FUTURE wireless systems will need to provide high data

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL., NO. 1, JANUARY 7 9 Downlnk Performance and Capacty of Dstrbuted Antenna Systems n a Multcell Envronment Wan Cho, Student Member, IEEE, and Jeffrey G. Andrews, Senor Member, IEEE Abstract Dstrbuted antenna systems DAS have been wdely mplemented n state-of-the art cellular communcaton systems to cover dead spots. Recent academc studes have shown that n addton to coverage mprovements, DAS can also have potental advantages such as reduced power and ncreased system capacty n a sngle cell envronment. Ths paper analytcally quantfes downlnk capacty of multcell DAS for two dfferent transmsson strateges: selecton dversty where ust one or two of the dstrbuted antennas are used and blanket transmsson where all antennas n the cell broadcast data. Smple repeaters are a specal case of our analyss. A generalzed nformaton theoretc analyss s provded to llumnate the fundamental lmts of such systems n the cellular context. The results show that DAS reduces other-cell nterference n a multcell envronment and hence sgnfcantly mproves capacty by about x, wth partcularly large mprovements for users near cell boundares. Less obvously, from a communcaton theory standpont, t s shown that selecton dversty s preferable to blanket transmsson n terms of achevable ergodc capacty. For blanket transmsson, we show that the optmal transmsson strategy s ust phase steerng due to the per antenna module power constrants n DAS. Index Terms Capacty, cellular communcatons, dstrbuted antennas systems, other-cell nterference. I. INTRODUCTION FUTURE wreless systems wll need to provde hgh data rates to a large number of users. Experence tells us that these networks wll be nterference-lmted. Multuser recevers are one potental way to reduce nterference n cellular systems see e.g. [1] and the references theren, but ths requres a more complcated recever. An alternatve strategy s to try to reduce the overall transmt power and hence othercell nterference usng dstrbuted antennas, whch has the addtonal mert of provdng better coverage and ncreasng battery lfe []. Although dstrbuted antennas systems DAS were orgnally ntroduced to smply cover the dead spots n ndoor wreless communcatons [], recent studes have dentfed other potental advantages such as reduced power and ncreased system capacty [] [9]. In DAS, antenna modules are geographcally dstrbuted to reduce access dstance nstead of centralzng at a locaton. Each dstrbuted antenna module s connected to a home base staton or central unt va dedcated wres, fber optcs, or an exclusve RF lnk. Although the connectons va the same RF Manuscrpt receved March 1, ; revsed November, and Aprl 1, ; accepted Aprl 1,. The assocate edtor coordnatng the revew of ths letter and approvng t for publcaton was X. Wang. Ths work was supported n part by SOLD Technologes, and the Wllam S. Lvngston Fellowshp at the Unversty of Texas at Austn and has appeared n part n the Proc. of IEEE Wrelesscom, Mau, Hawa, June 1-1,. The authors are wth the Wreless Networkng and Communcatons Group, Department of Electrcal and Computer Engneerng, The Unversty of Texas at Austn, 1 Unversty Staton C8, Austn, TX 7871 USA emal: andrews@ece.utexas.edu; wcho@mal.utexas.edu. Dgtal Obect Identfer.19/TWC /7$. c 7 IEEE lnk as that used n a cell are possble, the connectons wth the same RF lnk construct nformaton-theoretc relay channels categorzed as another research area called cooperatve communcatons [] [1]. Snce the dstrbuted antenna modules and the home base staton together construct a macroscopc multple nput sngle output MISO vector channel, DAS can be also nterpreted as a macroscopc multple-antenna system. Based on potental advantages of DAS, many cellular servce provders or system manufacturers are serously consderng replacng legacy cellular systems wth dstrbuted antenna systems or adoptng the dstrbuted antenna archtecture n the future. However, most of the recent work on DAS has been focused on analyzng ts performance n the uplnk because of ts analytcal smplcty [] [8]. On the other hand, there are few studes on the downlnk performance of