Effective Capacity ofAdvanced Wireless Cellular Networks Invited Paper S. Glisic, Senior Member, IEEE, savo.glisicya-.ee.oulu. fi, Z. Nikolic, member IEEE, N. Milosevic, student member IEEE, and P. Pirinnen, student member IEEE University of Oulu, Telecommunication Laboratory, P.O.Box 4500, Fin-90401 Oulu, Finland Abstract - In this paper we analyze capacity losses in advanced Code Division Multiple Access (CDMA) network due to imperfections in the operation of the system components. In addition to the standard WCDMA technology both, base stations and mobile units use antenna beam forming and self steering to track the incoming (and transmitted) signal direction. By using high directivity antennas and antenna pointer tracking the level of multiple access interference (MAI) and the required transmitted power are reduced. In order to exploit the available propagation diversity signals arriving from different directions (azimuth qi, elevation p) and delay a, are combined in 3D (y,q,) RAKE receiver. This is expected to significantly improve the system performance. The main result of this work is a systematic mathematical framework for capacity evaluation of such CDMA network in the presence of implementation imperfections and fading channel. The theory is general and some examples ofpractical set of channel and system parameters are used as illustration. As an example, it was shown that in the case of voice applications and 2D (4 antennasx4 multipaths) RAKE receive, up to 90% of the system capacity can be lost due to the system imperfections. Further elaboration of these results, including extensive numerical analysis based on the offered analytical framework, would provide enough backgroundfor understanding ofpossible evolution of advanced W-CDMA and MC CDMA towards the fourth generation of mobile cellular communication networks. 1. Introduction Physical layer of the third generation of mobile communication system (3G) is based on wideband CDMA. The CDMA capacity analysis is covered in a number of papers and recently has become a subject in standard textbooks [1-7]. The effect of more sophisticated receiver structures (like multiuser detectors MUD or joint detectors) on CDMA or hybrid systems capacity have been examined in [9-13]. The results in [9] show roughly twofold increase in capacity with MUD efficiency 65 % compared to conventional receivers. The effect of the fractional cell load on the coverage of the system is presented in [10]. The coverage of MUD-CDMA uplink was less affected by the variation in cell loading than in conventional systems. References [ 1] and [12] describe CDMA system where joint data estimation is used with coherent receiver antenna diversity. This system can be used as hybrid multiple access scheme with TDMA and FDMA component. In [13] significant capacity gains are reported when zero forcing multiuser detectors are used instead of conventional single-user receivers. In most of the references it has been assumed that the service of interest is low rate speech. In next generation systems (4G), however, mixed services including high rate data have to be taken into account. This has been done in [14] where the performance of integrated voice/data system is presented. It is also anticipated that 4G will be using adaptive antennas to further reduce the MAI. The effects of adaptive base station antenna arrays on CDMA capacity have been studied e.g. in [5], [6] . The results show that significant capacity gains can be achieved with quite simple techniques. One conventional way to improve cellular system capacity, used in 3G systems, is cell splitting, i.e., sub- dividing the coverage area of one base station to be covered by several base stations (smaller cells) [15]. Another simple and widely applied technique to reduce interference spatially in 3G is to divide cells into sectors, e.g., three 1200 sectors. These sectors are covered by one or several directional antenna elements. Effects of sectorization to spectrum efficiency are studied in [16]. The conclusion in [16] is that sectorization reduces co-channel interference and improves signal-to-noise ratio of the desired link at the given cluster size. However, at the same time the trunking efficiency is decreased [17]. Due to the improved link quality a tighter frequency reuse satisfies the performance criterion in comparison to the omnicellular case. Therefore, the net effect of sectorization is positive at least for large cells and high traffic densities. By using M-element antenna arrays at the base station the spatial filtering effect can be further improved. The multiple beam adaptive array would not reduce the network trunking efficiency unlike sectorization and cell splitting [ 18]. These adaptive or smart antenna techniques can be divided into switched- beam, phased array and pure adaptive antenna systems. Advanced adaptive systems are also called spatial division multiple access (SDMA) systems. Advanced SDMA systems maximize the gain towards the desired mobile user and minimize the gain towards interfering signals in real time. According to [ 19], by applying a four-element adaptive array at the TDMA uplink frequencies can be reused in every cell (three-sector system) and sevenfold capacity increase is achieved.
Transcript
Effective Capacity ofAdvanced Wireless Cellular NetworksInvited Paper
S. Glisic, Senior Member, IEEE, savo.glisicya-.ee.oulu. fi, Z. Nikolic, member IEEE,N. Milosevic, student member IEEE, and P. Pirinnen, student member IEEE
University of Oulu, Telecommunication Laboratory, P.O.Box 4500, Fin-90401 Oulu, Finland
Abstract - In this paper we analyze capacity losses inadvanced Code Division Multiple Access (CDMA)network due to imperfections in the operation of thesystem components. In addition to the standardWCDMA technology both, base stations and mobileunits use antenna beam forming and self steering totrack the incoming (and transmitted) signal direction.By using high directivity antennas and antennapointer tracking the level of multiple accessinterference (MAI) and the required transmittedpower are reduced. In order to exploit the availablepropagation diversity signals arriving from differentdirections (azimuth qi, elevation p) and delay a,are combined in 3D (y,q,) RAKE receiver. This isexpected to significantly improve the systemperformance. The main result of this work is asystematic mathematical framework for capacityevaluation ofsuch CDMA network in the presence ofimplementation imperfections and fading channel.The theory is general and some examples ofpracticalset of channel and system parameters are used asillustration. As an example, it was shown that in thecase of voice applications and 2D (4 antennasx4multipaths) RAKE receive, up to 90% of the systemcapacity can be lost due to the system imperfections.Further elaboration of these results, includingextensive numerical analysis based on the offeredanalytical framework, would provide enoughbackgroundfor understanding ofpossible evolution ofadvanced W-CDMA and MC CDMA towards thefourth generation of mobile cellular communicationnetworks.
