Te sall-scale powe gain of te effective leaage cannel between use U, and a B intefeed by it, B n, n q n,, n, n,, ~, is v g Fo te sae of tactability, we assue a oogeneous lage-scale cannel odel in all cells We conside te sae patloss fo all uses signal cannels,,, g, M, K iilaly, te patloss gains in all intefeing cannels ae also te sae, n,, g, n In uplin, te aggegated leaage poduced by use U, to all Bs intefeed by it is p, qn,, ~ M (9) o, te INR in (7) can be ewiten as n, 4 Te Ipact of ceduling on LNR gs g p, Fist, we conside te distibution of RVs befoe sceduling, wic is call pe-sceduling distibution Te signal and pollution s cannel distibutions, f p, jointly, f s and deteine te distibution of pe-sceduling LNR Fo any use U,, it as pe-sceduling LNR, wic as DF of n, n,

9 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII By taing s ds f f s f pdp,,,, g p, d () g p s, and te assued DF of n, g N N g M g s and p n, into (), we can get N g p N g g M f g p e p dp,!! () Fute, by expending te te g p N N, we can get! N N g p N i N i g g M!! i!! f g p e p dp, N g M () N i i Te Eq () can be ewitten as f, Mi N g N e N! N i i g g i N i! i! g N N! g M! g M i p g g g e p dp g g Finally, by applying e z z M dz M DF (3)! to (3), we can get te exact fo of, s Mi N g N e N! N i i g!! i!! f,,! g M i N N g M N i i g (4) Tus, te CDF of, can be deived as,, F f x dx N N g M! N!! N N i i g M i! i i N i! i! N j Mi j M i! g wee, i, j N j n, j M i j! j! g g g Fo te special case tat N, it as siple closed fo n g g F e, g Based on te distibution of pe-sceduling RVs and te beavio of sceduling, te M (5)

10 F(x) 954 Yancun et al: LNR-based Use ceduling in Multi-cell netwo distibution of te post-sceduling RVs can be obtained We conside te ipact of use sceduling Te event tat te axial LNR in cell as value of is equivalent to te event tat any ote uses in cell ave LNRs salle tan,,,, Besides, tis use can be any one of K uses o, by ode statistics [], te DF of te sceduled use s LNR can be deived as And te CDF of, is f f K F,,, F F,, K K (6) Te CDFs of sceduled uses LNR, calculated by (6) fo te cases of M 4, K and N,6,56 is sown in Fig Te vaiance of LNR becoes salle wit te incease of B s antenna nube It can be intepeted by te adening of signal cannel at lage N Consideing te pefoance of edian use, te post-sceduling LNR as 9dB gain ove te pe-sceduling LNR 9 8 e-ceduling ost-ceduling N= N=6 N= dB 3dB 9dB ignal to Leaage and Noise Ratio (db) Fig Te CDF of pe- and post-sceduling LNRs wit vaious antenna configuations fo g / g 3dB and g / 5dB Te teoetical esults ae sown by solid lines, wile te Monte Calo esults of e-ceduling and ost-ceduling ae pesented by te aes and +, espectively Te aes ae all coincident wit tei coesponding lines 4 Analysis of ceduling s Effect on ignal Enanceent and Intefeence uppession ince te, is te lagest aong all K uses LNRs, te signal te in it, s,, tends

11 F(x) KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII to be lage wile te pollution te, q n,,, tends to be sall Fist, we conside te distibution of signal te, s, Te signal cannel powe gain of te selected use s, is associated wit te LNR, geate tan te ote K uses o te s, s DF is f s K F f s f p dp (7) K, g s,, s, s p g p In (7), te ultiplie K coes fo wic eans tat any use could be te one K wit igest LNR Wen p, taveses ove te ange,, te value of, is gs K adjusted to, accodingly F is te pobability tat all uses ote tan, g p in cell ave LNR salle tan 9 8 e-ceduling ost-ceduling N= N=6 N= dB all-scale powe gain of signal cannel (db) Fig Te CDF of effective signal powe gain in sall-scale cannel fading Te teoetical esults ae sown by solid lines, wile te Monte Calo esults of e-ceduling and ost-ceduling ae pesented by te aes and +, espectively Unfotunately, tee s no closed fo expession fo te integal esult in (7) By taing (4) and (5) into (7), s, s DF can be calculated by nueical etod Te CDFs of sceduled uses signal cannel powe gain s, and all uses signal cannel powe gain, ae pesented in Fig Wen N is sall, s, as significant fluctuation Te scedule can easily exploit te cannel divesity to enance te signal cannel powe gain of sceduled uses oweve, wen N goes lage, te adening effect of assive s K

