Uplink CoMP under a Constrained Backhaul and Imperfect Channel Knowledge

Transcription

1 Uplink CoMP undr a Constraind Backhaul and Imprfct Channl Knowldg Patrick Marsch, Mmbr, IEEE, and Grhard Fttwis, Fllow, IEEE arxiv: v [cs.it] 7 Fb 00 Abstract Coordinatd Multi-Point (CoMP) is known to b a ky tchnology for nxt gnration mobil communications systms, as it allows to ovrcom th burdn of intr-cll intrfrnc. Espcially in th uplink, it is likly that intrfrnc xploitation schms will b usd in th nar futur, as thy can b usd with lgacy trminals and rquir no or littl changs in standardization. Major drawbacks, howvr, ar th xtnt of additional backhaul infrastructur ndd, and th snsitivity to imprfct channl knowldg. This papr jointly addrsss both issus in a nw framwork incorporating a multitud of proposd thortical uplink CoMP concpts, which ar thn put into prspctiv with practical CoMP algorithms. This comprhnsiv analysis provids nw insight into th potntial usag of uplink CoMP in nxt gnration wirlss communications systms. Indx Trms CoMP, ntwork MIMO, constraind backhaul, imprfct CSI, joint dtction, intrfrnc cancllation, multipl accss channl, intrfrnc channl Manuscript submittd. Part of this work has bn publishd in th procdings of th IEEE Intrnational Confrnc on Communications (ICC) 009 [].

2 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS I. INTRODUCTION A. Motivation Mobil ntwork oprators ar xprincing an xponntially growing dmand for mobil data rats at a stagnating avrag rvnu pr usr (ARPU), driving th nd for largr spctral fficincy. It is known, howvr, that spcially urban cllular systms ar mainly limitd through intr-cll intrfrnc []. To ovrcom this limitation, coordinatd multi-point (CoMP) was proposd in [3], [4], and has bn slctd as a ky tchnology for long trm volution (LTE)-Advancd [5]. In th uplink, for instanc, multi-cll joint signal procssing nabls th xploitation of intrfrnc [6], [7], rathr than trating it as nois, promising vast gains in spctral fficincy and fairnss [8], [9]. Bsid ky challngs, such as synchronization in tim and frquncy, a major concrn of uplink CoMP is its dmand for additional backhaul [0], and its snsitivity to imprfct channl stat information (CSI) []. This papr prforms an analysis of various uplink CoMP concpts undr a constraind outof-band backhaul and imprfct CSI. Th joint obsrvation of ths two major issus from a thortical and practical prspctiv shds a nw light on th valu of particular CoMP schms in nxt gnration wirlss communication systms. B. Rlatd Work Considring th aspct of a constraind backhaul, an uplink CoMP scnario is rlatd to th CEO-problm [], whr a numbr of agnts mak noisy, but corrlatd obsrvations on th sam random sourc, and us capacity-constraind links to a cntral stimation officr (CEO), who aims at rconstructing th sourc with minimum distortion. For a Gaussian sourc and nois, and a quadratic distortion masur, th rat-distortion trad-off was found in [], rspctivly. In [3], transmission from a two-antnna usr quipmnt (UE) to two bas stations (BSs) linkd to a cntral procssing unit was considrd as a particular CEO problm stup. Th work was basd on distributd Wynr-Ziv comprssion [4], though its optimality could not yt b provd. Th work was xtndd in [5], [6] to th cas of multipl UEs, pointing out that comprssion can trad-off on UE s rat vrsus th othr, and to an arbitrary numbr of BSs with symmtric intr-cll intrfrnc in a circular Wynr modl in [7] [0]. Whil prvious citations considrd th xchang of quantizd rciv signals and cntralizd dcoding, it can b bnficial undr strongly constraind backhaul to us dcntralizd dcoding

3 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS whr th BSs xchang dcodd data bits [] [3], or quantizations of transmit squncs [3], [4] for (partial) intrfrnc subtraction. Th bnfit of adapting btwn diffrnt coopration stratgis dpnding on th channl ralization has bn pointd out in [], [5]. Concrt CoMP algorithms hav bn proposd using cntralizd [6], [7] or dcntralizd dcoding [8], [9], whr th lattr schms involv an itrativ xchang of liklihood information on transmittd bits. Considring th ovrall rat/backhaul trad-off, howvr, itrativ schms ar only marginally suprior to singl-shot coopration [7], [30]. In gnral, ach BS may only xchang information connctd to its own UEs [3], or also that on intrfring UEs [3], and th rat/backhaul trad-off strongly dpnds on th quantization approach [33]. A diffrnt prspctiv on backhaul-constraind uplink CoMP is to s th stting as an intrfrnc channl (IC) with partial rcivr-sid coopration [34], distinguishing btwn gains in dgrs of frdom [35] and in powr. Howvr, th citd work also considrs scnarios of strong intrfrnc (acc. to [35]) that ar unlikly to occur in th contxt of cllular systms, as th assignmnt of UEs to BSs would simply b swappd on a rasonabl tim basis, and xcluds th important option of cntralizd multi-usr dcoding. Considring th aspct of imprfct CSI, first information thortical stps concrning th impact on singl-input singl-output (SISO) links wr takn in [36], and xtndd to point-topoint multipl-input multipl-output (MIMO) links in [37]. Th impact on uplink CoMP was studid from a signal procssing prspctiv in [38], [39] and in information thory in []. C. Main Contribution of this Work This work yilds nw conclusions on uplink CoMP in practical systms, providing a framwork incorporating a multitud of information thortic concpts providd by various authors, putting ths in prspctiv with a varity of proposd signal procssing schms. numrical rsults considring both information thortic bounds as wll as practical constraints, and hnc yilding an insight into th valu of sophisticatd signal procssing. rasonably complx modls rflcting intrfrnc scnarios likly to occur in practical cllular systms. Whil ths modls do not nabl closd-form analysis, thy yild mor rlvant conclusions than ovrly simplifid modls as,.g., in [7] [9].

4 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 3 D. Trminology In this work, th trms CoMP and BS coopration rfr to schms whr BSs xchang rcivd signals or information connctd to th data bits of crtain UEs in ordr to improv data rats. Schms that only mak us of coordination btwn BSs, for xampl joint schduling or intrfrnc rjction combining (IRC), ar considrd non-cooprativ. Th trm backhaul infrastructur rfrs to th ovrall connctivity of BSs and th ntwork, whil any backhaul quantity always rfrs to th backhaul capacity rquird by a cooprativ schm in addition to that of a non-cooprativ systm. E. Outlin In Sction II, th transmission modl and basic BS coopration schms ar introducd, innr bounds on capacity rgions undr imprfct CSI for infinit, no, or partial BS coopration ar drivd, and prformanc rgions ar introducd. In Sction III, th ovrall CoMP gain is quantifid for diffrnt scnarios, and th introducd BS coopration schms ar valuatd w.r.t. th achivabl rat/backhaul trad-off. Th valu of BS coopration in conjunction with sourc coding or suprposition coding is discussd, bfor Mont Carlo simulations using a slightly largr stup mphasiz th gain of adaptation btwn diffrnt BS coopration stratgis. In Sction IV, parallls ar drawn btwn th analyzd thortical concpts and proposd practical algorithms, and th valu of itrativ BS coopration and othr practical aspcts ar discussd. Th work is concludd in Sction V. II. SYSTEM MODEL AND BASICS A. Transmission Modl W considr an uplink transmission from K UEs to M BSs, as shown in Fig., and dnot th sts of UEs and BSs as K = {..K} and M = {..M}, rspctivly. W assum that ach UE has N u = transmit antnna, as this is th configuration in th rcntly compltd standard LTE Rlas 8 [40]. Th BSs can b quippd with any numbr N bs of rciv antnnas ach. W assum that transmission taks plac ovr a frquncy-flat channl, whr all ntitis ar prfctly synchronizd in tim and frquncy. Each UE k K has a st F k of discrt mssags which it maps onto a st X k of Gaussian unit powr transmit squncs of lngth N sym symbols,