1. IntroductionPhysical layer of the third generation of mobilecommunication system (3G) is based on widebandCDMA. The CDMA capacity analysis is covered in anumber of papers and recently has become a subjectin standard textbooks [1-7].The effect of more sophisticated receiver structures(like multiuser detectors MUD or joint detectors) onCDMA or hybrid systems capacity have beenexamined in [9-13]. The results in [9] show roughlytwofold increase in capacity with MUD efficiency 65% compared to conventional receivers. The effect ofthe fractional cell load on the coverage of the systemis presented in [10]. The coverage of MUD-CDMAuplink was less affected by the variation in cellloading than in conventional systems. References [ 1]and [12] describe CDMA system where joint dataestimation is used with coherent receiver antenna
diversity. This system can be used as hybrid multipleaccess scheme with TDMA and FDMA component. In[13] significant capacity gains are reported when zeroforcing multiuser detectors are used instead ofconventional single-user receivers.In most of the references it has been assumed that theservice of interest is low rate speech. In nextgeneration systems (4G), however, mixed servicesincluding high rate data have to be taken into account.This has been done in [14] where the performance ofintegrated voice/data system is presented. It is alsoanticipated that 4G will be using adaptive antennas tofurther reduce the MAI. The effects of adaptive basestation antenna arrays on CDMA capacity have beenstudied e.g. in [5], [6] . The results show thatsignificant capacity gains can be achieved with quitesimple techniques.One conventional way to improve cellular systemcapacity, used in 3G systems, is cell splitting, i.e., sub-dividing the coverage area of one base station to becovered by several base stations (smaller cells) [15].Another simple and widely applied technique toreduce interference spatially in 3G is to divide cellsinto sectors, e.g., three 1200 sectors. These sectors arecovered by one or several directional antennaelements. Effects of sectorization to spectrumefficiency are studied in [16]. The conclusion in [16]is that sectorization reduces co-channel interferenceand improves signal-to-noise ratio of the desired linkat the given cluster size. However, at the same timethe trunking efficiency is decreased [17]. Due to theimproved link quality a tighter frequency reusesatisfies the performance criterion in comparison tothe omnicellular case. Therefore, the net effect ofsectorization is positive at least for large cells andhigh traffic densities.By using M-element antenna arrays at the base stationthe spatial filtering effect can be further improved.The multiple beam adaptive array would not reducethe network trunking efficiency unlike sectorizationand cell splitting [ 18]. These adaptive or smartantenna techniques can be divided into switched-beam, phased array and pure adaptive antennasystems. Advanced adaptive systems are also calledspatial division multiple access (SDMA) systems.Advanced SDMA systems maximize the gain towardsthe desired mobile user and minimize the gain towardsinterfering signals in real time.
According to [ 19], by applying a four-elementadaptive array at the TDMA uplink frequencies can bereused in every cell (three-sector system) andsevenfold capacity increase is achieved.
popirine
Rectangle
popirine
Rectangle
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
Correspondingly, a four-beam antenna leads to reuseof three or four and doubled capacity at small angularspread.
Some practical examples of the impact of the useof advanced antenna techniques on the existingcellular standards are described in [20] and [21]. In[20] the reference system is AMPS and in [21] GSM.The analysis in [3 1 ] uses ideal and flat-topbeamformers. The main lobe of the ideal beamformeris flat and there are no sidelobes whereas the flat-topbeamformer has a fixed sidelobe level. The idealbeamformer can be seen as a realization of theunderloaded system, i.e., there are less interferers thanthere are elements in the array. The overloaded case isbetter modeled by the flat-top beamformer because allinterferers cannot be nulled and sidelobe level isincreased. Performance results show that reuse factorof one is not feasible in AMPS, but reuses four andthree can be achieved with uniform linear arrays(ULA) with five and eight elements, respectively.
Paper [21] concentrates on the design andperformance of the frequency hopping GSM networkusing conventional beamforming. Most of the resultsare based on the simulated and measured data ofeight-element ULA. The simulated C/I improvementfollows closely the theoretical gain at low azimuthspreads. In urban macrocells the CII gain is reducedfrom the theoretical value 9 dB down toapproximately 5.5 - 7.5 dB. The designed direction ofarrival (DoA) algorithm is shown to be very robust toco-channel interference. The potential capacityenhancement is reported to be threefold in a 1/3 reuseFH-GSM network for an array size ofM = 4 - 6. Anumber of papers [22-29] present the analysis ofcapacity improvements by using spatial filtering.
In our paper we go even beyond the existingproposals and assume that both base station and themobile unit are using beam forming and self-steeringto continuously track transmitter-receiver direction(two side beam pointer tracking 2SBPT).
Due to user mobility and tracking imperfectionsthere will be always the tracking error that will resultin lower received signal level causing the performancedegradation.
In this paper we provide a general framework forperformance analysis of a network using thistechnology . It is anticipated that this technology willbe used in 4G systems.