12 F(x) 956 Yancun et al: LNR-based Use ceduling in Multi-cell netwo MIMO s signal cannel eeges Fo N 56, te vaying of s, is so sall tat LNR-based scedule could adly pic any use wit ige s, Wile te ige LNR tends to be associated wit a ige signal cannel gain s,, it also pusues a lowe leaage cannel gain q n,, oweve, te situation fo q n,, is oe coplicate tan fo s,, since in,, te cannel powe gains of leaage to seveal Bs ae sued, p, qn,, n e-ceduling ost-ceduling N =56,6, all-scale gain of individual intefeing cannel (db) Fig 3 Distibution of individual intefeence cannel s sall scale gain q n,,, n, unde vaious antenna configuations Te teoetical esults ae sown by solid lines, wile te Monte Calo esults of e-ceduling and ost-ceduling ae pesented by te aes and +, espectively Fist, we conside te aggegated pollution by te use in cell to all intefeed Bs except a intefeed B i, wic is denoted as p i,,, pi,, q j,, ~ M 4 Te DF of p i,, is j, i M3 p f p p p e i,, M 3! Obviously, fo te definition in (9), we can now p, qi,, p i,, (9) By (8) and (9), we can get K i,,,, gs i,, f q f q f s K F f p dpds qi,, q s p gq gp (8) () Tee is no closed fo expession fo te sceduled pollution cannel powe gain s

13 F(x) KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII expession eite We calculate () by nueical integation Te CDF of individual intefeence cannel s sall-scale gain at B is sown in Fig3 Te distibution of pe-sceduling intefeence cannel gain q n,, is independent of N Afte sceduling, te intefeence cannel gain is suppessed effectively And te suppession is oe significant wen N is lage It is because tat wen signal cannel is adened at lage antenna nube egie, te fluctuation in LNR is doinated by te vaying in pollution cannel Denote te aggegate intefeence in uplin data INR (3) as,, n, nq, n, n nm, n We can get its CDF based on (), F f q f q f q dq dq dq, qi,, qi,, qi,, M M q q qm 9 8 e-ceduling Min-Leaage ceduling Max-LNR ceduling N =,6, all-scale powe gain of aggegate intefeing cannel (db) Fig 4 Aggegate intefeing cannels sall-scale gain unde vaious antenna configuations )Te teoetical esults ae sown by solid lines, wile te Monte Calo esults of ( N,6, 56 e-ceduling, Min-Leaage ceduling and Max-LNR ceduling ae pesented by te aes, and +, espectively Te consequent aggegate intefeence cannel gain s distibutions ae sown in Fig4 Te agax p ost left CDF cuve (geen) is fo in-leaage sceduling scee,, K We copae te esult of ax-lnr sceduling wit it At N 56, te, s CDF cuve unde ax-lnr sceduling is alost aligned wit te cuve unde in-leaage sceduling It is because tat te signal cannel becoes adened as sown in Fig Te fluctuation in, is piaily contibuted by te vaiance of q n,, o, in lage antenna egie, ax-lnr scedule beaves siila to in-leaage scedule Note tat we conside te intefeence is uc oe significant tan noise Altoug in

14 F(x) 958 Yancun et al: LNR-based Use ceduling in Multi-cell netwo enegy effient ( geen ) egie, te B s tansit powe fo asive MIMO ay be low enoug tat te inte-cell intefeence is down in teal noise, te acievable ate fo eac spatial stea is also low To acieve extee ig data ate and satisfy use s applicatin deand, te pe-stea ate ust be ig since te suppotable spatail stea nube at eac use is liited Tus, ig-ode odulations ae used Te intefeence will be significantly above te noise level We can conclude tat ) Te LNR-based sceduling exploits te fluctuations in signal and intefeence cannel ) It always tends to find a use wit lage signal cannel powe gain and salle leaage cannel powe gain aong all uses in a B And te pefeence is adapted to te vaiances in signal and leaage cannels 43 Te ipact of ceduling on INR Te INR s DF can be deived in siila way of obtaining, f, ds f f s f d,,,, d, g s g Rando-ceduling Max-ignal ceduling Min-Leaage ceduling Max-LNR ceduling N= N=6 N= INR (db) Fig 5 INR distibution unde vaious antenna configuations Te teoetical esults ae sown by solid lines, wile Monte Calo esults of Rando ceduling, Max-ignal ceduling, Min-Leaage ceduling and Max-LNR ceduling ae pesented by te aes,, and +, espectively Te aveage pe-cell capacity in syste is C Elog log, f d, M M Te final INRs CDF unde vaious scee and diffeent antenna configuations is sown in Fig 5 By oppotunistically selecting te use wit ig R, te spectu efficiency of all