5 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 4 using an ncoding function ( ). W dnot all mssags of all UEs as F all = F F F K, and all transmit squncs as X all = X X X K. Th ovrall transmission from all UEs to th BSs in on singl channl accss t N sym is givn as y [t] = Hs [t] +n [t], () whr y [t] = [y [t],..y [t],n bs,y [t],..y [t],n bs,,y [t] M,..y[t] M,N bs ] T C [N BS ] ar th signals rcivd at th BSs, and th channl matrix is givn as H = [h h h K ] C [N BS K], whr ach column h k is connctd to UE k. Th channl is assumd to b block-fading, whr ach lmnt is takn from an indpndnt, zro-man Gaussian distribution h i,j N C (0,E{ h i,j }). s [t] C [K ] ar th symbols transmittd from th UEs, which ar givn as k K : s [t] k = F F k ρf [(F)] [t], () whr ρ F R + 0 is th transmit powr assignd to mssag F. W us P = {ρ F : F F all } to captur th ovrall powr allocation. According to (), ach UE k transmits a wightd suprposition of squncs in st X k. n [t] = [n [t],..n [t],n bs,n [t],..n [t],n bs,,n [t] M,..n[t] M,N bs ] T C [N BS ] is additiv Gaussian nois at th rcivr sid with covarianc E t {n [t] (n [t] ) H } = σ I. W stat th covarianc of th transmittd signals as E t {s [t] (s [t] ) H } = P = diag(p) with p R +[K ] 0, whr ach lmnt p k corrsponds to th ovrall transmit powr (ovr all transmittd squncs) of UE k, and assum that th transmit powrs ar subjct to th powr constraint P max P 0. Hnc, ach UE has an individual powr constraint dfind by th ntris of th diagonal matrix P max = diag(p max ) with p max R +[K ] 0. Th transmit covarianc connctd to only a subst of mssags F F all is dnotd as P(F), whr th diagonal lmnts ar givn as [P(F)] k,k = ρ F. (3) W also us k K : S k = {s [] k..s[nsym] k F (F k F) } as th suprposition of all squncs transmittd by UE k, m M : Y m as th squnc of all symbols rcivd at all antnnas of BS m, and m M, a N bs : N m,a as th nois squnc rcivd by BS m at antnna a. As indicatd in Fig., th BSs ar assumd to b connctd through a msh of rror-fr out-of-band backhaul links, whr w dnot as β R + 0 th sum backhaul capacity rquird in addition to that of a non-cooprativ systm. Not that in our stup, it is sufficint if a UE can b dcodd by any involvd BS, which thn forwards th dcodd bits to th ntwork, circumvnting cass of strong intrfrnc [35]. Th symbol indx t is omittd in th squl for brvity.

6 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 5 B. Modling of Imprfct Channl Knowldg To incorporat th impact of imprfct (rcivr-sid) CSI into our modl, w assum that all BSs hav th sam knowldg of th compound channl stimat Ĥ = H+E, (4) with Ĥ C[N BS K], whr th rror trm E C [N BS K] is a random variabl of covarianc E { vc(e)vc(e) H} = σ pilots I = σe I. (5) N p p pilots Th stimatd channl Ĥ and rror E ar assumd to hav multipl indpndnt ralizations pr block ofn sym symbols (du to multipl pilots pr block). Equation (5) is basd on th Kramr-Rao lowr bound [4], yilding th absolut stimation rror varianc, if optimal channl stimation has bn prformd basd on N p pilots of powr p pilots, subjct to Gaussian nois with varianc σ pilots. Not that σ pilots can diffr from σ if multi-cll (quasi-)orthogonal pilot squncs ar mployd. In th squl, w assum unit-powr pilots (p pilots = ), and choos N p =, which has bn motivatd through th obsrvation of a concrt channl stimation schm in a frquncyslctiv OFDMA systm for a channl of avrag cohrnc tim and bandwidth in [4]. Lt us now stat th following thorm: Thorm (Modifid transmission quation undr imprfct CSI): An innr bound for th capacity rgion (considring avrag rats ovr many stimation rrors) of th transmission in () undr imprfct CSI can b found by obsrving th capacity rgion connctd to th transmission y = H s+v+n, (6) which involvs a powr-rducd ffctiv channl H C [N BS K] with lmnts i,j : h i,j = +σ E h i,j / { (7) E hi,j }, and is subjct to an additional Gaussian nois trm v C [NBS ] with diagonal covarianc E { vv H} (Ē = Φ vv = P(F all ) ( Ē ) ) H, whr i,j : ē i,j = E { h i,j } σ E E { h i,j }, (8) +σe and ( ) sts all off-diagonal valus of th oprand to zro. Proof: Brifly, th thorm is basd on th fact that (6) ovrstimats th dtrimntal impact of imprfct CSI by assuming v to b a Gaussian random variabl with a diffrnt ralization in ach channl us. Th proof is statd in th Appndix.

7 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 6 Not that our modl of th channl stimat in (4) dviats from that in,.g., [37], whr th authors start with th assumption of an unbiasd minimum man squar rror (MMSE) channl stimat which is uncorrlatd from its stimation rror. Both modls, howvr, lad to Thorm, whil th modl considrd in this work has th advantag that σ E is givn as an absolut channl stimation nois trm, whr th diffrnt impact on wak or strong links bcoms vidnt in (8). In gnral, th modl implis that σe, as wll as th avrag gain of all links E{ h i,j }, ar known to th rcivr sid. C. Capacity Rgion Undr Infinit BS Coopration If an infinit backhaul infrastructur nabls full coopration btwn all BSs, w ar obsrving a multipl accss channl (MAC). In this contxt, thr is no bnfit of suprimposd mssags [43], hnc w can constrain th usd mssags to k K : F k := {F k }, F all := {F,F,,F K } and P := {ρ F,ρ F,,ρ FK } (9) and stat th following thorm: Thorm (Capacity rgion undr infinit BS coopration): An innr bound for th capacity rgion of th uplink transmission in () undr infinit BS coopration is givn as R = R (P) (0) P : P max P(F all ) 0 whr dnots a convx hull opration, and all rat tupls r R (P) fulfill k K : 0 r k ν Fk and F F all : I+ ( ν F log σ I+Φ vv) H P(F)(H ) H, () F F whr ν F is th rat connctd to mssag F. Proof: Th proof is a straightforward application of [44] to (6) and givn in [45]. Equation () stats that th sum rat of any subst of UEs is limitd by th sum capacity of th channl, assuming that all othr UEs hav alrady bn dcodd and thir signals subtractd from th systm. Not that undr imprfct CSI, a crtain xtnt of nois covariancφ vv rmains, having a dtrimntal impact on any coopration stratgy that will b xplord latr. If th sum rat is to b maximizd and all links hav qual avrag powr, () simplifis to th xprssion drivd for point-to-point MIMO transmission undr imprfct CSI in [37].

