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Hindawi Publishing Corporation
EURASIP Journal on Wireless Communications and Networking
Volume 2007, Article ID 89780, 9 pages
doi:10.1155/2007/89780
ResearchArticle
On Sum Rate and Power Consumption of Multi-User
Distributed Antenna System with Circular Antenna Layout
Jiansong Gan, Yunzhou Li, Limin Xiao, Shidong Zhou, and Jing Wang
Department of Electronic Engineering, Tsinghua University, Room 4-405 FIT Building, Beijing 100084, China
Received 18 November 2006; Accepted 29 July 2007
Recommended by Petar Djuric
We investigate the uplink of a power-controlled multi-user distributed antenna system (DAS) with antennas deployed on a circle.
Applying results from random matrix theory, we prove that for such a DAS, the per-user sum rate and the total transmit power
both converge as user number and antenna number go to infinity with a constant ratio. The relationship between the asymptotic
per-user sum rate and the asymptotic total transmit power is revealed for all possible values of the radius of the circle on which
antennas are placed. We then use this rate-power relationship to find the optimal radius. With this optimal radius, the circular
layoutDAS(CL-DAS)isprovedtoofferasignificantgaincomparedwithatraditionalcolocatedantennasystem(CAS).Simulation
results are provided, which demonstrate the validity of our analysis.
Copyright © 2007 Jiansong Gan et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. INTRODUCTION
Information theory suggests that for a system with a large
number of users, increasing the number of antennas at the
base station leads to a linear increase in sum-rate capacity
without additional power or bandwidth consumption [1].
However, previous studies have mostly focused on scenar-
ios with all antennas colocated at the base station. Suppose
antennas are connected but placed with geographical separa-
tions, each user will be more likely to be close to some an-
tennas, and the transmit power can therefore be saved. This
is the concept of distributed antenna system (DAS) which
was originally introduced for coverage improvement in in-
door wireless communications [2].
Recent interests in DAS have shifted to advantages in ca-
pacityorsumrate.Thechannelcapacityofasingle-userDAS
and the sum rate of a multi-user DAS were investigated and
compared with those of co-located antenna systems (CAS)
using Monte Carlo simulation in [3] and [4], respectively,
where significant improvements have been observed. How-
ever, these works did not provide theoretical analysis to char-
acterize the exact gain that a DAS offers over a CAS. Nei-
therdidtheypresentoptimalparametersforantennadeploy-
ment.
Another line of work introduces coordination between
base stations and suggests an architecture quite similar to
DAS[5].Sumrateofsuchasystemhasbeenstudiedin[6,7].
However,unlikeinvestigationsinDASwhichevaluateperfor-
manceimprovementbyscatteringco-locatedantennas,these
works mainly assess performance enhancement by introduc-
ing coordination between base stations. In addition, analysis
in [7], for example, assumes a large number of antennas co-
located at the base station, which differs from ideas of DAS.
In this study, we demonstrate the advantage of scattering
co-located antennas in an analytical way. Though there are
different ways to scatter antennas and different antenna lay-
outs may result in different performances, investigating all
possible layouts is rather difficult. For analytical tractability
we only consider a special DAS with antennas deployed on
a circle. A similar model has been used in [8] to study the
capacity of CDMA system with distributed antennas. Since
distributed antennas are relatively cheap, it is feasible to de-
ploy a large number of antennas, which makes application of
random matrix theory possible. Applying recent results from
this theory, we prove that for a circular-layout DAS (CL-
DAS), the per-user sum rate and the total transmit power
both converge as user number and antenna number go to
infinity with a constant ratio. Then, the relationship between
the asymptotic per-user sum rate and the asymptotic total
transmit power is disclosed for all possible values of the ra-
dius of the circle on which antennas are deployed. We fur-
ther show how the rate-power relationship can be used to
find the optimal radius. A CL-DAS with this optimal radius
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2 EURASIP Journal on Wireless Communications and Networking
R0
a
b
R
Antenna
Central processor
User
Figure 1: Illustration of CL-DAS.
is proved to offer a significant gain over a traditional CAS.