2. System modelAlthough the general theory of MIMO systemmodeling is applicable for the system description,performance analysis will require more details andslightly different approach will be used. This modelwill explicitly present signal parameters sensitive toimplementation imperfections.
Transmitted signalThe complex envelope of the signal transmitted byuser k e {1,2,...,K} in the nth symbol intervalte[nT,(n+l)T] is
Sk =AkTk (l,0p)e Sk0'(t k ) (1
where Ak is the transmitted signal amplitude of user
k, Tk (y,, q,) is the transmitting antenna gain pattern as afunction of azimuth qi and elevation angle q',I k isthe signal delay, okO is the transmitted signal carrier
phase, and Skn)(t) can be represented as
S"(t) =S = Sk = Sik +ISqk = dIkCek + jdqkCqk (2)
In this equation d,k and dqk are two information bits
in the I- and Q-channel respectively, ci and c" arethe mth chips of the kth user PN codes in the I- and Q-channel respectively. Equations (1) and (2) are generaland different combinations of the signal parameterscover the most of the signal formats of practicalinterest. In practical systems the codes will be acombination of a number of component codes [1].Channel ModelThe channel impulse responses consist of discretemultipath components represented as
hk(W,,t) = E h (V, fo)g(t-,r'=IL
-Z H>J(Y,o,)ejl-)(t- 47)
/11
If antenna lobes are narrow we can use a discreteapproximation of this functions in spatial domain tooand implement 3D RAKE receive as follows:
L
I'~~~~~~~~'l~~~Lkn)L
=E1 H,,e y-t --(n)ejo)f=lZH 1e /( Ytkl (kt-VkI )1=1
(3a)
h-,"= Hk(n)ejA, (3b)where L is the overall number of spatial-delaymultipath components of the channel. Each path ischaracterized by a specific angle of arrival (y,, p) anddelay r. Parameter hk,') is the complex coefficient(gain) of the lth path of user k at symbol interval withindex n, r(7n) [0,Tm) is delay of the lth pathcomponent of user k in symbol interval n and d(t) isDirac delta function. We assume that Tm is delayspread of the channel. In what follows indices n willbe dropped when ever this does not produce anyambiguity. It is also assumed that Tm < T.The received signalThe base station receiver block diagram is shown inFig. 1. The overall received signal at the base stationsite during Nb symbol intervals can be represented as
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
)N-1 K }
r(t) = Re< ejv h 1 "(t) * h(n'(t)n=O k=1
+ Re{z(t)ei4 }
=Retei ZE , ,ak,S,k)(t - nT - rk -kl)}n=O k I
+ Re{z(t)eJ)t }
where akl= AkTk(y,,'P)Hk'!ej"k =Ak e
AkTk )k= Ak! ok =0k+IOkO kJI 00 iSfrequency down-conversion phase error and z(t) icomplex zero mean additive white Gaussian niprocess with two-sided power spectral density .2wo is the carrier frequency. In general, in the secwe will refer to {k as received signal amplitude. 1amplitude will be further modified by the receiantenna gain pattem. The complex matched filteiuser k with receiver antenna pattern RkW(0,1)create two correlation functions for each path
(n+l)T+rk +r0
=) Jr(t)Rk ( -',)c,(t nT -tVk + rkl)nT+r +rk,
CoS(co0t + ikI )dt
=]EE Ak.. [dik'i ,ikl COS kr',kik' I'
+dqk Pqk'qikl sin gk'1.,kI]
= yZ,y(klI)k' I'
where AkI. = Ak.1.Rk(yV,), parameter&1/, isestimate of okl and
(n+1)T±rk+r±k(n) rtRYqki = Jr(t)Ik (Yt, (P)Cqk(t - nT - +kki)
nT+rx +rj
sin(oot + 4)_kI)dt=E EA>Dykl,qkl cos I'1',k (
k I'
_dik'Pik'1,qk1 sin -k'1',k
= y YqkI(kl),k' /'
YqkI (k'l') = Yqkl (k'l') + Yqiu (k'I )= Ak lt[dqk(PqkJgqk1 COS8k- d!k'Pikl sinkkk CO 1
where Pt, are crosscorrelation functions betweencorresponding code components x and y.Each of these components is defined with thindices. Parameter a-,b=(Da cb where a and bdefined with two indices each.