DAS although the demand for hgh speed data wll be domnant n the downlnk. There are also few papers that consder the advantages of DAS n a multcell context. A recent paper [9] addressed downlnk performance of code dvson multple access CDMA DAS n a multple cell envronment, but t reled on computer smulatons and only nvestgated SIR levels perceved at moble statons. Computer smulatons are useful but mathematcal analyss enables us to effcently dentfy the key desgn parameters and to understand ther effects. Partcularly, nformaton-theoretc analyss provdes ntuton on achevable system capacty. For ths reason, the authors of [1], [1] analyzed downlnk capacty n terms of multpleantenna MIMO nformaton theory. However, they dd not consder a multcell envronment, ether. In addton, ther analyss was lmted to the case wth specfc assumptons: 1 channel state nformaton s known to the transmtter and to the recever, and transmt power s shared among dstrbuted antenna modules,.e., there s no per antenna module power constrant. In ths context, we analyze the realstc potental gans of downlnk DAS n a multcell envronment. We nvestgate the downlnk advantages of DAS n terms of achevable ergodc capacty for two dfferent transmsson strateges: selecton dversty where ust one or two of the dstrbuted antennas are used and blanket transmsson where all antennas n the cell broadcast the data. Smple repeaters are a specal case of our analyss. The result of ths paper shows that a dstrbuted antenna archtecture effectvely addresses other-cell nterference OCI n a multcell envronment, especally at the cell boundares, and acheves a non-trval capacty ncrease over a conventonal cellular archtecture. II. SYSTEM MODEL A. Cellular Archtecture In DAS, the man processng modules such as channel cards are centralzed at a locaton central unt and are connected

2 7 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL., NO. 1, JANUARY 7 Fg. 1. Structure of a dstrbuted antenna system. W R 1 : Base staton : Remote Anteannas Module RNA W : Example worst case locaton wth dstrbuted antenna modules. Each dstrbuted antenna module s physcally connected wth a home base staton va dedcated wres, fber optcs, or an exclusve RF lnk. A general archtecture of DAS n a multcell envronment s gven n Fg. 1, where a cell s covered by a small base staton and sx dstrbuted antenna modules. In contrast, the same area s covered by only a sngle hgh-power base staton n tradtonal cellular systems. The actual number of dstrbuted antenna modules would be determned by coverage, user denstes, and other envronmental factors but we only consder dstrbuted antenna modules as a reasonable example. The total transmt power of the th dstrbuted antenna module of the th cell s P, where the small base staton of each cell and home cell are ndexed by =and =, respectvely. Throughout ths paper, we assume that = P where P s the total transmt power of the conventonal base staton for a far comparson. The radus of a cell a bold dotted crcle s R and the coverage radus of a dstrbuted antenna module s r. We also consder the 1-ter cellular structure wth unversal frequency reuse, where a gven cell s surrounded by one contnuous ter of sx cells as shown n Fg. 1. Although ths assumpton of only 1-ter of nterferng cells s optmstc, a pessmstc assumpton that all the dstrbuted antenna modules and the base statons are transmttng full power f they are selected for transmsson easly compensates. = P B. Transmsson Strategy and Multple Access Scenaro In cellular DAS, there are several possble transmsson strateges usng multple dstrbuted antenna modules. Although many methods of usng the dstrbuted antenna modules are possble, we consder two lkely transmsson strateges: the blanket transmsson scheme and sngle transmt selecton scheme. The blanket transmsson scheme s to transmt sgnals through all the dstrbuted antenna modules and the home base staton. In ths scheme, the dstrbuted antennas construct a macroscopc multple antenna system. In the sngle transmt selecton scheme, only a sngle dstrbuted antenna module or the home base staton s selected for transmsson by the crteron of mnmzng propagaton pathloss. Although smarter selecton