15 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII uses is inceased, especially in ig spectu efficiency egion Te LNR based sceduling s INR is always beyond te INR unde ax-ignal scee and in-leaage scee Fo te analysis above, we conclude te ain diffeences between te LNR-based sceduling in taditional MIMO and Massive MIMO in Table Table Copaison of LNR based sceduling in assive MIMO and taditional MIMO Taditional MIMO Massive MIMO Effective ignal Cannel Fluctuating adened Effective Intefeence Cannel Fluctuating Fluctuating LNR Fluctuating Less Fluctuating ost-ceduling INR ignificantly ipoveent contibuted by te fluctuation in bot signal and intefeing cannels Ipoveent ainly contibuted by te fluctuation in intefeing cannels 5 iulation Results We copae te pefoance of vaious scees by Monte Calo siulations Unless specified otewise, we assue te pe-cell use nube is K And te ajo intefeed B nube M is 3 Te total B nube is M 4 Te lage scale signal to intefeence g M g 3dB Te lage scale intefeence to noise atio is powe atio is M g 5dB Te aveage pe-cell tougputs wit inceasing B antenna nube is sow in Fig 6 It sows tat te ax-lnr sceduling scee as te igest tougput fo all B antenna configuations We povide Fig 6(b) to give a detailed view of te tougputs in low antenna nube cases Initially, wen B antenna nube is sall, te ax-lnr sceduling scee acieves 87 ties tougput of te ando sceduling scee And te gain of ax-signal sceduling ove ando use selection is also significant By ecalling te esult fo ection 4, we can find tat te vaiance in signal cannel is uc lage tan te vaiance in intefeence (leaage) cannel, so te ax-signal can acieve alost te sae pefoance as ax-lnr scee Wen B antenna nube becoes exteely lage ( N 8 ), te gain of ax-signal sceduling ove ando use selection vanises It can be intepeted as tat uses signal cannels ae adened wit inceasing antenna nube Copaing to te pefoance gap between ax-signal sceduling and ando sceduling at N 8, te pefoance gain of ax-lnr sceduling ove ax-signal sceduling is peeinent It is because tat te fluctuation in leaage cannel does not vanis wit te inceasing of B antenna nube Te vaying in leaage cannel becoes doinant wen te signal cannel powe gain is alost fixed It is wot noting tat te MUD gain fo signal cannel is so liited wile te cost of acquiing signal cannel state inceases linealy wit N [] Tis cost ay outweig te MUD gain benefit witin it wen cannel does not incease wit N oweve, te cost of acquiing effective leaage N Te tougput of in-leaage sceduling is vey appoacing te tougput of ax-lnr sceduling It suggests tat te gain of MUD in leaage cannel is doinant in lage-scale antenna egie

16 e-cell Tougput (bps/z) e-cell Tougput (bps/z) 96 Yancun et al: LNR-based Use ceduling in Multi-cell netwo Rando-ceduling 3 Max-ignal ceduling Min-Leaage ceduling Max-LNR ceduling Max-INR Dual Capacity Nube of Antennas at B N 7 (a) Lage-scale antenna nube egie Rando-ceduling Max-ignal ceduling Min-Leaage ceduling Max-LNR ceduling Max-INR Dual Capacity Nube of Antennas at B N (b) all-scale antenna nube egie Fig 6 Te tougputs in vaious scees wit inceasing antenna nube We evaluate te tougput acieved by vaious sceduling scees wit inceasing pe-cell use nube K To sow ow tougput is ipoved wit K, we use te dual capacity of uplin MAC cannels, te su ate of te downlin boadcast cannel, as te baseline It is well nown tat, te pe-cell su-ate of te ax-inr sceduling in downlin deonstates te gowt ate of loglog K, asyptotically wit inceasing nube of uses pe-cell K [3] Fo Fig 7 we can see tat te loglog K lie MUD gain is also acieveable in ulticell uplin Te acievable ate of loglog K lie as been found in ealy wo [4] It adopts a leaage-tesold based pe-qualifying stage to peclude te use wo ay cause