8 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 7 D. Capacity Rgion without BS Coopration Without BS coopration, our scnario is similar to a Gaussian IC, whr th capacity is known only for crtain intrfrnc cass. Th tightst known innr bound [46] is basd on suprposition coding (SPC), whr common mssags ar dcodd individually by multipl rcivrs. Our stup diffrs in th way that w can swap th assignmnt of UEs to BSs, or lt BSs dcod multipl UEs, such that scnarios of strong intrfrnc [35] ar avoidd. This rducs th rang of scnarios for which common mssag concpts ar known to b bnficial, and th incrasd background nois lvl du to imprfct CSI rndrs ths vn lss attractiv. As SPC in gnral suffrs from signal-to-nois ratio (SNR) gaps inhrnt in practical coding schms, and rquirs UE modifications in conjunction with mor complx signaling, w again constrain ourslvs to on mssag pr UE as in (9). Trm a {..M} [K ] capturs BS-UE assignmnt, i.. dnots th BS whr ach UE is dcodd at, and w introduc m M : F [m] (a) = {F k F all : a k = m} and F [m] (a) = {F k F all : a k m} () as th sts of mssags dcodd or not dcodd by BS m, rspctivly. W now stat: Thorm 3 (Innr bound on th capacity rgion without BS coopration): An innr bound of th capacity rgion of th transmission in () without BS coopration is givn as R 0 = a,p : P(F all ) P maxr 0(a,P), (3) whr all rat tupls r R 0 (a,p) fulfill k K : 0 r k ν Fk and m M : F F [m] (a) : I+ ( ) ν F log Φ ii H m m P(F )(H m) H F F with Φ ii m = σ I+ }{{} Φ vv +H mp ( F[m] (a) ) (H m) H, (4) }{{} Impact of imp. CSI Intrfrnc whr H m and Ē m dnot ffctiv channl and part of Ē from (8), rsp., connctd to BS m. Proof: Th thorm is a straightforward xtnsion of th work in [46] to th transmission in (6) with an arbitrary numbr of communication paths but a singl mssag pr UE. Not that th non-cooprativ capacity rgion from Thorm 3 implicitly maks us of IRC, as (4) xploits th spatial structur of intrfrnc. W will latr also obsrv th prformanc of frquncy division multiplx (FDM), whr th UEs focus thir transmit powr on orthogonal rsourcs, and hnc intrfrnc is avoidd. As such schms play a minor rol in th contxt of CoMP, howvr, corrsponding capacity xprssions ar omittd.

9 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 8 E. Bas Station Coopration Schms For Finit Backhaul W invstigat four BS coopration schms, constraind to scnarios with M = K = for clarity. Th schms ar initially considrd with only on phas of information xchang btwn BSs, but th bnfit of itrativ BS coopration will b discussd in Sction IV-A. ) Distributd Intrfrnc Subtraction (DIS) []: This concpt is oftn parallld to dcodand-forward in rlaying: On BS dcods (part of) on UE s transmission and forwards th dcodd data to th othr BS, in th CoMP cas for (partial) intrfrnc cancllation. For a particular BS-UE assignmnt a = [,] T and coopration dirction b = as shown in Fig. 3(a), lt us assum UE transmits mssags F and F, mappd onto squncs X and X. Both mssags ar dcodd by BS, aftr which mssag F is forwardd to BS. As th signals rcivd by both BSs ar corrlatd, w considr comprssing th dcodd bits via Slpian-Wolf sourc coding [47] at BS, bfor forwarding w(f ). At BS, mssag F is rconstructd with Y as sid-information (if sourc coding was applid), and mssag F is dcodd basd on th intrfrnc-rducd rciv signals Ỹ = Y Ĥ ρf (F ). Thorm 4 (Innr bound on DIS capacity rgion): An innr bound on th capacity rgion of a DIS stup (with any assignmnt a and coopration dirction b) undr backhaul β is givn as R dis (β) = a,b,p : P max P(F all ) 0 Rdis (β,a,b,p), (5) whr all r R dis (β,a = [,] T,b =,P) fulfill k {,} : r k 0, r ν F +ν F and ( ν F log I+ σ I+Φ vv +H P( F) (H ) H) H P ( F) (H ) H (6) ν F ν F log I+ ( β + log I+ r log I+ ( σ I+Φ vv +H P ({ F,F σ I+Φ vv +H P({ F,F }) (H ) H) H P ( ) F (H ) H (7) }) (H ) H) H P ( ) F (H ) H } {{ } =0 without Slpian-Wolf sourc coding (8) ( σ I+Φ vv +H P ( F ) (H ) H) H P ( F ) (H ) H, (9) whr Φ vv and Φ vv ar th submatrics of Φ vv in (8) connctd to BSs and, rspctivly. Proof: Th rat of of mssag F is constraind on on hand in (7) as it has to b dcodd by BS (intrfrd by mssags F and F ), and on th othr hand in (8) by th rat of th backhaul plus th rat at which it could b dcodd by BS without coopration. Mssag F can thn b dcodd fr of intrfrnc from mssag F (s Eq. (9)).

10 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 9 Not that th dcoding ordr at th forwarding BS is important, i.. th forwardd mssag has to b dcodd first such that its rat is low w.r.t. th lvl of intrfrnc it rprsnts. ) Comprssd Intrfrnc Forwarding (CIF) [3], [4]: This schm is similar to DIS in th way that both BSs dcod thir UE individually, whil on BS offrs th othr a crtain xtnt of intrfrnc subtraction. Hr, howvr, th BSs xchang quantizd transmit squncs. Using CIF, th rat/backhaul opration point can b adjustd through choosing an appropriat dgr of quantization, rathr than using SPC. Lt us again fix th assignmnt a = [,] T and coopration dirction b = as in Fig. 3(b), and obsrv th cas whr BS dcods mssag F, calculats th originally transmittd squnc X = (F ) and forwards a quantizd vrsion q(x ) to BS. W optionally considr that a sourc-ncodd vrsion w(q(x )) is forwardd, xploiting sidinformation at BS. Th lattr BS thn rconstructs q(x ) and computs an intrfrnc-rducd vrsion of its rcivd signalsỹ = Y Ĥ ρf q(x ), from which mssagf can b dcodd. Thorm 5 (Innr bound on CIF capacity rgion): An innr bound on th capacity rgion of a CIF stup (with any assignmnt a and coopration dirction b) undr backhaul β is givn as R cif (β) = a,b,p : P max P(F all ) 0 Rcif (β,a,b,p), (0) whr all rats r R cif (β,a = [,] T,b =,P) fulfill k {,} : r k 0 and ( r log I+ σ I+Φ vv +H P ( F) (H ) H) H P ( F) (H ) H () with κ = E { ( ) } x x H Y = r log I+ ρ F max( β,) ξ F } {{ } Pract. quantizr ( σ I+Φ vv +h, ξ ( ) ) F h H H, P ( ) F (H ) H () or ξ F ρ F β }{{} rat-distortion thory or ξ F ρ F κ (3) } {{ β +κ } rat-dist. th. and sourc coding (+ρ F ( h, ) H ( σ I+Φ vv +h P ( F ) (h ) H) h, ),(4) and whr h m,k C[N bs ] is th ffctiv channl btwn BS m and UE k. Proof: Equation () bounds th achivabl rats of mssag F intrfrd by mssag F, whil () bounds th rat of mssag F that is subjct to a rsidual xtnt of intrfrnc from mssag F, dpnding on th quantization nois powr ξ F R+ 0. Equation (3) givs xactly this quantity as a function of backhaul β, whr w distinguish btwn th cass of a practical quantizr as givn in [48] or opration on th rat-distortion bound [43], without or with sourc

