Energy Efficient Antenna Deployment Design
Scheme in Distributed Antenna Systems
Tiankui ZHANG Congqing ZHANG
Beijing University of Posts and Telecommunications
School of Information and Telecommunication Engineering
Beijing, China
Abstract—In a distributed antenna system, the optimal antenna
deployment design scheme is proposed, in which both the
location and the number of the distributed antennas (called
access point, AP) are considered for energy efficiency. By
minimizing the average distance between users and the APs, the
optimal AP distribution is given. The optimal number of APs can
be obtained considering both the circuit power and the
transmission power for each AP. The simulation results show
that the transmission power can be reduced by optimal AP
location design. The simulation also considered the trade-off
between the circuit power and the transmission power
consumption and the total system power can be reduced
significantly.
Keywords-energy efficiency; distributed antenna systems;
antennas deployment design
I.
INTRODUCTION
The increasing volume of data being transmitted now is
leading to an increase in the associated energy consumption.
The cost of network operation has now become a critical
factor for mobile and wireless networks operations. Therefore,
lowering energy consumption of future wireless networks is
demanding greater attention and requires new technologies
and solutions and is becoming an important factor in
specification of future standards.
In 3GPP, the base station is separated into baseband unit
(BBU) and remote radio unit (RRU) parts [1]. In fact, the
RRU is a distributed antenna of the cell, and the BBU and
RRUs are connected via optical fiber [2], so forming a kind of
distributed antenna system (DAS). By decentralizing the
deployment of antennas, the coverage of the cell is expanded
and therefore system capacity is increased. Meanwhile, as the
distance between the user and antennas decreases, the
transmission power between the user and antennas can be
reduced. Therefore, the DAS can be used to reduce the system
transmission power consumption. Since different distances
between a user and the antennas will result in different
transmission power, antenna deployment is an important
factor to be considered for energy efficiency.
There are two aspects of the research on antenna
deployment problem in DAS: (i) the study of system
performance with fixed antenna positions [3-6] (such as
uniform antenna distribution and random antenna
Laurie Cuthbert
Yue CHEN
Queen Mary, University of London
School of Electronic Engineering and Computer Science
London, UK
distribution); and (ii) research on antenna location design with
certain system performance requirements (such as capacity,
coverage, outage probability, bit error rate) [7-10]. In [7], the
optimal antenna location for minimum cell average bit error
rate in linear cells is derived. In [8], a squared distance
criterion for antenna location design in DAS is proposed to
maximize the cell average ergodic capacity. [9] defines a
maximum minimum-access distance criterion to obtain the
antenna position layout and proves that the total power of
DAS is much lower than that in centralized antenna system
(CAS). A recent work in [10] investigates the optimal radius
for antenna deployment with circular antenna layout to
maximize the user capacity. However, there is little literature
about antenna deployment design in terms of system energy
efficiency.
Energy efficiency problem has been considered in the
radio resource allocation of cellular systems [11], but without
considering the circuit power consumption for equipment
operation. [12] considers both the circuit and transmission
power when designing link adaptation and resource allocation
schemes in OFDMA systems.
In this paper, the optimal distributed antenna (called access
point, AP, in this paper) deployment design is investigated
with the target of energy efficiency. The deployment design
considers the optimal location and the number of the APs.
Both the circuit power and the transmission power are
considered in the AP deployment design.
The rest of this paper is organized as follows: the system
model is described in section II. The theoretical analysis of the
optimum location and optimum number for the antennas is
given in Section III. The simulation results are shown in
Section IV. The conclusions are given at the end.
II.
SYETEM MODEL
In a DAS system, let the number of APs in the cell be N ,
and each AP has L co-located antennas, and assume each
user terminal has one single antenna. The users can receive
signal from all antennas. The channel model includes largescale fading (including path-loss and shadow fading) and
small-scale fading (e.g., Rayleigh fading). The channels
between the L antennas of a AP and a user suffer the same
large-scale fading since the L antennas on the AP are colocated.
This work is supported by National Natural Science Foundation of China
(60772110), and the Fundamental Research Funds for the Central Universities
978-1-4244-3574-6/10/$25.00 ©2010 IEEE
f ( x, y ) = 1 / N .
The downlink received signal can be written as
y = Hx + z .
(1)
where y is the received symbol vector, x is the transmitted
symbol vector of size
NL ×1 with covariance
matrix R xx = E xxH , H is the channel matrix with size of
1× NL , z is a zero-mean complex additive white Gaussian
( )
noise vector with variance σ . The channel matrix can be
expressed as
2
H = [H1 , H 2 ,"H N ] .
where H n (n
to the
(2)
= 1,2, " , N ) is a channel matrix from the user
th
1×L
n AP and H n ∈ C .