algorthms can potentally be used such as maxmzng SINR or capacty, we consder ths smple one for smplcty of analyss and snce t should mnmze the requred transmt power and hence the nterference caused to other cells. Ths scheme explots macroscopc selecton dversty and s expected to addtonally reduce OCI because the number of OCI sources s reduced. We also assume a sngle user scenaro for smplcty of analyss, but ths assumpton holds for most practcal multuser systems such as tme dvson multple access TDMA, frequency dvson multple access FDMA, orthogonal code dvson multple access CDMA, and orthogonal frequency dvson multple access OFDMA systems. C. Channel Model and Receved Sgnal When the blanket transmsson scheme s used, the multple dstrbuted antenna modules and the home base staton together construct a macroscopc MISO vector channel gven by h =[ h 1 h 1 h ] 1 where h denotes short term fadng from the th dstrbuted antenna module n the th cell and s an..d. complex Gaussan random varable CN, 1. The fadng channel s assumed to be statc durng a symbol duraton. L denotes propagaton pathloss and shadow fadng from the th dstrbuted antenna module n the th cell. Let the transmtted sgnal vector be x =[x x 1 x ]T,wherex s the transmtted sgnal from the th dstrbuted antenna module n the th cell wth E[ x ]=P. Then, the receved sgnal at a moble staton at a gven symbol duraton s gven by y = hx + h L x + n =1 = where n s the addtve Gaussan nose wth varance E[nn H ] = σn. Snce the number of nterferng source s suffcently large and nterferng sources are ndependent of each other, the nterference plus nose s assumed to be a complex Gaussan random varable z wth varance σ z = =1 = L P + σn by the Central Lmt Theorem CLT, whereas the nterference plus nose power of the conventonal cellular system s gven by σc = =1 L P + σn. When the sngle transmt selecton scheme s used, the receved sgnal s gven by y = m h m x m + =1 h q L q x q + n

3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL., NO. 1, JANUARY 7 71 where m =argmax {,1,,} {L,L 1,,L } and q s randomly selected among {, 1,, }. The nterference plus nose s assumed to be a complex Gaussan random varable z 1 wth varance 1 = =1 L q P q + σn. Snce other cells adopt the same transmsson scheme as the home cell, only one of the nterferng sources n the other cell s randomly selected n a sngle transmt selecton scheme. III. ACHIEVABLE CAPACITY OF DISTRIBUTED ANTENNA NETWORKS A. Ergodc Capacty Only Wth CSIR If we assume the channel state nformaton s known only at the recever CSIR and the channel s ergodc, the ergodc Shannon capacty at a gven locaton of the target moble staton can be acheved by [ C e = E h log 1+ 1 ] hsh H where S s the covarance matrx of the transmtted vector x and gven by dagp,p 1,,P. If ergodcty of the channel s assumed, the ergodc capacty can be obtaned as [ ] C e = E h log 1+ 1 σ z = h P = log 1 + γf γ γdγ x= where γ = 1 = h P s a weghted ch-squared dstrbuted random varable wth p.d.f. gven by f γ γ = π exp σ z γ = P P where π = P, k=,k P k P k Then, the ergodc capacty can be obtaned n a smple form by [1] C e = 1 ln π exp = σ z P E σ z P 7 where Ex s the exponental ntegral functon Ex = x et /t dt and can be easly calculated wth popular numercal tools such as MATLAB, MATHEMATICA, and MAPLE. Snce the dervaton for ths MISO vector channel s a generalzaton of a SISO channel, the ergodc capactes of the sngle transmt selecton scheme and the conventonal cellular system are gven, respectvely, by C e,sel = 1 ln exp C e,conv = 1 ln exp σ z1 m P m σ c P E E σ z1 m P m σ c P 8 Fg. shows the ergodc capacty of cellular DAS versus the normalzed dstance from the home base staton n the drecton of the worst case poston W when the pathloss exponent 9 Capacty bts/hz 1 Conventonal cellular system DAS w/ blanket transmsson scheme DAS w/ sngle transmt selecton scheme Normalzed dstance from a home base staton dstance/r Fg.. Ergodc capacty wth CSIR versus the normalzed dstance from the home base staton. s.. The transmt power of each dstrbuted antenna module s.1p and the transmt power of the home base staton s.p n DAS whereas the transmt power of the base staton n the conventonal cellular system s