11 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 0 coding [49]. For th lattr cas, (4) dnots th varianc of th symbols in X conditiond on th signals Y rcivd by BS. 3) Distributd Antnna Systm - Dcntralizd Dcoding (DAS-D) [50]: In a third coopration schm basd on dcntralizd dcoding, th BSs xchang quantizd rciv signals rathr than dcodd bits or transmit squncs. For a particular assignmnt a = [,] T as shown in Fig. 3(c), w assum th UEs transmit mssags F and F, rspctivly, mappd onto squncs X and X. Both BSs now crat quantizd vrsions q(y ), q(y ) of thir rcivd signals, and forward ths ovr th backhaul. Optionally, sourc coding can b applid, such that w(q(y )), w(q(y )) ar xchangd. Both BSs thn us this information and thir rcivd signals to rconstruct q(y ), q(y ), and thn dcod mssags F, F, rspctivly. Thorm 6 (Innr bound on DAS-D capacity rgion): An innr bound on th capacity rgion of DAS-D (for any BS-UE assignmnt a) undr sum backhaul β is givn as R dasd (β) = a,p : P max P(F all ) 0 Rdasd (β,a,p), (5) whr all rats r R dasd (β,a = [,] T,P) fulfill k {,} : r k 0 and ( r log I+ H P ( [ ] ) F) (H ) H Φ vv +σ I H P ( F) (H ) H (6) with r log I+ ( H P ( [ F) (H ) H + 0 Φ qq Φ qq log I+(Φ qq m ) (Φ yy m ) +MNbs β m= } {{ } Prformanc of a practical quantizr ] ) +Φ vv +σ I H P ( F) (H ) H, (7) or log I+(Φ qq m ) Ψ m β m= } {{ } Rat-dist. th. (opt. sourc coding) whrψ m is ithr th rciv signal covarianc at BSm, i..ψ m := Φ yy m = H m P(F all)(h m )H + Φ vv m +σ I, or th rciv signal covarianc conditiond on th signals rcivd by th othr BS (if w considr sourc coding), i.. Ψ m := Φ yy m m with m {,},m m : [5], [6] ( Φ yy m m = H m I+P(F all )(H ( m )H Φ vv m +σ I ) ) P(Fall H m )(H m )H +Φ vv m +σ I (9) Proof: Th mssag rats ar constraind in (6) and (7) du to intrfrnc and quantization nois on th antnnas of th corrsponding rmot BS. Th quantization nois covariancs ar limitd through (8), whr w again considr a practical schm quantizing ach dimnsion sparatly (losing on bit to th rat-distortion bound in ach ral dimnsion) [48], opration on th rat-distortion bound [43], or th lattr including sourc coding [5], [6]. (8)

12 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Invsting diffrnt portions of backhaul into th two coopration dirctions allows trading th rat of on UE against th othr. Th calculation of (wightd sum-rat) optimal quantization nois covariancs for (8) has bn studid in dtail in [5], [6]. 4) Distributd Antnna Systm - Cntralizd Dcoding (DAS-C): W finally considr th cas that both UEs ar dcodd jointly by on of th BSs, and th othr BS is dgradd to a rmot radio had (RRH) that quantizs and forwards rcivd signals, possibly bing oblivious to transmittd codwords [0]. To incorporat various proposd concpts, lt us assum for a fixd a = [,] T and b = that UE transmits mssag F, which is dcodd non-cooprativly by BS. Th UEs furthr transmit mssags F {,} and F {,}, rspctivly, which ar individually dcodd by both BSs, and mssags F and F, rspctivly, which ar jointly dcodd by BS. This modl (s Fig. 3(d)), hnc rflcts th concpt of common mssags, known to b bnficial in th contxt of an IC [46] and for cntralizd dtction [5], and also th concpt of local, non-cooprativ dcoding [7], [0], [5]. BS dcods mssags F, F {,} and F {,}, and subtracts th corrsponding transmit squncs from th rcivd signals to construct ρf Ȳ = Y,( ĥ {,} X {,} + ) ρ F X ĥ, ρ {,} F X {,}. (30) This is thn quantizd to q(ȳ) (and optionally sourc-ncodd to w(q(ȳ))) and forwardd to BS. Th lattr BS also dcods mssags F {,} and F {,}, subtracts thir impact on Y, and uss Y plus th information providd by BS to finally dcod mssags F and F. Thorm 7 (Innr bound on DAS-C capacity rgion): An innr bound on th capacity rgion of DAS-C (for any assignmnt a and coopration dirction b) undr backhaul β is givn as R dasc (β) = P : P max P(F all ) 0 Rdasc (β,a,b,p), (3) whr all rat tupls r R dasc (β,a = [,] T,b =,P) fulfill k {,} : r k 0 and r = ν F +ν F, F { } F,F,,F, : ν F log I+ F F } : F { F,,F, F F ν F log I+ +ν F and r = ν F, ( H P({ F,F,F ( H P ({ F,F F { } F,F : ν F log F F I+ Φqq 0 ( ) 0 ρ F h, h H, +ν F (3) ) Ψ (33) }) (H ) H +Φ nn }) ) Ψ (H ) H +Φ nn (34) +Φ nn Ψ, (35)

