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Optimization of Femtocell Network Configuration
under Interference Constraints
Kwanghun Han,∗Youngkyu Choi,†Dongmyoung Kim,∗Minsoo Na,‡Sunghyun Choi,∗and Kiyoung Han§
∗School of Electrical Engineering and INMC, Seoul National University, Korea
†WiMAX System Lab, Samsung Electronics, Suwon, Korea
‡Institute of Network Technoloy, SK Telecom, Sungnam, Korea
§Communication Lab, Samsung Electronics, Suwon, Korea
Email: {khhan, ykchoi, dmkim}@mwnl.snu.ac.kr, minsoo.na@sktelecom.com, schoi@snu.ac.kr, kiyoung.han@samsung.com
Abstract—Femto BS (Base Station) is emerging as a key
technology to secure the coverage and capacity in indoor en-
vironments. However, since the existing macrocell network is
overlaid on femtocell networks utilizing the same set of frequency
channels, femtocell networks can originate severe co-channel
interference to the macrocell network unless the femtocell net-
work is carefully configured. Therefore, according to a desired
network-wide objective, we optimize the femtocell network with
constraints such that the service connectivity with a femto BS
is secured in the target indoor area while the signal emitted
out of the building, playing as interference to the outdoor users,
should be controlled with an appropriate strength in order not
to interrupt the communication between macro BS and outdoor
users. Each optimization problem is formulated as a mixed
integer programming, and as the results, we obtain not only
the transmit power and operational frequency channel of each
femto BS, but also the optimal femto BS-to-user association pair
at each geographical position.
I. INTRODUCTION
Femto BS (Base Station) is a small low-cost BS with a
short service range (i.e., 10 to 15 m), referred to as femtocell.
It is typically designed to serve under 10 users in indoor
environments such as small office and home. A femto BS is
typically connected with a macrocell network via a broadband
wired connection, e.g., an IP (Internet Protocol) network over
xDSL (x Digital Subscriber Line), or a dedicated backhaul
network. Today, it is strongly considered a practical candidate
solution to secure both the seamless indoor coverage and the
high network capacity. The emerging IMT-advanced candidate
systems including 3GPP LTE-advanced and IEEE 802.16m
also feature this femtocell technology [1]–[3].
Conventional outdoor BSs are referred to as macro BSs in
this paper. The functionality of femto BS is almost the same
as that of typical macro BS, while the price of femto BS can
be significantly lower because (1) a femto BS is expected to
serve a small number of users and (2) a relatively low transmit
power is enough to cover the service area. Such low cost of
the hardware is expected to make the femtocell technology
0This work is in part supported by Saumsung Electronics and the Ministry
of Knowledge Economy, Korea, under the Information Technology Research
Center support program supervised by the Institute of Information Technology
Advancement (grant number IITA-2009-C1090-0902-0006).
widely accepted since femto BSs can be bought in the market
by users and easily installed in a plug-and-play manner.
However, as more and more femto BSs are deployed in a
given area, unless the femtocell network is properly optimized,
the overall network capacity might be significantly compro-
mised due to the co-channel interference. Besides, since the
existing macrocell network is assumed to be overlaid on fem-
tocell networks utilizing the same set of operating frequency
channels, femtocell networks can originate severe co-channel
interference to the macrocell network if the configuration of a
femtocell network is not carefully managed. In the meantime,
a seamless coverage inside the target indoor area should be
also ensured. However, considering the expected huge number
of femto BSs, it is almost impossible to keep the network
optimized via the manual setting by a human engineer as done
in conventional cellular networks. Therefore, the femtocell
network is desired to be self-organizing such that the network
configuration automatically keeps updated by being aware of
the network environmental changes, e.g., addition/deletion of
neighboring femto BSs. Consequently, it is very important to
address the problem how to optimize the femtocell network
(specifically, configuring the transmit power and frequency
channel of femto BS) in a systematic manner.
In the literature, there has been some related work, es-
pecially, in the context of WLAN AP deployments [4]–[6].