Though the maximum achievable gain that a general layout
DAS provides over a CAS has not been found yet, it can be
lower bounded by the presented gain for the optimized CL-
DAS (OCL-DAS). Hence, we demonstrate the possibility of
greatperformanceenhancementbyscatteringthecentralized
antennas.
The remainder of this paper is organized as follows.
Section 2 describes the system model. Sum rate, power con-
sumption,andtheirrelationshipareanalyzedinSection 3.In
Section 4,weshowhowtousetherate-powerrelationshipfor
antenna deployment optimization and how much gain can
be obtained. Simulation results can be found in Section 5.
Finally, concluding remarks are given in Section 6.
2. SYSTEM MODEL
Beforeproceedingfurther,wefirstexplainthenotationsused
in this paper. All vectors and matrices are in boldface, XT
and XHare the transpose and the conjugate transpose of X,
respectively, Xi,jis the (i, j)th element of X, Xi,:is the ith row
of X, X:,j is the jth column of X, and E is the expectation
operator.
As illustrated in Figure 1, an isolated coverage area of ra-
dius R is considered. To describe antenna and user distribu-
tions, we use polar coordinates (r,θ) relative to the center of
thecoveragearea.TheCL-DASunderstudyconsistsofN an-
tennas which are independent and uniformly distributed on
the circle with r = a. (We do not assume deterministic de-
ployment scheme here, considering that the complex terrain
may make deploying a large number of antennas with de-
terminate positions difficult.) These antennas are connected
to the central processor via optical fibers. K single-antenna
users are mutually independent and uniformly distributed in
the coverage area excluding the radius R0neighborhood of
each antenna [9]. To describe user distribution, b is used to
denote user polar radius in the following analysis.
2.1.Signalmodel
Let xkand pkbe the transmitted signal with unit energy and
the transmit power of the kth user, respectively. Let hk ∈
CN×1denote the vector channel between the kth user and the
distributed antennas. Then, the received signal y ∈ CN×1can
be expressed as
y =
K?
k=1
hk
?pkxk+n = HP1/2x +n, (1)
where x = [x1,x2,...,xK]Tis the transmitted signal vec-
tor, P = diag(p1, p2,..., pK) is the transmit power matrix,
n ∈ CN×1is the noise vector with distribution CN(0,σ2
and H = [h1,h2,...,hK] is the channel matrix. Since anten-
nas are geographically separated, to model DAS channel, we
should encompass not only small-scale fading but also large-
scale fading. Here, we model H as
nIN),
H = L ◦ Hw, (2)
where “◦” is the Hadamard product or element-wise prod-
uct, Hw, a matrix with independent and identically dis-
tributed(i.i.d.),zeromean,unitvariance,circularlysymmet-
ric complex Gaussian entries, reflects the small-scale fading,
and L represents large-scale fading between users and anten-
nas. Adding shadowing to path loss model used in [3], we
model entries of L as
?
where Dn,kand Sn,kare independent random variables rep-
resenting the distance and the shadowing between the nth
antenna and the kth user, respectively, γ is the path loss ex-
ponent. {Sn,k | n = 1,2,...,N, k = 1,2,...,K} are i.i.d.
random variables with probability density function (pdf),
Ln,k=
D−γ
n,kSn,k,
R0≤ Dn,k< 2R ∀n,k, (3)
fS(s) =
1
√2πλσssexp
?
−(lns)2
2λ2σ2
s
?
,
s > 0, (4)
where σsis the shadowing standard derivation in dB and λ =
ln10/10. Since these Sn,ks are i.i.d., we will not distinguish
them in the following analysis and simply use S instead.
We note that the system model used in this study differs
from that in [6, 7] where the large-scale fading part L is as-
sumed to be fixed. A fixed L is applicable for performance
comparisonbetweensystemswithandwithoutcoordination,
since coordination does not impact L. However, this fixed
L does not apply to performance comparison between CAS
and DAS, since it cannot fully reflect the large-scale fading
between antennas and users for different antenna layouts.
Therefore, a stochastic L must be included, which makes our
work quite different from analyses in [6, 7].
Power allocation policy impacts system performance to a
great extent. To investigate performance of DAS, we assume
a power control scheme widely used in CDMA systems, with
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