13 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS whr Φ nn = Φ vv +σ I and Ψ = H P(P)(H ) H, and w hav th backhaul constraint log I+(Φ qq ) ( Φyy ) +Nbs β, log I+(Φ qq }{{} ) Φyy β }{{} or log I+(Φ qq ) Φyy β, }{{} Pract. quant. Sourc coding (36) whr Φ yy is th signal covarianc at BS aftr th subtraction of dcodd mssags, and Φ yy is th sam quantity, but conditiond on th signals at BS aftr mssag subtraction. Proof: Eq. (3) stats that th ovrall UE rats ar th sum of th rats of th suprimposd mssags. Eqs. (33) and (34) stat th sum rats of any tupls of mssags dcodd without BS coopration by BSs and, rspctivly, and (35) stats th sum rat bound on th two mssags F and F that ar jointly dcodd by BS. In th lattr quation, w hav to considr not only quantization nois (making th sam diffrntiations w.r.t. quantization as bfor), but also th fact that th signals rcivd at BS ar still subjct to intrfrnc from mssag F, as this mssag is not known to BS. Th backhaul constraint in (36) is basd on [5], [6]. In this work, w also considr FDM scnarios whr th UEs ar srvd on orthogonal rsourcs, but nhancd through th xchang of rcivd signals ovr th backhaul. W will s that ths schms play a minor rol, and hnc omit quations for brvity. F. Prformanc Rgions Th concpt of prformanc rgions was introducd in [] to jointly captur achivabl rat tupls and th corrsponding backhaul rquirmnt. A prformanc point is dfind as Z = r,β, (37) and a prformanc rgion connctd to an arbitrary BS coopration schm yz is dfind as Z yz = { r,β : r R yz (β)}. (38) Not that th convx hull opration in (38) implis th option of tim-sharing along th backhaul dimnsion, whil ach rgion R yz alrady incorporats tim-sharing btwn diffrnt BS-UE assignmnts and coopration dirctions. An xampl prformanc rgion is shown in Fig. for DIS, CIF, DAS-D, DAS-C or FDM (all assuming practical quantization and no SPC) for M = K =, N bs = and H = [, 0.5; 0.5,]. W obsrv imprfct CSI with N p =, and st σ = 0. (SISO SNR of 0 db on th main links). W plot th achivabl UE rats on th

14 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 3 x- and y-axis, and th rquird backhaul on th z-axis. Th top surfac of th prformanc rgion hnc rflcts th capacity rgion in th non-cooprativ cas, whil its intrsction with th x-y plan innr bounds th capacity rgion for infinit BS coopration. Not that th lattr dviats from a pntagon shap [43] du to imprfct CSI. For th xampl channl, FDM schms ar bnficial in th rgim of no or vry limitd backhaul, DIS concpts ar intrsting for modrat backhaul, whras DAS-C is th only schm approaching MAC prformanc for larg backhaul. DAS-D and CIF ar infrior for all xtnts of backhaul and hnc not visibl. A. Scnarios and Channls Considrd III. ANALYSIS OF COOPERATION CONCEPTS In th squl, w ar intrstd in th sum-rat achivabl in a small scnario withm = K = and N bs =, for infinit or no BS coopration, and for th CoMP schms from Sction II-E. W obsrv diffrnt scnarios charactrizd by th location of th UEs, whr for ach UE k a normalizd distanc d k [0,] dnots whthr it is clos to its assignd BS (small d k ), at th cll-dg (d k = 0.5), or closr to th othr BS (d k > 0.5). W us xmplary channl matrics λ, λ, j( ϕ / ϕ /) λ, λ, j(+ϕ / ϕ /) H = with (39) λ, j( ϕ / ϕ /) λ, λ, j(+ϕ / ϕ /) d θ k λ, ( d k ) θ k {,}, m k : λ k,k = d θ k +( d k ) θ, λ m,k = d θ k +( d k ) θ, (40) whr λ m,k is th linar path gain from UE k to BS m, basd on a flat-plan pathloss modl with pathloss xponnt θ = 3.5, is normalizd by th transmit powr of th UEs. W hr assum multi-cll powr control, whr th avrag powr by which a UE is rcivd by both BSs is normalizd to. W can thn us P max = I rgardlss of UE location, and th dominant links ar normalizd to unit gain in th cas of d k = 0. Trms ϕ, ϕ and ϕ in (39) ar phass connctd to th orthogonality of th channls sn by BS or, rspctivly, or th additional orthogonality of th compound channl. Unlss statd othrwis, w obsrv channls of avrag orthogonality, i.. ϕ = ϕ = ϕ = π/, and choos σ = 0., lading with (40) to a cll-cntr SISO SNR of 0 db, which is motivatd through systm lvl simulations in [45].

15 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 4 B. Ovrall CoMP Gain undr Imprfct CSI Lt us first obsrv th gain from no to infinit BS coopration according to th bounds from Sctions II-C and II-D. Fig. 4 shows th achivabl sum-rat of both UEs, whil ths ar simultanously movd from th cll-cntr (d k = 0.) to th cll-dg and slightly byond (d k = 0.6). W obsrv diffrnt xtnts of CSI, with N p {,, }. As intuitiv, th CoMP gain is largst at th cll-dg (for avrag channl orthogonality), and diminishs towards th cll-cntr. In conjunction with multi-cll powr control, CoMP can provid fairly homognous prformanc throughout all scnarios, hnc improv fairnss. Intrstingly, th rlativ gain of CoMP at th cll-dg incrass with dcrasing CSI, whil th opposit is th cas towards th cll-cntr, as shown in Fig. 5. Th formr is du to array gain from which channl stimation can bnfit, whil th lattr is th cas as th wak intrfrnc links bcom difficult to stimat, and hnc cannot b xploitd for CoMP. Fig. 5 also shows rsults for M = K = 3, whr th CoMP gains ar largr, as (for N bs = ) ach BS by itslf cannot spatially sparat all 3 UEs. C. Prformanc of CoMP Schms for Spcific Channls Lt us now analyz th rat/backhaul trad-off achivabl with th CoMP schms from Sction II-E. W obsrv a scnario with d = d = 0.5, hnc a symmtric cll-dg cas, in Fig. 6, and a scnario with d = 0.4 and d = 0., hnc asymmtric and wakr intrfrnc, in Fig. 7. For all schms, w show (from right to lft, i.. from lss to mor fficint) th prformanc basd on a practical quantizr [48] (not applicabl to DIS), that givn by th ratdistortion bound [43], or through additional sourc coding. Th dottd lin shows th cut-st bound [43], rsmbling th cas whr ach backhaul bit lads to an qual sum-rat incras of on bit, until MAC prformanc is rachd. In th cll-dg cas, DAS-C is suprior for any xtnt of backhaul, and sourc coding is highly bnficial, as th corrlation of rcivd signals is strong. Th gap to th cut-st bound is du to th fact that backhaul is invitably wastd into th quantization of nois [5], [6]. Dashd lins indicat th (marginal) bnfit of SPC, which hr can b attributd to th fact that common mssags can b dcodd by th BSs without coopration, rducing th xtnt of signal powr that is quantizd for coopration [50]. In this symmtric cll-dg cas, DIS and CIF yild no gain, as ach BS can dcod both UEs without coopration. DAS-D provids array gain, but is infrior to DAS-C du to its inability to prform intrfrnc cancllation. In th asymmtrical scnario in Fig. 7, DIS and CIF ar suprior in