However, the considered problem is quite different from the
WLAN AP deployment problems due mainly to the co-
channel interference to/from macrocells. Moreover, none of
the existing schemes deals with BS location determination,
power control, frequency channel allocation, and user asso-
ciation altogether , and with Shannon’s capacity directly as
an optimization objective. We formulate joint optimization
problems, which yield the transmit power, frequency channel,
and deployment location for each femto BS along with the
desired femto BS-to-user association pair at each geographical
position.
The rest of the paper is organized as follows: In Section II,
we describe the system model. Section III formulates the
optimization problems, and then the performance results are
discussed in Section IV. We conclude the paper in Section V
along with the remark on our ongoing work.
2
Fig. 1. Three simulation scenarios.
II. SY ST EM MO DE L
A. Macrocell and Femtocell Networks
We assume WiBro, i.e., a Korean version of Mobile
WiMAX, for our system modeling and evaluation [7]. The
macrocell network is modeled by a conventional multi-cell
honeycomb structure. Each single macrocell is divided into
three sectors denoted by S0, S1, and S2 as shown in Fig. 1,
and a sector labeled by Sx(x= 0,1,2) uses the (x+ 1)th
frequency channel out of three available channels. Assuming
that both macrocell and femtocell networks are perfectly
synchronized, the macro BS plays as a downlink interferer
to the users in a femtocell network.
The architecture of the femtocell-based enterprise network
in consideration is illustrated in Fig. 2. A femtocell network
is composed of a number of femto BSs and a WSM (Wire-
less System Management) server, which is a network entity
in charge of the optimization of femto BSs’ configuration.
The WSM server jointly optimizes the radio parameters of
the femto BSs, e.g., transmit power and frequency channel,
according to a given network-wide objective. Here, we assume
that the WSM server has no authority for configuring the
radio parameters of macro BS, and hence, the interference
from macrocell network is an uncontrollable factor in the
optimization of the femtocell network. Throughout this paper,
we assume that the WSM server has the knowledge of all
the required information, e.g., the channel gains between each
BS and users, required for the network optimization. How to
acquire such information should be a separate research topic.
We assume that the building, within which the femtocell
network is deployed, is a rectangular parallelepiped with a
side length of Wbuilding as its first floor plan is illustrated in
Fig. 3, and has three floors as shown in Fig. 2. We assume
that all the indoor users are associated with one of femto
BSs, and all the outdoor users are served by macro BSs.
Based on these assumptions, we consider the outdoor region
surrounding the building with the width of Wstreet/2to assess
the impact of the interference from the femtocell network on
the signal quality, e.g., SINR (Signal to Interference plus Noise
Ratio), experienced by outdoor users. We assume that the
nine equidistant candidate locations, where femto BSs can be
Fig. 2. Femtocell network architecture.
installed, exist on each floor of the building as shown in Fig. 3,
and the indices of candidate locations at the same horizontal
position on each floor are labeled as x/y/z, where x,y, and z
are the index of the 1st, 2nd, and 3rd floor’s candidate location,
respectively.
B. TPs (Testing Points)
In order to evaluate the performance of the target area, i.e.,
the indoor and outdoor regions, in a mathematically efficient
manner, we consider the notion of TP (Testing Point), which
is used to measure a continuous object via quantization. The
target area can be divided into many square grids and a TP
is located at the center of each grid. A particular metric
value corresponding to a TP represents the metric at all the
other points within the square grid, which the TP belongs
to. For instance, the channel gain between a femto BS and
a user is represented by the channel gain between the TPs
of two grids, which the femto BS and the user belong to,
respectively. Specifically, we use the term of internal TP
(ITP) and external TP (ETP) to differentiate the indoor users
from the outdoor users since different constraints need to be
considered depending on the location of a user. Throughout
the rest of the paper, we consider that the SINR at every
ITP should be at least −3dB to meet the requirement for
the indoor coverage, and the degradation of SINR due to the
overall interference from the femtocell network observed at
every ETP should not be larger than 1 dB.
C. Antenna and Channel Models
Macro BSs are assumed to use directional antennas for
sectorization. The antenna gain, A(in dBi), is given as a
function of the angle θbetween a given location of interest
and the predefined reference direction.