(4)
In order to receive the incoming signal without anylosses, the receiving antenna should be directing(pointing) the maximum of its radiation diagramtowards the angle of arrival of the incoming signal. Inthis segment we will use the following terminology.The direction of the signal arrival is characterized bythe pointer Pa = (i/,a, qp) In order to receive themaximum of the signal available the receiver antennapointer should be P,r = (V,r,"r) = (VL'a + "VPa + t) . Thereceiver will be tracking the incoming signal pointerand the pointer tracking error will be defined asAP =Pr-Pa = = (rYa, p- ) = (AVYAfp) . Dueto this error the amplitude of the received signal willbe reduced by ep with respect to the maximum value.These issues will be elaborated latter. When necessarywe should make distinction between the amplitudeseen by the receiver (asr) for a given pointer trackingerror Ap and the maximum available amplitude(maa) obtained when Ap = 0.Let the vectors 3( ) of MF output samples for thenth symbol interval be defined as
the 3. Performance Analysis: CDMA system capacityThe starting point in the evaluation of CDMA systemcapacity is the parameter Y,, = Ebm/NO , the received
(6) signal energy per symbol per overall noise density in agiven reference receiver with index m. For thepurpose of this analysis we can represent thisparameter in general case as
= = ~STNo Io, + Ioi +Iin +l7th
where Io,, Ioi, and Jo,,, are power densities of intracell,7a) intercell and overlay type intemetwork interference
respectively and t7th is thermal noise power density. Sis the overall received power of the useful signal andT= l/Rb is the information bit interval. Contributionsof Ioic and Ioin to No have been discussed in a numberof papers [1] In order to minimize repetition in our
7b) analysis we will parameterize this contribution byintroducing i7 = Ioi + I,,in + i7,h and concentrate on theanalysis of the intracell interference in CDMA
the network based on advanced receivers using imperfectrake and MAI cancellation. A general block diagram
ree of the receiver is shown in Fig. 1. An extension of theare analysis, to both intercell and intemetwork
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
A. Multipath channel: near-far effect & powercontrolWe start with the rejection combiner which willchoose the first multipath signal component and reject(suppress) the others. In this case (9) for I-channelbecomes
yibmaiim1 (ml)S / Rb
{aiqml(ml)+I(k'l')} S/Rb +17o_ aiiml (ml)
aiqml (ml) + I(k'l') + QoRb / S
where a,,(z), (for x = iiml,iqml,iml and z = ml,k'l') isthe power coefficient defined as
ax(:) = Ee yxy(z)I' } S, S is normalized power level ofthe received signal and parameters yx(z) are in
K L
general defined by (6). I(k'l') = Z Zaimi(k'l) isk'=1 '=1(k'.m)
P =2k'=m)
the equivalent MAI. E{ } stands for averaging withrespect to corresponding phases 6a b defined by (7).Based on this we haveaim, (k 1') = Eg, (k' l k)}=A 1p, l(kIm /2
> A-1%. / 2=> {Ak,Hka, Tk(yI, (p)Rm./f )}(
wherept,,1 (kTI ) = Pi2Iiml + P2kI im1
p2 = Ep {Pvikjml + P2k1,iml }and normalizationA",p' /2 => Ah /2.A similar equation can be obtained for the Q-channeltoo. It has been assumed that all 'interference perpath' components are independent. In what followswe will simplify the notation by dropping all indicesiml so that aimi(k'l') => k,. With no power control(npc) akx will depend only on the channelcharacteristics. In partial power control (ppc) only thefirst multipath component of the signal is measuredand used in power control (open or closed) loop. Fullpower control (fpc) will normalize all components ofthe received signal and rake power control (rpc) willnormalize only those components combined in therake receiver. The (rpc) control seems to be morefeasible because these components are alreadyavailable. These concepts for ideal operation aredefined by the following equationsnpc > ak, = ak,,, Vk, I
ppc=i>ak =1, VkL
fpc=.a, =1, Vk
rpc=EIZakf=l, Vk1=1
(12)
where Lo is the number of fingers in the rakereceiver. The contemporary theory in this field doesnot recognize these options which causes a lot ofmisunderstanding and misconceptions in theinterpretation of the power control problem in theCDMA network. Although fpc is not practicallyfeasible the analysis includingfpc should provide thereference results for the comparison with other, lessefficient options.Another problem in the interpretation of the results inthe analysis of the power control imperfections iscaused by the assumption that all users in the networkhave the same problem with power control. Hence, theimperfect power control is characterized with thesame variance of the power control error. This is morethan pessimistic assumption and yet it has been usedvery often in analyses published so far. The abovediscussion is based on the signal amplitude seen bythe receiver (asr). System losses due to differencebetween the asr and maa will be discussed in the nextsection. If we now introduce matrix am withcoefficients lIakI, Vk,j except for mml = 0 and usenotation 1 for vector of all ones, (10) becomes
1bm=a1T+qRm /15 (13)
Compared with (10) the index i is dropped in order toindicate that the same form of equation is valid forboth, the 1- and Q-channel defined by (8).