P.Fg. shows an nterestng non-monotonc relatonshp between capacty and the normalzed dstance from the base staton. Ths s because the sgnal from a dstrbuted antenna module becomes domnant around.r. In ths fgure, the sngle transmt selecton scheme acheves the hghest throughput owng to the OCI reducton and macroscopc selecton dversty. Although the acheved throughput of the blanket transmsson scheme n the cellular DAS s slghtly lower than that of conventonal cellular system near the home base staton due to reduced transmt power, the acheved throughput of the blanket transmsson scheme n DAS has substantally hgher throughput beyond the normalzed dstance.. Note that 8% of the users wll be n.r, R assumng a unform dstrbuton, whle the other % have very hgh SINR snce they are close to the home base staton and farther from the nterferng cells. Assumng that the target moble statons are unformly dstrbuted, we can obtan achevable average capacty, whch s plotted versus pathloss exponents n Fg.. When the pathloss exponent s., the capacty of the blanket transmsson scheme and the sngle transmt selecton scheme n cellular DAS are about % and 19% of capacty of conventonal cellular system, respectvely. Ths large mprovement s due to the fact that three tmes more users are outsde of the radus 1/R wthn a cell assumng unform dstrbuton. B. Ergodc Capacty Wth CSIT When channel s known to the transmtter sde, the ergodc Shannon capacty at a gven locaton of the target moble staton can be gven by [17] [ C e = E h max log 1+ 1 ] hsh H S P where S s the th dagonal element of S. The maxmum capacty s acheved by a proper desgn of the transmt power

4 7 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL., NO. 1, JANUARY Conventonal cellular system DAS w/ blanket transmsson scheme DAS w/ sngle transmt selecton scheme 7 Avg. capacty Bps/Hz Capacty bts/hz 1 Conventonal cellular system DAS w/ blanket transmsson scheme DAS w/ sngle transmt selecton scheme 1... Pathloss exponent Normalzed dstance from a home base staton dstance/r Fg.. Average Ergodc capacty wth CSIR versus the pathloss exponent. Fg.. Ergodc capacty wth CSIT versus the normalzed dstance from the home base staton. spectrum matrx S under ndvdual power constrants of the dstrbuted antenna modules and the home base staton. If power cooperaton among the dstrbuted antenna modules and the home base staton s allowable, ths problem reduces to a standard water-fllng problem n a macroscopc MISO vector channel [1], [17] and the maxmum capacty s smply gven by [ C e = E h log 1+ P ] h 11 where P =. We note from 11 that the capacty achevng strategy for DAS wthout per antenna module power constrants s the transmt MRC. However, the per-antenna power constrants make t meanngless to apply the smple water-fllng algorthm. Therefore, we should fnd another soluton nstead of the conventonal water-fllng algorthm. In, the ergodc capacty s maxmzed wth the maxmum value of hsh H because the log functon s a monotonc ncreasng functon wth respect to hsh H. Therefore, the optmal transmt power spectrum matrx S opt s obtaned by solvng the followng optmzaton problem: max S P, = = P h S + ==, h h 1 where h denotes the conugate of h and S s the, entry of the matrx S. It can be easly found that the frst term of the obectve functon 1 s maxmzed by settng the dagonal components of S opt to be dag S opt = P,P 1,,P and hence we should only fnd the optmal values of off-dagonal components. Although there s no explct constrants on off-dagonal components S, they should satsfy S P P for,, because S opt s a covarance matrx. Therefore, the second term of the obectve functon 1 s maxmzed by settng S = P P e hh for,,. As a result, the achevable ergodc capacty wth per antenna module power S constrants s gven by [ C e = E h log = =, = h P h h P P. 1 We can fnd from ths result that the SINR maxmzng transmsson strategy for DAS s phase steerng wth allowable full power transmsson, whereas the best transmsson strategy of DAS wthout per antenna module power constrants s transmt MRC. Ths result also ndcates that DAS wth per antenna module power constrants does not requre any channel ampltude nformaton at the transmtter to explot the