The AP deployment considered here is minimizing the
distance between AP and user to reduce path-loss and improve
signal quality, which can also save transmission power. The
average minimum access distance criterion is defined as
follows
Ed (d min ) = ³³ ( x − x0 ) 2 + ( y − y0 ) 2 f ( x, y )dxdy . (6)
where d min is the minimum access distance between the
user and the nearest AP, f ( x, y ) is the probability density
function, ( x, y ) are the coordinates of the user, and
( x0 , y0 ) are the coordinates of the nearest AP to the user.
For simplicity, change the user’s coordinate into polar
coordinate
H n is modeled as follows
α
H n = csn / d n [ hn ,1 , hn , 2 ," hn ,L ] .
where
(5)
­ x = r cosθ
.
®
¯ y = r sin θ
(3)
(7)
hn ,l is zero mean circularly symmetric complex
Gaussian random variables of variance 1/2 per dimension
representing the small-scale fading of the channel, and
csn / d n
α
is the large-scale fading.
ċ
Ċ
d n is the distance
5
U
between the user and the n AP, and α is the path loss
exponent, typically between 3.0 and 5.0 [13]; c is the median
th
of the mean path gain at a reference distance [14].
sn is a log-
Č
ĉ
normal shadow fading variable, where 10 log10 s n is a zeromean Gaussian random variable with standard deviation σ s
č
and probability density function (PDF) [10]
f s ( s) =
III.
1
2π λσ s
exp( −
(ln s) 2
), s > 0 .
2λ2σ s2
(4)
ANALYSIS OF OPTIMAL AP LOCATION AND NUMBER
A. Optimal AP Location
Since the coverage of a cell in a cellular system is
generally circular, the APs also tend to be located on a circle
[8][10]; this is called circular layout (CL). The cell is
approximated by a circle of radius R and the RRUs are
placed on a circle of radius r and uniformly distributed on
that circle. The AP location design here reduces to find the
optimal r that minimizes Ed ( d min ) . As shown in Fig. 1, the
coverage region of APs are separated by solid lines, which are
congruent sectors with central angles 2π / N , and the AP
locates on the bisector of the central angle. Then the user in
each sector with the probability density function is
Ď
Figure 1. The AP uniform distribution on a circle
Because the user distribution is uniform, the analysis in
each sector is the same and the start angle of AP distribution
has no effect on the solution of optimal radius, so we only
consider the AP location in the first sector, where the polar
coordinate of AP is ( r0 , 0) . The minimum square distance is
used instead of the minimum access distance in the analysis
for simplicity. According to (6) and (7), the expectation of the
minimum square distance is given as follows
2
[
]
1
(r cos θ − r0 ) 2 + (r sin θ ) 2 rdrdθ
N ³³
(8)
( R 4 + 2r02 R 2 )π 4r0 R 3
π
=
−
sin
2N 2
3N
N
Ed (d min ) =
According to (8), the optimum theoretical value of
r0 is
when the derivative of r0 is equal to zero. This minimizes the
expectation of the minimum square distance, which is then
r0 =
2 RN sin
3π
π
N .
B. Optimal AP Number
In the section, the optimal number of APs is obtained by
maximizing the system energy efficiency. The power
consumption of the system mainly lies in two aspects, one is
circuit power denoted as PC which is independent of
transmission data rate; another is transmission power denoted
as PT which can be seen as a function of transmission data
rate of each AP.
If the circuit power for the AP is omitted, the more APs,
there are, the more transmission power that can be saved since
more APs can be provided for users. However, adding more
APs increases the power that will be used to operate the APs.
If the energy efficiency is considered in the AP position
design, the optimal number of APs can be obtained from the
balance between the circuit power increasing and the
transmission power reducing by increasing the APs in the cell.
The channel information is assumed to be known at the
transmitter and the receiver and the transmission power is
equally allocated to each antenna. Each user can only access
one AP according to the minimum access distance criterion.
So the downlink channel ergodic capacity of the
given by
nth AP is
= NPC
P( N ) = NPC +
Where
(2
w=
d n is the distance between the user and the n AP, σ 2
th
is the variance of additive white Gaussian noise. According to
the relationship between channel capacity and transmission
power, the transmission power can be derived from (10)
)
)
w
.
N α −1
(
(13)
)
α /2
− 1 Lσ 2 R 4π
cE ( sn ) E ( g n )18α / 2
C /W
can be seen as a
transmission power is reversely proportional to the number of
APs, so there exists a reasonable value of N which depends
on the relationship between the value of
PC and w to
minimize the overall power consumption.
From
∂P ∂N = PC − (α − 1)wN −α
­ 2Cn /Wn − 1 Lσ 2 d nα ½
PT = Esn , g n Ed n ®
¾.
csn g n
¯
¿
when
(14)
Thus the best number of APs can be obtained from (14)
from the view of energy efficiency.
IV.
SIMULATION RESULTS
In this section, the numerical result of the AP deployment
design is given to evaluate the performance of the proposed
scheme. The simulation parameters are shown in Tableĉ.
TABLE I.
SIMULATION PARAMETERS
Parameters
Cell number
Cell Radius R
System bandwidth Bw
User number
Path loss exponent α
The standard deviation of shadow fading σ s
(11)
and
∂P ∂N = 0 , the optimal number of APs is
1α
2
(12)
constant in terms of N .