B. Multipath channel: pointer tracking error, rakereceiver & interference cancellingIf Lo -fingers rake receiver (Lo < L) with combinercoefficients w,nr (r = 1, 2, ..., Lo ) and interferencecanceller are used the signal-to-noise ratio willbecome
r(Lo )
bm f(m,a, c,r)K +;1qRb ISwhere
50 Z Wsr WmWm;r=l
(14)
(15)
Wm = (WmVI VWm2, ... Wmn)is due to Gaussian noise processing in the rakereceiver, and noise density q0becomes q due to
additional signal processing. Also we haveK 4 L
fk(m,a, c, r) =-E w, O -C4,I)K=1-= r=l 1=1kt-m
i , L
+ IEE W.-liF, (1-Cml )Kr=l 1=1
1.r
*acmr *T)Tj
(16)
with aLmr being a matrix of size KxL with coefficients
I|a (1- Ckl )lI except for Emr(I -Cm.) = 0 and Ce,, is
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
efficiency of the canceller. The parameterakl= Ep(, ,,l{a,} is the average value of theinterfering signal power akl coming from direction(azimuth, elevation) (YVkl"pkI) = (§Vm + A /kl,(0m + Apklj)with respect to the reference pointer P(y/m'6Pm) of theuseful signal. Formally this can be represented as
'7ki || akl (§,f )O,o,Ao,,A (I16a)pdf(A Vu, Aq k)dyd(od(Ayk,)d(Aok,)
were pdf(A yk,,A9pk) is probability density functionof the arguments. For the first insight into the systemperformance a uniform distribution of A Y'kl andAqp,, can be assumed along with a rectangular shapeof T(Vl,(o) and R(lt,(p) in the range yicy0+ T,pE- + D, so that evaluation of (I 6a) becomestrivial. For the amplitudes Ak, seen by the receiver
asr, the parameter r,(L,) in (14) called rake receiverefficiency is given as
r,,m '=(Zwmr cOsm½mr4aJ =(wm amm) (17)
with CEMm = (cos £6jMj va-cos- nram2l-*
Parameter £nmr = 6mmr 9mmr is the carrier phasesynchronization error in receiver m for signal of userm in path r. We will drop index mkl when ever it doesnot result into any ambiguity. In the sequel we willuse the following notation: ctk, = A,/2, Am1 is theestimation of Ak, by the receiver m,
= AAmkI / Ak, = (Ak, - AmkJ) / AkI is the relative
amplitude estimation error, cm = BER = bit error rate
that can be represented as mm' = 1- 2BER, and so =carrier phase estimation error.For the equal gain combiner (EGC) the combinercoefficients are given as wmr = 1. Having in mind thenotation used so far in the sequel we will drop indexm for simplicity. For the maximal ratio combiner(MRC) the combiner coefficients are based onestimates as
=cose~.6 Ar, (1 / 2) Ar ( -ar) (18)cos Cl Al (1-4/1 2) Al (1-ca1 )
+ZE °r ( -246 +34)For MRC the same relation becomes
I{()}=l,( 4 2 l6) 2
|t0 a2 (I- /2)r (1-_/2)2 l
rl aI (1- 1 / 2)2 (Iai )2 j
r=i a1 o+lEE.r ' (1 - 2c,2 + 3a,4)(1-2 +30_4)
l#r
(20)
(21)
x (I + 2C;, -3a ?91 )(I1-£ar. )(I a ( +ga)In order to evaluate the first term we use limits. Forthe upper limit we have 462 4.1 By using this wehave(1- 2/ 2)4 1(I 42 / 2)2 (1 / )2
and the first term becomesZ r(1-2o + 361 )(1- ) 1(1 )2r=l 1
For the lower limit we use 4 >4 and the first termbecomes
E r(12U2) + 3Cr&)(-ar ) /1gar=1 a1For a signal with the I- and Q-component theparameter cos .6 should be replaced byCos6 =* COS£* + mp sin e,,. where m is theinformation in the interfering channel (I or Q), and pis the crosscorrelation between the codes used in the l-and Q-channel. For small tracking errors this term canbe replaced as cosE + mp sin e1+ MpE - £2 / 2, where the notation is further
simplified by dropping the subscript ( ),. Similarexpressions can be derived for the complex signalformat. In the above discussion signal amplitude seenby the receiver (asr) is used for A. . In the presence ofpointer estimation error this is related to the (maa) asAr => A,.- p So, to account for the losses due to ep,parameter ar in the above equation should be
replaced by a,.=>E(A.- )2 = a,.-2 +C
where £p and Op = E(ep) are the mean and varianceof the pointer tracking error. The power control will
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
compensate the pointer tracking losses by increasingthe signal power by the amount equal to the losses.This means that the level of interference will beincreased which can be taken into account in ourmodel by modifying the parameters Cak, as follows
ak => akI + 2£p Zo;a
C Interference canceller modelling: nonlinearmultiuser detectorsFor the system performance evaluation a model forthe canceller efficiency is needed. Linear multiuserstructure might not be of much interest in the nextgeneration of the mobile communication systemswhere the use of long codes will be attractive. Analtemative approach is nonlinear (multistage)multiuser detection, that would include channelestimation parameters too. This would be based oninterference estimation and cancellation schemes(OKI standard-IS-665/ITU recommendation M. 1073or UMTS defined by ETSI)In general if the estimates of (8) are denoted as yiand then the residual interference aftercancellation can be expressed as
Ayi =Y1-Yi,AYq Yq Yjq9 (22)Ay =Ayi + AYq = Vec{Ay;}where index ; => k,l spans all combinations of k and
l. By using (22) each component atk,(1-CkI) in (16)can be obtained as a corresponding entry of
Vec1Ay.|ITo further elaborate these components we will use asimplified notation and analysis.After frequency downconversion and despreadingsignal from user k, received through path / at thereceiver m would have the form
S.k1 -Akil hk coSO.k1 (23)
= (Amki + AAmkI )hk C°S(OmkI + -6W)for a single signal component andSIkl=AmkM-icos.mkI +Amklh sinOmk2mki k-q ~~~ikl(24)Sqk =-A kI1ih sin 9,.nk + Amkrmkkq COsOmklfor a complex (I&Q) signal structure. In a givenreceiver m,, components S,,k and S~k, correspond to
Ay,*k and AYqk1. Parameter Am,k includes both
amplitude and correlation function. In (23) AA,,Id andf6*,kj are amplitude and phase estimation errors. The
canceller would create Sm.k - Smkl = ASmk-I and thepower of this residual error (with index m dropped forsimplicity) would be
Eo[(ASk,)2]= E[A,mk cos ,4
where E,[ ] stands for averaging with respect to 9k1and Mk. Parameter (ASkI)2 corresponds to 1AY,|2 . Thiscan be represented as
E L(ASkI)2]= Ckj+2(1+6a) (26)
-2(1 + £a) * (1-2e,?t cos £,
From this equation we have 1-CkI = EA (ASk,,) ,]/and Ck,= 2(1 +ea Xl-2cm)cosO-(I +
,,Y)-By expanding cos e. as 1-42/2 and averaging gives
C = 2(l + £,, XIl-2£m XI-C2 )_ (I + £a )2* (27)For zero mean eq, Cr = E[£; / 2] is the carrier phasetracking error variance. For the complex (I&Q) signalstructure cancellation efficiencies in I- and Q-channelscan be represented asCi = 4(I+£aX1-2£m1(+ )-2(1+e ) -1