16 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 5 rgims of low backhaul. Hr, th cll-dg UE is dcodd first (undr littl intrfrnc), and thn th dcodd bits or a quantizd transmit squnc ar providd from BS to BS. It can b shown that DIS with SPC is always suprior to comprssd intrfrnc forwarding (CIF) [45], whil th lattr has practical advantags. Whil gains from sourc coding hav dcrasd du to lss signal corrlation, it is bnficial to us DAS-C with SPC, mor spcifically with th option of local, non-cooprativ dcoding, as pointd out in [7], [8], [0]. Howvr, th prformanc is infrior to that of a simpl tim-shar btwn a dcntralizd and cntralizd approach [45]. Fig. 8 shows th bst coopration schm as a function of d and d, for a fixd backhaul of β = 4 bits pr channl us, summarizing and xtnding prvious obsrvations. DAS-C is clarly suprior in rgims of strong, possibly asymmtric intrfrnc, DIS in rgims of wakr, asymmtric intrfrnc, CIF in rgims of vn wakr intrfrnc, whil DAS-D is only intrsting for vry wak and highly symmtric intrfrnc. Considring that th CoMP gain in th lattr rgims is marginal, it appars sufficint to adapt btwn DAS-C and DIS. Th hashd aras in Fig. 8 indicat whr such adaptation yilds mor than 0% sum-rat bnfit. D. Bnfit of Sourc Coding and Suprposition Coding Fig. 9 shows th sum-rat gain (in %) of using sourc coding and/or SPC for DIS and distributd antnna systm - cntralizd (DAS-C) (taking th maximum gain ovr all rgims of backhaul). As notd bfor, th gain of sourc coding tchniqus can b substantial for cass of strong intrfrnc, but ths lad to a significantly incrasd complxity [5]. A main problm as that such schms rquir th intrfrnc covarianc to rmain constant ovr a rasonabl xtnt of tim, which is qustionabl in a cllular uplink that is typically subjct to a flashlight ffct, i.. to quickly changing background intrfrnc du to schduling. Invsting ffort into SPC is clarly not attractiv, as th rat incras or improvmnt of quantization fficincy through common mssags is marginal. Furthr, th gain of partial local dcoding is marginal for distributd intrfrnc subtraction (DIS), or can b suprcdd by simpl tim-sharing btwn diffrnt coopration stratgis for DAS-C. E. Mont Carlo Simulation Rsults for M = K = 3 W now provid Mont Carlo simulation rsults for a scnario with M = K = 3. Hr, avrag path gains ar gnratd from (40) for d =d =d 3 =0.5 and d =d =d 3 =0.3, and thn many

17 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 6 Rayligh fading ralizations ar gnratd that fulfill E{ h (m )+,k } = E{ h m,k } = λ m,k, providing diffrnt channl orthogonalitis. W compar th following schms: Non-cooprativ dtction mploying maximum ratio combining (MRC) Non-cooprativ dtction basd on IRC Non-coop. dtction with IRC and arbitrary BS-UE assignmnt (s Sction II-D) Only DIS concpts, only DAS-C concpts, or hybrid combinations, as modld in [] All BSs quantiz and forward to a cntral ntwork ntity [8], [9], dnotd DAS-N Backhaul-nhancd FDM, as mntiond at th nd of Sction II-E W again considr both information thortical limits with or without sourc coding, and prformanc basd on practical quantization. In Fig. 0, for th cll-dg cas, w can s that IRC is alrady substantially bnficial ovr MRC, and an instantanous BS-UE assignmnt furthr improvs non-cooprativ prformanc. For coopration, pur DAS-C stratgis appar bst, vn undr practical quantization. FDM is strongly infrior, as th avoidanc of intrfrnc is infficint whn backhaul is availabl, and DAS-N has th disadvantag of prforming quantization ovr on mor link than schms basd on cntralizd dcoding by a BS. In Fig., in th cll-cntr cas, w can s a significant bnfit of adapting btwn DAS-C and DIS, spcially for practical quantization schms. Undr such adaptation, about 50% of CoMP gain can b achivd with about.5 bits of backhaul pr bit of sum-rat. IV. PRACTICAL CONSIDERATIONS A. Parallls btwn Thory and Practic, and th Valu of Itrativ BS Coopration Th prvious sction has rvald a cntral trad-off inhrnt to uplink CoMP: If BSs oprat cod-awar, hnc prform (partial) dcoding prior to coopration, any backhaul-usag is mor fficint (s rsults for DIS and CIF), but th schms fail to achiv MAC prformanc in rgims of larg backhaul. If BSs ar oblivious to th usd codword, backhaul is wastd into th quantization of nois, but th schms (i.. DAS-C) asymptotically obtain th complt CoMP gain. Proposd practical algorithms typically prform a combination of both stratgis. In,.g., [3] [33], ach BS (partially) dcods both th strongst intrfrr and its own UE, and forwards soft-bits to th othr BS. Hnc, cod-awarnss is usd to xploit th structur in signals and

18 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 7 intrfrnc for fficint backhaul usag, whil th soft-bits inhrit information on uncrtainty, which yilds array and divrsity gain. Th fact that trminal rats ar strongly constraind through th first (partial) dcoding procss can b allviatd by using itrativ BS coopration [8], [9], [34], hnc starting with coars dcoding and rfining this in ach itration. It has bn shown in [30], [45], howvr, that for th cas of itrativ DIS and vn undr vry thortical considrations, th rat/backhaul trad-off is only marginally improvd ovr on-shot coopration (though th asymptotic sum-rat is improvd). In practic, vry backhaul usag will always inhrit additional rdundancy (and introduc latncy), hnc rndring itrativ schms vn mor qustionabl, as also obsrvd in [7]. B. CSI Distribution and Complxity Issus Tabl I summarizs ky aspcts of th CoMP concpts tratd in this work, and adds considrations connctd to th rquird distribution of CSI and complxity. DIS and CIF, for xampl, hav th advantag that ach BS only rquirs local CSI connctd to thir sub-part of th channl, whil DAS-C rquirs knowldg on th compound channl at th dcoding BS, hnc rquiring th distribution of CSI ovr th backhaul. In trms of complxity, CIF offrs th bnfit that it dos not rquir r-modulation by a BS that prforms (partial) intrfrnc subtraction. Complxity incrass drastically if sourc coding (Wynr-Ziv, Slpian-Wolf) is prformd. V. CONCLUSIONS Diffrnt thortical uplink CoMP concpts hav bn analyzd with a spcial focus on a constraind backhaul infrastructur and imprfct CSI. Th work has shown that strongst CoMP gains can b xpctd at th cll-dg, and in fact incras for diminishing CSI, whras gains quickly vanish towards th cll-cntr. This rducs th st of attractiv CoMP concpts to DAS- C, intrsting in rgims of strong intrfrnc and basd on oblivious BSs, and DIS, basd on local dcoding and an xchang of dcodd bits, whr adaptation has shown to b bnficial. Various proposd concpts basd on SPC hav shown to b of minor intrst, whil sourc coding appars attractiv, but has to b put in prspctiv to major implmntation challngs. A comparison of ths thortical concpts to proposd practical algorithms has shown th fundamntal trad-off btwn fficint backhaul usag and maximum CoMP gain that has to b mad, and put th practical usag of itrativ BS coopration into qustion.