A(θ) = −min "12 µθ
θ3dB ¶2
, Am#,−180 ≤θ≤180,
where Amis 20 dBi and θ3dB is 70 degrees. On the other
hand, both femto BSs and users are assumed to use an omni-
directional antenna, whose gain amounts to 2 and −1dBi,
respectively. Different channel models are considered depend-
ing on the point-to-point link of particular interest since the
indoor channel characteristic is quite different from that of
outdoor channel. More specifically, we consider four different
3
Fig. 3. Candidate locations for femto BS deployment and TPs covering both
indoor and outdoor regions.
channel models for the channel link 1) between macro BS and
outdoor user; 2) between macro BS and indoor user (including
femto BS); 3) between femto BS and indoor user; 4) between
femto BS and outdoor user. Basically, all the channel models
are based on the ITU-R M.1225 model [8].
First, the path loss P L between a macro BS and an outdoor
user is expressed as follows:
P L = 40 log10 (d/1000) + 30 log10 (f) + 49,
where dis the distance from the macro BS (in meters) and f
is the center frequency of the channel adopted by the macro
BS (in MHz). In the case of a WiBro network, three frequency
channels are available at the 2.3 GHz band. Second, the path
loss between a macro BS and an indoor user (including femto
BS) is given as follows:
P L = 40 log10 (d/1000) + 30 log10 (f)+49+σ,
where σis the penetration loss arising when the signal comes
into (goes out of) the building. We assume σ= 12 dB while it
actually varies depending on whether the signal traverses the
concrete wall or the glass window. Third, the path loss between
a femto BS and an indoor user is represented as follows:
P L = 37 + 30 log10 (d) + 18.3n((n+2)/(n+1)−0.46),
where nis the number of floors placed between the transmitter
and the receiver. On the same floor, nis zero. Last, the path
loss between an femto BS and an outdoor user is represented
as follows:
P L = 37 + 30 log10 (d) + 18.3n((n+2)/(n+1)−0.46) +σ,
where nand σare also the number of floors and the penetra-
tion loss, and we determine the value nas if all the outdoor
users are located on the first floor. Using these equations, we
generate the channel gains without considering the shadowing
and fast fading.
TABLE I
DEFI NIT IO N OF NOTATI ON S
Notation Definition
JiSet of all the internal testing points (ITPs)
JeSet of all the external testing points (ETPs)
ASet of candidate locations for installing femto BSs
ESet of macro BSs
FSet of frequency channels
gjaf Channel gain between TP jand candidate location afor
frequency channel f
g0
jef Channel gain between TP jand Macro BS efor frequency
channel f
zaf 1if the femto BS is deployed at location awith frequency
channel f, zero otherwise
paf Normalized transmit power of femto BS awith frequency
channel f,0≤paf ≤1
xjaf 1if ITP jis associated with femto BS awith frequency
channel f, zero otherwise
III. PROB LE M FOR MU LATI ON
We consider two optimization problems specified by differ-
ent objectives: 1) maximizing the sum of femto BS transmit
powers, referred to as ‘MaxPwr Problem’ and 2) maximizing
the sum of Shannon capacity at each ITP, referred to as
‘MaxCap Problem.’ Since we are dealing with the non-linear
equations for objectives and constraints, it is quite challenging
to formulate each optimization problem with MIP (Mixed
Integer Programming). We in this section present the detailed
procedure of the problem formulation. A set of notations for
the optimization variables used during the problem formulation
is presented in Table I. Finally, the solution of each optimiza-
tion problem yields 1) where to deploy femto BSs, 2) transmit
power of each femto BS, 3) frequency channel of each femto
BS, and 4) desired association at each ITP, simultaneously.
A. MaxPwr Problem
Intuitively, the inbuilding coverage can be assured by letting
the femto BSs use high transmit powers. For example, if we
consider the case that the greedy BSs, which want to maximize
their own signal quality, compete each other, they will try to
increase their transmit powers. This motivates us to consider
the objective of maximizing the total sum of femto BSs’
transmit powers:
max X
a∈A X
f∈F
paf .