ki cr; ~~~~~~. (28)Cq = 4(1+h£aeXI -2£ lXI + &)-2(1+la)-So, in this case the canceller efficiency is expressed interms of amplitude, phase and data estimation errors.These results should be now used for analysis of theimpact of large scale of channel estimators on overallCDMA network sensitivity. Performance measure ofany estimator is parameter estimation error variancethat should be directly used in equations (28) forcancellation efficiency and (19-22) for rake receiver.If joint parameter estimation is used, based on MLcriterion, then Cramer Rao bound could be used forthese purposes. For the Kalman type estimator, theerror covariance matrix is available for each iterationof estimation. If each parameter is estimatedindependently, then for carrier phase and code delayestimation error a simple relation C2 =I/SNRL can
be used where SNRL is the signal to noise ratio in
the tracking loop. For the evaluation of this SNRLthe noise power is in general given as N = BLNO. Forthis case, the noise density No is approximated as aratio of the overall interference plus noise powerdivided by the signal bandwidth. The loop bandwidthwill be proportional to fD where fD is the fading rate(Doppler). The higher thejL, the higher the loop noisebandwith, the higher the equivalent noise power(NfD). If interference cancellation is performed priorto parameter estimation, No is obtained from J()defined by (16). If parameter estimation is usedwithout interference cancellation the sameAf ) is usedwith C,4 = 0 . In addition to this
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
where c. is the code delay
6A =(A-A)1A=1-A1A .
estimation we have
= fl4y) exp- + I{I+ y
estimation error and
For noncoherent
Y + YIY)} (30)
where Io( ) and II( ) are the zeroth and first orderBessel functions, respectively, and y is the signal-to-noise ratio.
D. ApproximationsIf we assume that the channel estimation is perfect( e = co = 0 ) the parameter CmkI becomesCk, = 2(1 - 2&m) - 1 = 1 - 4am . For DPSK modulationX- (1 / 2) exp(-y / 2) where y is signal to noise ratioand for CPSK cm -(1/ 2) erfc(I) . So CkI = l- 2e-Y
for DPSK, and C.,=1- 2erfc(f) for CPSK. Forlarge y, Ck, > 1 and for small y in DPSK system wehave e-Y =1- y and Ck, _ 2y -1. This can bepresented as Ck = 2Y, - l,where Yb is given by (14).Bearing in mind that Yb depends on Ck, the wholeequation can be solved through an iterative procedurestarting up with an initial value of Ck, = 0, Vm,kl .
Similar approximations can be obtained for o-;' and8a From practical point of view an attractive solutioncould be a scheme that would estimate and cancelonly the strongest interference (e.g. successiveinterference cancellation schemes [1]).
E. Outage probabilityThe previous section already completely defines thesimulation scenario for the system performanceanalysis. For the numerical analysis furtherassumptions and specifications are necessary. First ofall we need the channel model. The exponentialmultipath intensity profile (MIP) is widely usedanalytical model realized as a tapped delay line [1]. Itis very flexible in modeling different propagationscenarios. The decay of the profile and the number oftaps in the model can vary. Averaged powercoefficients in the multipath intensity profile area,=a0e211 1,2A0 (31)where A is the decay parameter of the profile. Powercoefficients should be normalized asL-1
Iaoe-2=1.1=0
For A = 0 the profile will be flat. The number ofresolvable paths depends on the channel chip rate andthis must be taken into account. We will start from(14) and look for the average system performance forp2 =1 / G where G = W / Rb is the system processing
gain and W is the system bandwidth (chip rate). Theaverage signal to noise ratio will be expressed as
- r(LO)Gb f(a)K +;07'W/S (32)
Now, if we accept some quality of transmission,BER= 10-e e that can be achieved with the given SNR= Y0, then with the equivalent average interferencedensity 1io = IUi + IWU + mIth signal to noise ratio will be
r(LO)G (3YO= (33)ro
To evaluate the outage probability P,,,, we need toevaluate [1]
= Pr(BER > O-'e) = Pr{MAI+.7i > rio )
= Pr{MAI > rio - S = Pr(MAI>>)where 6 is given as
r(Lo)G -ffYO S
(34)
(35)It can be shown that this outage probability can berepresented by Gaussian integral
(36)45)U1
where mg and 0rg are the mean value and thestandard variance respectively of the overallinterference. From (32) we have for the systemcapacity K with ideal system components
r,oL')GKmax = (a) -;01qW / Sf0o (a) (37)Due to imperfections in the operation of the rakereceiver and interference canceller this capacity willbe reduced to
r(Lo )GK'= - 5u5'-q,W / Sf(a) (38)
where reL,) and fot(a) are now replaced by realparameters r(LO) and f(a) that take into accountthose imperfections. The system sensitivity function isdefined as
4. Numerical examplesIn this section we present some numerical result forillustration purposes. The results are obtained for achannel with double exponential (space and delay)profile with decay factors 2A and 2, . Graphical results
2005 IEEE 16th Intemational Symposium on Personal, Indoor and Mobile Radio Communications
are presented with: Solid line: 4 x 4 Rake, Dashedline: 4 x I Rake. In the case of 3db-approximation ofthe real antenna the beam forming is approximatedwith rectangular shape of antenna pattern in the rangeQ3dB = 300 (for Pc = 1), and uniform distribution ofAykfk and A 'k, ([0,z], [0,2z], respectively) , A, = A, =0 if not specified otherwise, Y0 = 2, L = 4, interferencemargin SNR = (20*ao/alfa mean)-'The users are uniformly distributed in the sphere(q',pr) with p,y E (0,3600) . The results can be easilyscaled down for a more realistic scenario whereq' e (0,360°) and Y/ e (mnmin, /max) . Cancelingefficiency, when estimation errors are included, iscalculated according to (27). Carrier phase trackingerror variance is assumed to be cr9 =1/SNRL. ForMRC the amplitude estimation error is approximatedfrom (30) to follow £a = I/ 4SNRL . For real antennasthe amplitude patterns are specified in Fig.2. The basestation amplitude antenna pattern is given as
A(9p,yN)=-1exp [-fpsinycos(p-2ff-;IN nilL N)j
and four examples cover relatively wide range ofshapes, from a wide lobe for pc = 1 to a rather narrowlobe for Pc = 12. At mobile station an omnidirectional antenna pattern A(q, v) =1 is assumed .