19 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 8 APPENDIX W hr sktch th proof of Thorm, providing dtails in [45]. Eqs. () and (4) yild ) y = Hs+n = (Ĥ E (Ĥ ) s+n = E s+n, (4) whr Ĥ is an unbiasd channl stimat, and E is an uncorrlatd stimation rror with i,j : ĥ i,j = ĥ i,j / { +σ E E hi,j } and E{ i,j } =E { i,j } ĥ i,j = E{ h i,j } σ E E { h i,j }. (4) +σe Trating product E s in (4) as a Gaussian random variabl with a diffrnt ralization in ach channl accss lads to an ovrstimation of th impact of imp. CSI [37], i.. w can stat { (S;Y Ĥ )} E E I log I+ ( Φ vv +σ I ) ) Ĥ H P (Ĥ. (43) In this work, w ar intrstd in obsrving th rats achivabl with a fixd channl H, avragd ovr many channl stimation ralizations Ĥ, which w can approximat by { (S;Y Ĥ )} I+ ( I (S;Y) EĤ I log Φ vv +σ I ) H P(H ) H. (44) withh givn in (7). Clarly, th RHS of (44) is largr or qual to (43) du to Jnsn s inquality, but numrical valuation has shown that this aspct is ngligibl unlss nois powr and channl powr ar of th sam ordr, spcially in considration of th nois ovrstimation in (43). REFERENCES [] P. Marsch and G. Fttwis, On Uplink Ntwork MIMO undr a Constraind Backhaul and Imprfct Channl Knowldg, in Proc. of th IEEE Int. Conf. on Comm. (ICC 09), Jun 009. [] P. Gupta and P. Kumar, Th capacity of wirlss ntworks, IEEE Trans. Inf. Thory, vol. 46, no., pp , 000. [3] P. Bair, M. Murr, T.Wbr, and H. Trogr, Joint Transmission (JT), an altrnativ rational for th downlink of Tim Division CDMA using multi-lmnt transmit antnnas, in Proc. ISSSTA 00, Spt. 000, pp. 5. [4] S. Shamai and B. Zaidl, Enhancing th cllular downlink capacity via co-procssing at th transmittr nd, Proc. of th IEEE Smiannual Vhicular Tchnology Confrnc (VTC 0 Spring), pp , 00. [5] S. Parkvall and D. Astly, Th Evolution of LTE towards IMT-Advancd, Journal of Comm., vol. 4, no. 3, 009. [6] A. Sklavos, T. Wbr, E. Costa, H. Haas, and E. Schulz, Joint Dtction in multi-antnna and multi-usr OFDM systms, Multi-Carrir Sprad Spctrum and Rlatd Topics, pp. 9 98, 00. [7] S. Shamai, O. Somkh, and B. Zaidl, Multi-cll communications: An information thortic prspctiv, in Proc. of th Joint Workshop on Communications and Coding (JWCC04), Oct [8] J. Andrws, Intrfrnc cancllation for cllular systms: A contmporary ovrviw, IEEE Transactions on Wirlss Communications, vol., no., pp. 9 9, 005.

20 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 9 [9] P. Marsch, S. Khattak, and G. Fttwis, A framwork for dtrmining ralistic capacity bounds for distributd antnna systms, in Proc. of th IEEE Information Thory Workshop (ITW 06), Oct [0] P. Marsch and G. Fttwis, A Framwork for Optimizing th Uplink Prformanc of Distributd Antnna Systms undr a Constraind Backhaul, in Proc. of th IEEE Int. Conf. on Comm. (ICC 07), Jun 007, pp [] H. Viswanathan and T. Brgr, Th quadratic Gaussian CEO problm, IEEE Trans. Inf. Thory, vol. 43, no. 5, pp , Spt [] Y. Oohama, Th rat-distortion function for th quadratic Gaussian CEO problm, IEEE Transactions on Information Thory, vol. 44, no. 3, pp , May 998. [3] A. Sandrovich, S. Shamai, Y. Stinbrg, and G. Kramr, Communication via dcntralizd procssing, Proc. of th IEEE Int. Symp. on Information Thory (ISIT 05), pp. 0 05, Spt 005. [4] M. Gastpar, Th wynr-ziv problm with multipl sourcs, IEEE Trans. Inf. Th., vol. 50, no., pp , 004. [5] A. dl Coso and S. Simons, Distributd comprssion for th uplink channl of a coordinatd cllular ntworkwith a backhaul constraint, in Proc. 9th IEEE Ws. on Sign. Proc. Adv. in Wirl. Comm. (SPAWC 08), 008, pp [6] A. dl Coso and S. Simons, Uplink rat rgion of a coordinatd cllular ntwork with distributd comprssion, in Proc. of th IEEE Int. Symp. on Information Thory (ISIT 08), July 008, pp [7] A. Sandrovich, O. Somkh, and S. Shamai, Uplink macro divrsity with limitd backhaul capacity, in Proc. of th IEEE Int. Symp. on Information Thory (ISIT 07), Jun 007. [8] S. Shamai, O. Somkh, O. Simon, A. Sandrovich, B. Zaidl, and V. Poor, Cooprativ Multi-Cll Ntworks: Impact of Limitd-Capacity Backhaul and Intr-Usrs Links, in Proc. Joint Ws. on Comms. and Coding (JWCC 07), Oct [9] S. Shamai, O. Simon, O. Somkh, A. Sandrovich, B. Zaidl, and H. Poor, Information-Thortic Implications of Constraind Coopration in Simpl Cllular Modls, in Proc. PIMRC 08, 008, pp. 5. [0] A. Sandrovich, O. Somkh, H. Poor, and S. Shamai, Uplink macro divrsity of limitd backhaul cllular ntwork, IEEE Trans. on Inf. Thory, vol. 55, pp , 009. [] P. Marsch and G. Fttwis, On th rat rgion of a multi-cll MAC undr backhaul and latncy constraints, in Proc. of th Wirlss Communications and Ntworking Confrnc (WCNC 08), 008. [] O. Simon, O. Somkh, H. Poor, and S. Shamai, Enhancing uplink throughput via local bas station coopration, in Proc. of th Asilomar Confrnc on Signals, Systms and Computrs (ASILOMAR 08), 008. [3], Local bas station coopration via finit-capacity links for th uplink of simpl cllular ntworks, IEEE Transactions on Information Thory, vol. 55, no., pp , 009. [4] M. Grigr, P. Marsch, G. Fttwis, and J. Cioffi, Comprssd Intrfrnc Forwarding: A Nw Schm for Uplink Bas Station Coopration Undr a Capacity Constraind Backhaul Infrastructur, Novmbr 009. [5] P. Marsch and G. Fttwis, On Bas Station Coopration Schms for Uplink Ntwork MIMO undr a Constraind Backhaul, in Proc. of th th Int. Symp. on Wirlss Prsonal Multimdia Communications (WPMC 08), Spt [6] S. Khattak, W. Rav, and G. Fttwis, Multiusr turbo dtction in a distributd antnna systm, in Proc. of th 5th IST Wirlss and Mobil Communications summit (IST 06), Jun 006. [7] T. Mayr, H. Jnkac, and J. Hagnaur, Turbo bas-station coopration for intrcll intrfrnc cancllation, in IEEE Int. Conf. on Comm. (ICC 06), vol., 006. [8] S. Bavarian and J. Cavrs, Rducd Complxity Distributd Bas Station Procssing in th Uplink of Cllular Ntworks, in IEEE Global Tlcommunications Confrnc (GLOBECOM 07), 007, pp