17 e-cell Tougput (bps/z) e-cell Tougput (bps/z) KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma 4 96 Copyigt c 4 KII stong leaage to be te candidate Ten, te use wit best signal cannel is sceduled oweve, it is ad to be applied to te ulticell uplin wit lage-scale antenna because of te signal cannel adening In contast wit it, LNR based scee can adapt to te vaying of fluctuation caacteistics in cannels sootly 85 8 Rando-ceduling Max-ignal ceduling Min-Leage ceduling Max-LNR ceduling Max-INR Dual Capacity Nube of uses pe cell Fig 7 e-cell Tougput vs Use Nube 85 8 Rando-ceduling Max-ignal ceduling Min-Leaage ceduling Max-LNR ceduling Nube of Bs Fig 8 e-cell Tougput vs B Nube M Fig 8 sows te ipact of B nube s ipact on tougputs We can see tat all sceduling scees pe-cell tougputs decease wit te inceasing of M It is because tat te aggegated leaage tends to be less fluctuating wen M is lage, as we can see fo (9) Its ipact on leaage-awae scees including ou LNR-based sceduling is significant wen M oweve, in pactical netwos, te nube of Bs tat cause stong

18 96 Yancun et al: LNR-based Use ceduling in Multi-cell netwo intefeence to local cell is sall Fo all cases of M, 3 and 4, te pefoance gains of LNR-based sceduling copaed wit Max-ignal sceduling ae ove % 6 Conclusion In tis wo, we investigate te pefoance of te LNR-based use sceduling in uplin of ulti-cell wit lage-scale antenna syste We find tat in ig CI accuacy egie, wit awaeness of not only signal powe but also te leaage powe, te LNR-based sceduling can ty best effots to suppess uses intefeence powe leaage to ote cells B wen te signal cannel is adened in assive MIMO egie o, geneally, te LNR-base sceduling can povide excellent pefoance in all antenna nube configuations Wit te ateatic tool of Ode tatistics, we analyzed te signal and intefeence tes in LNR of a oogeneous ulti-cell netwo Te deived distibution function of signal and intefeence sows tat te leaage cannel s vaiance is uc oe influential tan te signal cannel s vaiance in lage-scale antenna egie o, te LNR-based sceduling can leveage MUD in a bette way tan te sceduling scees wic only focus on signal cannels Te Monte Calo siulations sow tat te tougput gain of LNR-based scedule ove signal cannel based one is significant Refeences [] F Ruse, D esson, L Buon Kiong, E G Lasson, T L Mazetta, O Edfos, and F Tufvesson, "caling Up MIMO: Oppotunities and Callenges wit Vey Lage Aays," ignal ocessing Magazine, IEEE, vol 3, pp 4-6, 3 Aticle (CossRef Lin) [] B M ocwald, T L Mazetta, and V Tao, "Multiple-antenna cannel adening and its iplications fo ate feedbac and sceduling," Infoation Teoy, IEEE Tansactions on, vol 5, pp , 4 Aticle (CossRef Lin) [3] J oydis, ten Bin, and M Debba, "Massive MIMO in te UL/DL of Cellula Netwos: ow Many Antennas Do We Need?," elected Aeas in Counications, IEEE Jounal on, vol 3, pp 6-7, 3 Aticle (CossRef Lin) [4] Yin, G D, F M, and Y Liu, "A Coodinated Appoac to Cannel Estiation in Lage-cale Multiple-Antenna ystes," elected Aeas in Counications, IEEE Jounal on, vol 3, pp 64-73, 3 Aticle (CossRef Lin) [5] F Fenandes, A Asiin, and T L Mazetta, "Inte-Cell Intefeence in Noncoopeative TDD Lage cale Antenna ystes," elected Aeas in Counications, IEEE Jounal on, vol 3, pp 9-, 3 Aticle (CossRef Lin) [6] D J Love, J Coi, and Bidigae, "A closed-loop taining appoac fo assive MIMO beafoing systes," in Infoation ciences and ystes (CI), 3 47t Annual Confeence on, 3, pp -5 Aticle (CossRef Lin) [7] oon, A M Tulino, and G Caie, "Netwo MIMO Wit Linea Zeo-Focing Beafoing: Lage yste Analysis, Ipact of Cannel Estiation, and Reduced-Coplexity ceduling," Infoation Teoy, IEEE Tansactions on, vol 58, pp 9-934, Aticle (CossRef Lin) [8] oon, G Caie, C apadopoulos, and A Rapasad, "Acieving "Massive MIMO" pectal Efficiency wit a Not-so-Lage Nube of Antennas," Wieless Counications, IEEE Tansactions on, vol, pp , Aticle (CossRef Lin) [9] B O Lee, Je, O- in, and K-B Lee, "A novel uplin MIMO tansission scee in a ulticell envionent," Wieless Counications, IEEE Tansactions on, vol 8, pp , 9 Aticle (CossRef Lin) [] Y Li, G Zu, and Zang, "Tansitte Centic ceduling in Multi-Cell MIMO Uplin yste," in Counications (ICC), IEEE Intenational Confeence on,, pp -6 Aticle