Capacity curves, defined as the number of users withdata rate R = chiprate / G=4.096/G, for differentantenna patterns, are shown in Fig.3. The highestcapacity is obtained for .o =12 because with thenarrowest lobe the spatial division multiple accesseffect is the most effective. With increased receivervelocity the capacity will be reduced due to increasedeffect of imperfections. Comparison of the systemsusing ideal and real antennas is shown in Fig.4. Fig.4presents the system capacity versus G. In generalhigher G means more users in the network and moreMAI resulting in more impact of imperfections. A 4x4rake performs better for lower G but for higher G(more users) it deteriorates faster. The degradation ismore severe for higher receiver velocities.Fig.5 represents the same results as a function of thereceiver velocity. The system sensitivity functiondefined by (39), is shown in Figs. 6. Sensitivity equalto one, means that all capacity has been lost due toimperfections. Figs.6 demonstrate that very highvalues for the system sensitivity, even in the rangeclose to 0.9, can be expected if a large number ofusers (low data rate corresponding to high G) is in thenetwork.
5. ConclusionsIn this paper we have presented a systematicanalytical framework for the capacity evaluation of anadvanced CDMA network. This approach provides a
relatively simple way to specify the required qualityof a number of system components. This includesmultiple access interference canceller and rakereceiver, taking into account all their imperfections.The system performance measure is the networksensitivity function representing the relative losses incapacity due to all imperfections in the systemimplementation. Some numerical examples arepresented for illustration purposes. These results areobtained for a channel with double exponential (spaceand delay) profile. It was shown that for the receivervelocity 100-200 km/h as much as 70% -90% of thesystem capacity can be lost due to the imperfections ofthe 3D rake receiver and interference cancellationoperation. A variety of results is presented fordifferent channel decay factor, fading rate and numberof rake fingers. In general, under ideal conditions, thesystem capacity is increased if the number of fingersis increased. At the same time one should be awarethat the system sensitivity is also increased if thefading rate and number of rake fingers are higher. Theresults and methodology presented in this paper offerenough tools and data for the careful choice of thesystem parameters in realistic environment which arecharacterized with imperfections.
References[1] Glisic. S -Adaptive WCDMA, Theory and Practice, John Wileyand Sons, 2003[2] A. Baiocchi et al., "Effects of User Mobility on the Capacity ofa CDMA Cellular Network," European Trans. Telecomm., Vol. 7,No. 4, pp. 305-314, July-Aug. 1996.[3] A. M. Viterbi and A. J. Viterbi, "Erlang Capacity of a PowerControlled CDMA System" IEEE J. Select. Areas Commun., vol.11, no. 6, pp. 892-899, Aug. 1993.[41 M. A. Landolsi, V. V. Veeravalli and N. Jain, "New results onthe reverse link capacity ofCDMA cellular networks," Proc. IEEEVTC'96, pp. 1462-1466, 1996.[5] J. C. Liberti, Jr. and T. S. Rappaport, "Analytical Results forCapacity Improvements in CDMA," IEEE Trans. Vehic. Tech., vol.43. no. 3, pp. 680-690, Aug. 1994.[6] A. F. Naguib et al., "Capacity Improvement with Base-StationAntenna Arrays in Cellular CDMA," IEEE Trans. Vehic. Tech., vol.43. no. 3, pp. 691-698, Aug. 1994.[7] L. Tomba, "Outage Probability in CDMA Cellular Systems withDiscontinuous Transmission," Proc. IEEE ISSSTA '96, pp. 481485,1996.[8] L. Tomba, "Computation of the Outage Probability in RiceFading Radio Channels," European Trans. Telecomm., Vol. 8, No.2, pp. 127-134, Mar.-Apr. 1997.[9]S. Hamalainen, H. Holma and A. Toskala, "Capacity EvaluationOf a Cellular CDMA Uplink With Multiuser Detection," Proc.IEEE ISSSTA '96, pp. 339-343, 1996.[10] H. Holma, A. Toskala and T. Ojanpera, "Cellular CoverageAnalysis Of Wideband MUD-CDMA System," Proc. IEEEPIMRC'97, pp. 549-553, 1997.[It] J. Blanz, A. Klein, M. Naflhan and A. Steil, "Capacity of acellular mobile radio system applying joint detection," COST 231TD94 002, 18 pages, 1994.[12] J. Blanz, A. Klein, M. Na,Bhan and A. Steil, "Performance of aCellular Hybrid CITDMA Mobile Radio System Applying JointDetection and Coherent Receiver Antenna Diversity," IEEE J.Select. Areas Commun., vol. 12, no. 4, pp. 568-579, May 1994.[13] S. Manji and N. B. Mandayam, "Outage Probability for a ZeroForcing Multiuser Detector with Random Signature Sequences,"Proc. IEEE VTCJ98. pp. 174-178, 1998.