21 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 0 [9] E. Aktas, J. Evans, and S. Hanly, Distributd Dcoding in a Cllular Multipl-Accss Channl, IEEE Transactions on Wirlss Communications, vol. 7, no., pp. 4 50, Jan [30] M. Grigr, P. Marsch, and G. Fttwis, Uplink Bas Station Coopration by Itrativ Distributd Intrfrnc Subtraction, in Proc. of th 0th IEEE Int. Symp. On Prsonal, Indoor and Mobil Radio Communications (PIMRC 09), Spt [3] S. Khattak and G. Fttwis, Distributd itrativ dtction in an intrfrnc limitd cllular ntwork, in Proc. of th 65th IEEE Vhicular Tchnology Confrnc (VTC 07 Spring), 007, pp [3] S. Khattak and G. Fttwis., Low Backhaul Distributd Dtction Stratgis for an Intrfrnc Limitd Uplink Cllular Systm, in Proc. of th 67th IEEE Vhicular Tchnology Confrnc (VTC 08 Spring), May 008. [33] S. Khattak, W. Rav, and G. Fttwis, Distributd itrativ multiusr dtction through bas station coopration, EURASIP Journal on Wirlss Communications and Ntworking, vol. 008, p. 3, 008. [34] I.-H. Wang and D. Ts, Intrfrnc Mitigation Through Limitd Rcivr Coopration: Symmtric Cas, Imprint, 009. [35] R. Etkin, D. Ts, and W. H., Gaussian intrfrnc channl capacity to within on bit, CoRR, 007. [36] M. Mdard, Th ffct upon channl capacity in wirlss communications of prfct and imprfct knowldg of th channl, IEEE Transactions on Information Thory, vol. 46, no. 3, pp , May 000. [37] T. Yoo and A. Goldsmith, Capacity and powr allocation for fading MIMO channls with channl stimation rror, IEEE Transactions on Information Thory, vol. 5, no. 5, pp. 03 4, 006. [38] M. Murr and T. Wbr, Imprfct channl knowldg: An insurmountabl barrir in Rx orintd multi-usr MIMO transmission? in Proc. of th 5th Int. ITG Confrnc on Sourc and Channl Coding (SCC 04), 004. [39] T. Wbr, A. Sklavos, and M. Murr, Imprfct channl-stat information in MIMO transmission, IEEE Transactions on Communications, vol. 54, no. 3, pp , March 006. [40] W. McCoy, Ovrviw of 3GPP LTE Physical Layr: Whit Papr by Dr. Ws McCoy, Whit Papr, 007. [4] S. Kay, Fundamntals of statistical signal procssing: stimation thory, 993, vol.. [4] P. Marsch, P. Rost, and G. Fttwis, Application Drivn Joint Uplink-Downlink Optimization, in ITG/IEEE Workshop on Smart Antnnas (WSA 0), Fbruary 00. [43] T. Covr and J. Thomas, Elmnts of Information Thory. Wily-Intrscinc Nw York, 006. [44] E. Tlatar, Capacity of multi-antnna Gaussian channls, Europan Trans. Tlcomms., vol. 0, no. 6, pp , 999. [45] P. Marsch, Coordinatd Multi-Point undr a Constraind Backhaul and Imprfct Channl Knowldg, 00, ph.d. thsis. [46] T. Han and K. Kobayashi, A nw achivabl rat rgion for th intrfrnc channl, IEEE Transactions on Information Thory, vol. 7, no., pp , Jan. 98. [47] D. Slpian and J. Wolf, Noislss coding of corrlatd information sourcs, IEEE Trans. Inf. Th., vol. 9, no. 4, pp , July 973. [48] Y. Lind, A. Buzo, and R. Gray, An Algorithm for Vctor Quantizr Dsign, IEEE Trans. Comms., vol. 8, 980. [49] A. Wynr and J. Ziv, Th rat-distortion function for sourc coding with sid information at th dcodr, IEEE Transactions on Information Thory, vol., no., pp. 0, Jan [50] P. Marsch and G. Fttwis, On Backhaul-Constraind Multi-Cll Cooprativ Dtction basd on Suprposition Coding, in Proc. of th IEEE Int. Symp. On Prsonal, Indoor And Mobil Radio Communications (PIMRC 08), Spt [5] A. Sandrovich, S. Shamai, Y. Stinbrg, M. Baldi, T. Fillr, J. Fridrich, D. Krotov, W. Zhang, U. Mitra, A. Lakus-Bckr, t al., Distributd MIMO rcivr-achivabl rats and uppr bounds, IEEE Trans. on Inf. Thory, 007. [5] Z. Xiong, A. Livris, and S. Chng, Distributd sourc coding for snsor ntworks, IEEE Signal Procssing Magazin, vol., no. 5, pp , 004.

22 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Ntwork Backhaul infrastructur BasB stationb BasB stationb Bas B station BM y, y,nbs y, y,nbs y M, y M,Nbs n, n,nbs n, n,nbs n M, n M,Nbs Channl h h h K s s s K UE UE UE K Figur. Uplink transmission considrd in this work. DIS DAS-C FDM backhaul [bpcu] r [bpcu] r [bpcu] Figur. Illustration of a prformanc rgion for an xampl channl with M = K = and N bs =.

23 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Ntwork Ntwork F, F F F or w ( F ) BBSB BBSB Y Y N, N, N, N, F F q ( X ) ( ( )) or w q X BBSB BBSB Y Y N, N, N, N, S S S S F UE F UE F F UE UE F (a) DIS: On BS forwards a dcodd mssag to th othr BS for (partial) intrfrnc subtraction. (b) CIF: On BS forwards quantizd transmit squncs to th othr BS for (partial) intrfrnc subtraction. Ntwork Ntwork F F F F,,F, F,,F q(y ) or w(q(y )) BBSB BBSB q(y ) or w(q(y )) Y Y N, N, N, N, q ( Ȳ ) or w ( q (Ȳ )) BBSB BBSB Y Y N, N, N, N, S S F UE UE F F, F, S S UE UE F F, F (c) DAS-D: Both BSs simult. xchang quantizd rciv signals, but dcod UEs locally. (d) DAS-C: On BS forwards quant. rciv signals to th othr BS for joint UE dcoding. Figur 3. Uplink CoMP schms for M = K = analyzd in this work.

24 SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 3 UPLINK DIS CIF DAS-D DAS-C Dcoding dcntralizd cntralizd Exchangd dcodd quantizd quantizd signals mssags squncs rciv signals Achivabl SIC gain partial array + array + gains (intrfrnc intrfrnc spat. mult. spat. mult. + cancllation) cancllation gain SIC gain wak, asymm. vry wak, vry wak, strong Suitabl in intrfrnc asymm. intrf. symm. intrf. intrfrnc scnarios low backh. low backh. low backh. larg backh. high SNR high SNR low SNR low SNR Sourc provid littl provid littl gain, major potntial coding gain, but possibl and ar highly qustionabl gains, concpts if intrfrnc from implmntation but highly is also dcodd point of viw qustionabl Channl local knowldg from global CSI global CSI knowl. rq. ach BS to all UEs sufficint at all BSs at on BS modrat, if intrf. only nds high, as r-ncoding / SIC low, du to low, as only all UEs ar Complxity (w/o src. coding), simpl signal on UE is succssivly high if dc. of subtraction dcodd or jointly mult. UEs / SIC dcodd + SIC (w/ src. coding) Tabl I COMPARISON OF UPLINK BS COOPERATION SCHEMES, CONSIDERING PRACTICAL ASPECTS.