In case of conventional cell-planning problems, this objective
is trivial because every BS simply uses its maximum transmit
power Pmax. In our case, however, the transmit power of
femto BS is constrained due to the requirement that the SINR
degradation observed at each ETP after the deployment of a
femtocell network, should be limited.
Since the transmission power of a certain femto BS plays
as an interference to users associated with other femto BSs,
the MaxPwr problem does not necessarily optimize the per-
formance with respect to the SINR. In spite of the inherent
limitation of the MaxPwr problem, it is meaningful to look at
4
this objective as an initial step thanks to the linear formulation
easiness.
Now we express the constraints mathematically one after
another. First, we assume that at most M(≤ |A|) femto BSs
can be deployed and each femto BS uses only one frequency
channel due to the assumption of no sectorization:
X
a∈A X
f∈F
zaf ≤M, (C1)
X
f∈F
zaf ≤1,∀a∈ A.(C2)
In addition, there exist both minimum and maximum bound
for transmit power:
C0zaf ≤paf ≤zaf ,∀a∈ A, f ∈ F,(C3)
where C0,Pmin/Pmax .Pmin and Pmax are the minimum
and maximum transmit powers of a femto BS, respectively. A
normalized power paf is 0 if zaf is 0, and paf ranges from
C0to 1, otherwise. Accordingly, if a femto BS should not be
deployed at the location a,zaf for all f∈ F are set to zero.
After the optimization problem is solved, the actual transmit
power Paf of femto BS ais determined by paf Pmax.
Assuming that each ITP corresponds to a user, any user is
allowed to associate with only one femto BS in one frequency
channel:
X
a∈A X
f∈F
xjaf = 1,∀j∈ J i,(C4)
X
f∈F
xjaf ≤1,∀j∈ J i, a ∈ A,(C5)
xjaf ≤zaf ,∀j∈ J i, a ∈ A, f ∈ F.(C6)
In order to guarantee the coverage, we need to maintain
both SNR and SINR of ITPs over the predefined threshold.
First, the SNR constraint with a threshold µis formulated as
follows:
Inf(1 −xjaf ) + gjaf Pmax paf
N0+P
e∈E
g0
jef PMacro
≥µ, ∀j∈ J i, a ∈ A, f ∈ F
(C7)
where Inf is a virtually infinite value; N0is the background
noise power; and P
e∈E
g0
jef PMacro is the total interference power
from macro BSs. The SNR constraint is valid only for ITP j,
which is associated with femto BS ausing frequency channel
f, namely, xjaf = 1. Note that if xjaf = 1, it also holds
that zaf = 1 by (C7). For this purpose, Inf(1 −xjaf )is
introduced because (C8) can be safely ignored unless xjaf is
1. This technique is frequently used during our formulation.
Definitely, it can be transformed to the linear inequality
constraint1for MIP:
Inf ·xjaf −gjaf Pmax paf ≤Inf −µÃN0+X
e∈E
g0
jef PMacro !.
1Other fractional constraints can be transformed to a linear form, similarly.
(a) Incorrect region: Intersection of affine functions.
(b) Correct region: Union of affine functions by selection tech-
nique.
Fig. 4. Linear approximation of −log(x).
While the SNR constraint looks unnecessary if the SINR con-
straint is also considered, we deliberately add this constraint
to reduce the solving time by shrinking the solution set.
Next, we consider the SINR constraint of ITP. Compared
with the above SNR constraint, it additionally considers the
cochannel interference from other femto BSs as follows:
Inf(1 −xjaf ) + gjaf Pmax paf
N0+P
e∈E
g0
jef PMacro +P
b∈A\a
gjbf Pmax pbf
≥γ,
∀j∈ J i, a ∈ A, f ∈ F,(C8)
where γis the SINR threshold for the coverage guarantee.