Under the same data rate requirement, minimizing the
overall power consumption can achieve the target of energy
efficiency and power saving. From (13), it can be seen that the
circuit power NPC increases with the number of APs, but the
g n = ¦ hn,l , Wn is the bandwidth allocated to nth
(
)
− 1 NLσ 2 E (d nα ) .
cE ( sn ) E ( g n )
C /W
Taking (9) and (11) into (12), the total power consumption can
be expressed as
l =1
AP ,
(2
+
N = ((α − 1)w PC ) .
­
P
§
H ·½
Cn = Esn , g n Ed n ®Wn log 2 ¨1 + T 2 H n H n ¸¾
© Lσ
¹¿
¯
(10)
­
§ PT csn g n ·½
¸
= Esn , g n Ed n ®Wn log 2 ¨¨1 +
2 α ¸¾
L
σ
d
n ¹¿
©
¯
L
P( N ) = NPC + NPT
(9)
Thus the optimal AP location is also obtained with the
optimal radius r0 .
Where
Assuming that all the users have the same rate
requirement and each AP has the same bandwidth, each AP
will have the same transmission power consumption. The total
power consumption in the cell is a function of the number of
APs N , which is
Fast fading
Rate requirement of the user
Value
1
1000m
10MHz
200
4
8dB
complex Gaussian
distribution with 0 mean
2Mbps
c meets c / d 0α = −78dB [14] (where reference
distance d 0 is 100m and α = 4 ). The users are distributed
uniformly in the cell and all the users have the same data rate
requirement.
Fig. 2 shows the AP distributions, which are located
uniformly on a circle.
1
User position
AP position
0.8
48
46
44
overall power (dBm)
The constant
Pc=- inf
Pc=27dBm
Pc=36dBm
42
40
38
36
0.6
34
0.4
32
0.2
30
0
1
2
3
4
5
6
the number of APs
7
8
9
10
-0.2
Figure 4. The total power consumption vs the number os APs
-0.4
Fig. 4 is the total system power consumption with the
number of APs. Using a different number of APs results in a
different optimal radius according to (9) and the simulation
results of Fig. 3. In Fig. 4, the APs are deployed based on the
optimal radius. When the value of PC is small (27 dBm in the
-0.6
-0.8
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Figure 2. The AP distributions in uniform user distribution scenario
Fig. 3 is the simulation result of the transmission power
(not including the circuit power) with AP’s radius. The optimal
radius value is taken as the lowest value of transmission power,
which is almost identical to the theoretical value in (9). For
example, with N = 4 the theoretical optimal radius is 0.6 km
and the lowest point in the figure is also 0.6km. When the
radius is equal to zero, which is means that all the APs are
located at the cell center, it is equivalent to the traditional
centralized multi-antennas system which consumes the largest
transmission power. The results show, therefore it can be seen
that using the DAS system can significantly reduce the
transmission power; for example, when N = 6 , the total
downlink transmission power is almost about 31dBm, which is
about 14dBm less than that of the CAS system. The simulation
results show that the transmission power can be reduced
greatly with optimal AP deployment design.
48
N=3
N=4
N=5
N=6
N=7
N=8
46
transmission-power (dBm)
44
42
38
36
34
32
0
0.1
0.2
0.3
0.4
0.5
radius
0.6
0.7
0.8
0.9
Figure 3. The transmission power vs AP radius
relative to that of PT (range from 37 dBm to 31 dBm in the
simulation), the overall power consumption is mainly decided
by circuit power and almost proportional to the number of APs,
so the reasonable number of APs cannot be very large. From
the view of power saving, it is recommended that the number
of AP is 1 or 2.
Note that when PC = 0 (- inf dBm), that is, the circuit
power is not considered, the total power is just transmission
power which is reversely proportional to the number of APs, If
the number of APs is larger than 8, there is little impact on
power saving (as shown in Fig. 4, from 8 APs to 10 APs the
total power is 31 dBm) but increases system costs. So the
optimal number of APs can be 7 in the simulation. Therefore it
can be seen that the circuit power of equipments has
significant effect on the number of APs. Both the circuit
power and transmission power must be considered when
designing the number of APs for practical networks.
V.
40
30
simulation), the total system power consumption declines
firstly and then increases. In Fig. 4, the optimal number of APs
is 4. If the value of PC (36 dBm in the simulation) is large
1
CONCLUSION
In this paper the optimal location and number of APs are
investigated to obtain the optimal system performance for
energy efficiency. An average minimum access distance is
proposed to obtain optimal AP distribution. Considering the
trade-off between the transmission power consumption and the
circuit power consumption, the optimal number of APs can be
obtained. The simulation results show that, with the proposed
AP deployment design, the transmission power can be reduced
greatly if the circuit power consumption is omitted.
Considering the circuit power consumption, the total system
power also can be saved if the optimal number of APs is used
for energy efficiency.
[8]
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