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
[14] W. Huang and V. K. Bhargava, "Performance Evaluation of aDS/CDMA Cellular System with Voice and Data Services," Proc.IEEE PIMRC'96, pp. 588-592,1996.[15] V. H. MacDonald, The cellular concept, Bell Syst. Tech. J., 58:1541, 1979.[161 G. K. Chan, Effects of sectorization on the spectrum efficiencyof cellular radio systems, IEEE Trans. Veh. Technol., 41: 217-225,1992.[ 17] S. G. Glisic and P. Pirinen Co-Channel Interference in DigitalCellular TDMA Networks, John Wiley Encyclopedia oftelecommunications, ed. J. Proakis, John Wiley, 2003[1 81 S. C. Swales, M. A. Beach, D. J. Edwards, and J. P. McGeehan,The performance enhancement of multibeam adaptive base stationantennas for cellular land mobile radio systems, IEEE Trans. Veh.Technol., 39: 56-67, 1990.[ 19] J. H. Winters, Smart antennas for wireless systems, IEEEPersonal Commun., 5: 23-27, 1998.[20] P. Petrus, R. B. Ertel, and J. H. Reed, Capacity enhancementusing adaptive arrays in an AMPS system, IEEE Trans. Veh.Technol., 47: 717-727, 1998.[21] P. E. Mogensen, P. L. Espensen, P. Zetterberg, K. I. Pedersen,and F. Frederiksen, Performance of adaptive antennas in FH-GSMusing conventional beamforming, Wireless Personal Commun., 14:255-274, 2000.[22] A. J. Paulraj and C. B. Papadias, Space-time processing forwireless communications, IEEE Signal Processing Mag., 14: 49-83,1997.[23] L. C. Godara, Applications of antenna arrays to mobilecommunications, part I: performance improvement, feasibility, andsystem considerations, Proc. IEEE, 85: 1031-1060, 1997.[24] J. Litva and T. K.-Y. Lo, Digital beamforming in wirelesscommunications. Boston: Artech House, 1996.[25] J. H. Winters, Optimum combining in digital mobile radio withcochannel interference, IEEE Trans. Veh. Technol., VT-33: 144-155, 1984.[26] P. Zetterberg, A comparison of two systems for downlinkcommunication with base station antenna arrays, IEEE Trans. Veh.Technol., 48: 1356-1370, 1999.[27] P. Zetterberg and B. Ottersten, The spectrum efficiency of abase station antenna array system for spatially selectivetransmission, IEEE Trans. Veh. Technol., 44: 651-660, 1995.[281 W. S. Au, R. D. Murch, and C. T. Lea, Comparison betweenthe spectral efficiency ofSDMA systems and sectorized systems,Wireless Personal Commun., 16: 15-67, 2001.[29] L.-C. Wang, K. Chawla, and L. J. Greenstein, Performancestudies of narrow-beam trisector cellular systems, Int. J WirelessInform. Networks, 5: 89-102, 1998.[30] 1. Howitt and Y. M. Hawwar, Evaluation of outage probabilitydue to cochannel interference in fading for a TDMA system with abeamformer, Proc. IEEE Veh. TechnoL Conf, 520-524, 1998.[3 1 ] E. Kudoh and T. Matsumoto, "Effect of Transmitter PowerControl Imperfections on Capacity in DS/CDMA Cellular MobileRadios," Proc. IEEE ICC 92, pp. 237-242, 1992.
Fig. I Receiver block diagram
0.4 ~ ~ ~ ~ ~ W L =90
=9 1350.2909O
(9 31?
90°(= 45'
(b)
0.6~~~~~~~5
(0)
0.2 ~ ~ ~ ~ ~~~~~~V 90.
( 135 '
W9 90)-(= 45°
(d)Fig. 2. Peak-amplituide pattern A ((py.)for nonsinusoidal Gautssianpulses received by the circular array with N = 4 elements and (a) p,
B - 3dB approximation ofthe real antennap-= 1; N = 4, 2, = A, = 0 Yo = 2, L = 4, SNR = (20*aIalfamean)-
(a) a - G= 256, b - G= 160 (b) a - G= 80, b - G =48, c - G=40
GFig. 6. Sensitivity versus processing gainfor EGC
a - v-e = 200 km/h, b - vre- =l50km/h, c - vr- = 100 km/h, d - v,50 km/h; Solid line: 4 x 4 Rake, Dashed line: 4 x I RakeA - Real antenna pattern ofcircular array at base stationB - 3dB-aproximation (Y'3dB - 30 ofthe real antenna pattern
Pc = 1; N= 4, AS =At =0, Yo = 2, L = 4SNR - (20*aJalfa_mean)-'