Another major concern is minimizing the impact of the
interference from femtocell network on the outdoor users, who
are connected to macro BSs. To meet this requirement, we
restrict the SINR degradation at each ETP junder 1 dB:
max
e∈E ³g0
jef PMacro ´+Inf (1 −yj f )
N0+P
e∈E0
g0
jef PMacro +P
a∈A
gjaf Pmax paf
≥κj,
E0,E\ arg max
e∈E ¡g0
jef PMacro ¢,∀j∈ J e, f ∈ F,(C9)
where κjis the minimum bound of the SINR at ETP j
experienced after the deployment of femtocell network. Since
the original SINR at ETP jcan be precomputed, κjcan be
also predetermined such that κj(dB) is equal to the original
SINR (dB) minus 1 dB. Note that ETP jis assumed to be
attached to macro BS arg max
e∈E³g0
jef PMacro ´. Since the SINR
constraint is valid only for the single frequency channel used
by the sector, which is associated by ETP j,Inf (1 −yj f )is
introduced to safely ignore the SINR constraint if yjf = 0.
To ensure that yj f = 1 for a certain frequency channel, an
additional constraint for auxiliary variable yjf is considered
as follows:
X
f∈F
yjf = 1,∀j∈ J e.(C10)
5
Finally, the MaxPwr problem is formulated as follows:
max X
a∈A X
f∈F
paf
s.t.
C1, C2, C3, C4, C5, C6, C7, C8, C9, C10.
As addressed previously, the MaxPwr problem does not nec-
essarily maximize the inbuilding capacity since the impact of
cochannel interference from other femto BSs is not reflected
to the objective. For this reason, we consider the MaxCap
problem in the next section.
B. MaxCap Problem
The achievable capacity at an ITP is given by Shannon
capacity, i.e., log2(1 + SINR), and hence we need to incor-
porate this equation to the objective function to address the
inbuilding capacity optimization. However, since log function
is nonlinear, it is impossible to directly deal with it via
MIP. Alternatively, we take the approach to approximate the
nonlinear Shannon capacity equation into piecewise linear
functions, which can be managed by MIP.
To do so, we first look at the characteristic of Shannon
capacity assuming that ITP jis associated with femto BS a:
log2(1 + SI N R)
= log ÃN0+X
e∈E
g0
jef PMacro +X
b∈A
gjbf Pmax Pbf !
−log
N0+X
e∈E
g0
jef PMacro +X
b∈A\a
gjbf Pmax Pbf
.
As seen above, Shannon capacity is decomposed into log and
−log function, which takes the sum of linear variables as the
input. Therefore, if we can approximate the log and −log into
linear functions, Shannon capacity is also approximated into
linear functions. Fortunately, log is a concave function, which
can be easily approximated as the sum of piecewise affine
functions:
anx+bn≤log(x)≤anx+bn+ ∆,
where nis an index variable and ∆is a positive value.
Specifically, the parameters of each line and the number of
lines can be adjusted according to the required precision. By
using this approximation technique, we can represent log part
of Shannon capacity at ITP jas follows:
Sj≤cnÃN0+X
e∈E
g0
jef PMacro +X
b∈A
gjbf Pmax Pbf !
+dn+Inf (1 −xjaf ) + W, ∀j∈ J i, a ∈ A, f ∈ F , n,
(C11)
where Sjis a real variable which delegates the intersection
region of the affine functions; cnand dnare approximation
parameters; and Wis the offset value to make Sjpositive.
Inf(1 −xjaf )term is for a selection technique.
(a) Before the deployment of femtocell network.
(b) After the deployment of femtocell network.
Fig. 5. Spatial distribution of SINR illustrated by using colormap at
1st/2nd/3rd floors. Each rectangle corresponds to a floor, and the boundary
region of the left-most rectangle represents the street region right next to the
building.
While log(x)can be directly approximated through simple
intersection, −log(x)cannot be done as shown in Fig. 4(a),
but can be approximated by getting the union region as shown
in Fig. 4(b). To do so, we need to select a proper affine function
depending on domain x. More specifically, we will add the
virtual infinite value to the other affine functions except the
proper affine function to safely ignore them. Accordingly, we
take the selection technique again, and hence, an indicator
variable vjn is introduced to choose the proper affine function,
which gives the biggest value for a given input. Finally, we
obtain the inequality conditions given as follows:
Qj≤ −cn
N0+X
e∈E
g0
jef PMacro +X
b∈A\a
gjbf Pmax Pbf
−dn+Inf(2 −vjn −xjaf ) + W, ∀j∈ J i, a ∈ A, f ∈ F, n,
(C12)
where Wis the offset used to make Qjpositive. A constraint
for vjn is also required:
X
n∈N
vjn = 1,∀j∈ J i.(C13)
Finally, we can define the MaxCap problem as follows:
max X
j∈J i
(Sj+Qj)
s.t.