advantage of CSIT. Fg. shows the ergodc capacty when channel state nformaton s known to the transmtter, wth the same setup as Fg.. Smlarly to the CSIR case, the sngle transmt selecton scheme acheves the hghest capacty owng to the OCI reducton and macroscopc selecton dversty. Although the acheved capacty of DAS s slghtly lower than or smlar to that of conventonal cellular system near the home base staton due to reduced transmt power, the acheved capacty of DAS has substantally hgher capacty beyond the normalzed dstance.. When the target moble statons are unformly dstrbuted n space, the average Shannon capacty s plotted versus pathloss exponent n Fg.. Ths fgure also shows a smlar trend to the CSIR case. IV. CONCLUSIONS In ths paper, we have analyzed achevable capacty of varous transmsson schemes n cellular DAS from an nformaton theoretc standpont. The results of ths paper suggest that dstrbuted antenna systems effectvely reduce OCI and mprove SINR especally for users near cell boundares, that normally are performance lmtng users, compared to conventonal cellular systems n an nterference-lmted multcell envronment. As a result, dstrbuted antenna systems acheve lower symbol

5 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL., NO. 1, JANUARY 7 7 Avg. capacty Bps/Hz Fg.. Conventonal cellular system DAS w/ blanket transmsson scheme DAS w/ sngle transmt selecton scheme... Pathloss exponent Average Ergodc capacty wth CSIT versus the pathloss exponent. error probablty and hgher capacty than conventonal cellular systems. Based on the results of ths paper, dstrbuted antenna archtectures appear to be an effectve soluton for reducng OCI n an nterference-lmted cellular envronment. REFERENCES [1] J. G. Andrews, Inteference cancellaton for celluar systems: A contemporary overvew, IEEE Wreless Commun. Mag., vol. 1, no., pp. 19 9, Apr.. [] F. Adach, Wreless past and future Evolvng moble communcaton systems, IEICE Trans. Funamentals Elec. Commun., vol. E8-A, no. 1, pp., Jan. 1. [] A. A. M. Saleh, A. J. Rustako, and R. S. Roman, Dstrbuted antennas for ndoor rado communcatons, IEEE Trans. Commun., vol., pp. 1 11, Dec [] M. V. Clark, et al., Dstrbuted versus centralzed antenna arrays n broadband wreless networks, n Proc. IEEE Veh. Technol. Conf., May 1, pp. 7. [] L. Da, S. Zho, and Y. Yao, Capacty analyss n CDMA dstrbuted antenna systems, IEEE Trans. Wreless Commun., vol., no., pp. 1, Nov.. [] W. Roh and A. Paulra, Outage performance of the dstrbuted antenna systems n a composte fadng channel, n Proc. IEEE Veh. Technol. Conf., Sep., pp. 1. [7] A. Obad and H. Yankomeroglu, Reverse-lnk power control n CDMA dstrbuted antenna systems, n Proc. IEEE Wreless Commun. Networkng Conf., Sep., pp [8] R. E. Schuh and M. Sommer, WCDMA coverage and capacty analyss for actve and passve dstrbuted antenna systems, n Proc. IEEE Veh. Technol. Conf., May, pp. 8. [9] R. Hasegawa, M. Shrakabe, R. Esmalzadeh, and M. Nakagawa, Downlnk performance of a CDMA system wth dstrbuted base staton, n Proc. IEEE Veh. Technol. Conf., Oct., pp [] A. Sendonars, E. Erkp, and B. Aazhang, User cooperaton dversty part I and part II, IEEE Trans. Commun., vol. 1, no. 11, pp , Nov.. [11] A. Nosratna, T. Hunter, and A. Hedayat, Cooperatve communcaton n wreless networks, IEEE Commun. Mag., vol., no., pp. 7 8, Oct.. [1] J. N. Laneman and G. W. Wornell, Dstrbuted space-tme coded protocols for explotng cooperatve dversty n wreless networks, IEEE Trans. Inform. Theory, vol. 9, no., pp. 1, Oct.. [1] M. Janan, et al., Coded cooperaton n wreless communcatons: Space-tme transmsson and teratve decodng, IEEE Trans. Sgnal Processng, vol., no., pp. 71, Feb.. [1] L. Xao, L. Da, H. Zhuang, S. Zhou, and Y. Yao, Informaton-theoretc capacty analyss n MIMO dstrbuted antenna systems, n Proc. IEEE Veh. Technol. Conf., Apr., pp [1] H. Zhuang, L. Da, L. Xao, and Y. Yao, Spectral effcency of dstrbuted antenna systems wth random antenna layout, IEEE Electron. Lett., vol. 9, no., pp. 9 9, Mar.. [1] I. Gradshteyn and I. Ryzhk, Table of Integrals, Seres, and Products. London, UK: Academc Press,. [17] T. Cover and J. Thomas, Elements of Informaton Theory. New York: Wley-Interscence, 1991.