19 KII TRANACTION ON INTERNET AND INFORMATION YTEM VOL 8, NO 3 Ma Copyigt c 4 KII (CossRef Lin) [] A David and N Nagaaja, Ode statistics, 3d ed: Jon Wiley & ons, Inc, 4 Aticle (CossRef Lin) [] A Rajanna and N Jindal, "Multiuse Divesity in Downlin Cannels: Wen Does te Feedbac Cost Outweig te pectal Efficiency Benefit?," Wieless Counications, IEEE Tansactions on, vol, pp 48-48, Aticle (CossRef Lin) [3] O oe, O ieone, Y Ba-Ness, and A M aiovic, "Distibuted Multi-Cell Zeo-Focing Beafoing in Cellula Downlin Cannels," in Global Telecounications Confeence, 6 GLOBECOM '6 IEEE, 6, pp -6 Aticle (CossRef Lin) [4] W-Y in, D a, and B C Jung, "Can One Acieve Multiuse Divesity in Uplin Multi-Cell Netwos?," Counications, IEEE Tansactions on, vol 6, pp , Aticle (CossRef Lin) Yancun Li eceived te Bc degees in Electonics and Infoation Engineeing fo uazong Univesity of cience and Tecnology (UT), Cina, in 6 e was gaduate inten in te Counication Tecnology Laboatoy of Intel Cop, wee e paticipate eseac on WiMAX, fo 7 to 8 e was eseac assitant in Copute cience and Engineeing depatent at ong Kong Univesity of cience and Tecnology, wee e paticipate te eseac on Geen Netwo, fo to e is cuently pusuing is D at te Electonics and Infoation Engineeing Depatent at UT is eseac inteests ae in te aeas of Counication Teoy, Infoation Teoy and ignal ocessing Guangxi Zu eceived is B in adio engineeing fo uazong Institute of Tecnology, Cina, in 969 e is te expet of assessent goup in Acadeic Degees Coittee of Cina tate Council fo Infoation and Counication Engineeing, co-sponso and diecto of Futue Mobile Counication FuTURE oject Fou, a Coittee fo National Tecnical tandadization e is a pofesso and caian of te acadeic boad of te Depatent of Electonics and Infoation Engineeing, UT is eseac inteests include wieless counication and edia signal pocessing e as publised ove 3 papes Cen ua is a associate pofesso in Wuan Textile Univesity e ain eseac field is Netwo Counications, include optiization teoy and tecnology, etc Fo 5 to now, e pesided oe tan 3 ubei natual science fund pojects and oe tan ubei yout fund pojects, publised oe tan 5 papes in te field of netwo counications

20 964 Yancun et al: LNR-based Use ceduling in Multi-cell netwo Mino Jo eceived is D in Dept of Industial and ystes Engineeing, Leig Univ, UA in 994 e eceived is BA in Industial Engineeing, Cosun Univesity, Koea e is now ofesso of Depatent of Copute and Infoation cience at Koea Univesity, ejong e is one of founding ebes of te LCD Division, asung Electonics in 994 e is te Founde and Edito in-cief of KII Tansactions on Intenet and Infoation ystes e is an Edito of IEEE Netwo and an Edito of IEEE Wieless Counications, espectively e is an Associate Edito of Wiley's ecuity and Counication Netwos and an Associate Edito of Wiley's Wieless Counications and Mobile Coputing, espectively e as publised any efeeed acadeic publications in vey ig quality jounals and agazines e is now te Vice esident of te Institute of Electonics and Infoation Enginees Aeas of is cuent inteest include cognitive adio, netwo algoits, optiization and pobability in netwos, netwo secuity, wieless counications and obile coputing in 5G and 6G, wieless body aea netwo (WBAN), and wieless ogan netwo (WON) Yingzuang Liu is a pofesso of uazong Univesity of cience and Tecnology (UT) is ain eseac field is boadband wieless counication, including LTE and IMT Advanced syste, etc, especially its Radio Resouce Manageent Fo to, e was a postdoctoal eseace in ais Univesity XI Fo 3 up to now, e as pesided ove national ey pojects, publised oe tan 8 papes and eld oe tan 3 patents in te field of boadband wieless counication e is now te goup leade of boadband wieless eseac of UT, wic as oe tan young teaces and oe tan D students