C1, C2, C3, C4, C5, C6, C7,
C8, C9, C10, C11, C12, C13.
The MaxCap problem directly addresses the improvement
of inbuilding SINR, and hence, it effectively optimizes the
femtocell network from the viewpoint of the site performance.
6
Fig. 6. The CDF of SINR, when the building is located at L#1.
TABLE II
SOLUTIONS OF MAX PWR AND MAXCA P OP TIM IZ ATION P ROB LE MS,
WH EN TH E BUI LD ING I S LO CATE D AT L#1
BS
index
MaxPwr MaxCap
Freq. Ch. Power (mW) Freq. Ch. Power (mW)
2 3 0.01 3 0.08
4 1 0.01 1 0.06
6 2 0.01 2 0.01
8 2 0.01 2 0.05
11 3 0.01 1 0.01
13 1 0.02 1 0.08
15 2 0.03 2 0.02
17 2 0.01 2 0.01
20 3 0.13 3 0.05
22 1 0.18 1 0.64
24 3 0.05 2 0.01
26 2 0.13 2 0.04
IV. PERFORMANCE EVALUATION
In this section, we compare both the MaxPwr and MaxCap
problems. Note that no other algorithms in the literature
can satisfy all the constraints in consideration, so they are
not compared. We are interested in the overall performance
improvement of the target inbuilding area and the overall
performance degradation of outdoor region. As a result, we
expect to obtain the theoretical performance bound of the
femtocell deployment optimization with the proposed objec-
tives. For this purpose, we evaluate the cumulative distribution
function (CDF) of the SINR measured at all the grids.2The
SINR at an outdoor grid is defined as the maximum SINR,
which can be observed from one of macro BSs, assuming
that the user selects the BS to associate with according to
the maximum SINR policy. Without femtocell network, the
SINR at any inbuilding grid is determined exactly in the same
manner as the outdoor SINR. When the femtocell network
is employed, the SINR at each inbuilding grid is defined as
the maximum SINR, which can be observed from one of
femto BSs, assuming that the indoor user also follows the
maximum SINR policy for its association. From the CDF of
2The grid size for SINR measurement is not necessarily equal to that used
to build TPs since it has nothing to do with the problem complexity.
SINR, we can obtain various interesting information, e.g., the
probability of coverage hole due to SINR outage, the statistics
of transmission rate, the performance degradation of outdoor
users due to the interference from femtocell network.
For the numerical analysis, we use CPLEX as the MIP
solver [9]. We consider two-tier cellular environment for the
macro network as presented in Section II and the cell radius
is assumed 800 m. The transmit power PMacro of macro BS is
fixed to 20 W and the maximum transmit power Pmax of femto
BS is assumed 100 mW. We consider that the building size
Wbuilding =50 m and street size Wstreet =30 m, respectively.
We consider three building location cases, where a building
in cell 0 is located at different positions within the same cell,
i.e., L#1, L#2, and L#3 indicated in Fig. 1. The reason why we
consider these three cases is that each position holds distinctive
features of interference originating from macro BSs: in the
case of L#1, the signals from sector 1 of cell 0, sector 2 of
cell 0 and sector 0 of cell 2 are almost of the same strengths,
and hence, it is likely that whatever a frequency channel is
chosen, the outdoor users operating at that frequency channel
would be found in the vicinity of the building. In the case of
L#2, the signal levels both from sectors 1 and 2 of cell 0 are
relatively stronger than that from sector 0 of cell 2, and the
strengths of two signals are almost the same. Therefore, it is
highly probable that there is no outdoor user using frequency
channel 1. For L#3, the signal level from sector 0 of cell 0 is
the strongest one, and hence, most outdoor users around the
building will operate in frequency channel 1.
Among these three locations, we present the results obtained
only for L#1 and L#2. The major difference between L#2 and
L#3 cases is whether the number of frequency channels, which
are mainly used by the outdoor users around the building,
is 2 or 1. Note that, at building location L#3, the degree of
freedom in determining the radio parameters of femto BS will
increase, since the constraint, i.e., limiting the interference on
the outdoor users, is easily satisfied if a frequency channel
dominantly used by the outdoor users is avoided by femto
BSs.
For our evaluation, we exclude the decision problem of the
location of femto BSs, which is less relevant to our major
interest, namely, an automatic radio parameter configuration
of femto BSs. To do so, we fix M= 12 such that the four
locations at each floor are considered including the location
indices, i.e., 2, 4, 6, 8, 11, 13, 15, 17, 20, 22, 24, and 26. For
other location indices a,zaf is fixed to zero for all f∈ F. For
the evaluation of MaxPwr and MaxCap problems, we place
an ITPs on each of 2-by-2 m grids, which cover the whole
inbuilding region.
Fig. 5 shows the effect of femtocell network configured by
MaxCap optimization via illustrating the spatial distribution of
SINR when the building is located at L#1. While the entire
indoor region of the building experiences SINR under −5dB
before deploying the femtocell network due to the heavy
penetration loss of the signal from macro BSs, the femtocell
network is observed to boost up the SINR of the whole indoor
area to over −3dB. Looking at the color of the street region
7
Fig. 7. The CDF of SINR, when the building is located at L#2.
TABLE III
SOLUTIONS OF MAX PWR AND MAXCA P OP TIM IZ ATION P ROB LE MS,
WH EN TH E BUI LD ING I S LO CATE D AT L#2
BS
index
MaxPwr MaxCap
Freq. Ch. Power (mW) Freq. Ch. Power (mW)
2 3 0.01 1 100
4 1 0.01 1 0.01
6 1 20.11 1 0.01
8 2 0.22 2 0.04
11 3 0.03 3 0.08
13 1 0.01 2 0.01
15 1 100 2 0.01
17 3 0.01 1 0.04
20 1 60.97 1 0.01
22 1 59.95 1 0.06
24 1 100 2 0.01
26 1 60.98 1 14.74
surrounding the 1st floor, we see that there is no significant
degradation in the SINR the outdoor users experience due to
the deployment of the femtocell network.
The solutions given by MaxPwr and MaxCap optimization
at L#1 are listed in Table II. The transmit power value (in mW)
is rounded off to the second decimal place. Both solutions
exploit all the frequency channels because all the frequency
channels are used by the outdoor users near the building.
That is, if any femto BSs in any frequency channel use large
transmission power values, the SINR constraints of some ETPs
will not be satisfied. Consequently, all the femto BSs use small
transmission power values for both MaxPwr and MaxCap.
Fig. 6 shows that the SINR of the indoor region is dramatically
improved by both optimizations. Indeed, the SINR degradation
at the outdoor region is observed be to less than 1 dB, which
was given as the requirement. Interestingly, we can observe
that MaxCap improves the region with the low-to-mid SINR
(less than 15 dB) more efficiently than MaxPwr optimization.
The solutions given by MaxPwr and MaxCap optimization
at L#2 are listed in Table III. The CDF of the SINR is also
depicted in Fig. 7. For both cases, some femto BSs operating
in frequency channel 1 use large transmission power values,
since all the outdoor users on the street use either frequency
channel 2 or 3 to satisfy their QoS requirements since sectors 1
and 2 use frequency channels 2 and 3, respectively. Compared
with the previous case, the most noteworthy observation from
Fig. 7 is that the gap of the indoor SINR performance between
MaxPwr and MaxCap is quite remarkable. This phenomenon
can be explained as follows: from the discussion about the
implication according to the building location, we can infer
that it plays more strictly at L#1 than at L#2 the constraint
that the SINR degradation of the outdoor users should be
limited. Therefore, MaxPwr optimization at L#2 can have
more chances to increase the transmit power of femto BS
without violating the constraints. However, as we discussed the
limitation of MaxPwr optimization earlier in its formulation,
the higher transmit power of the entire BSs does not neces-
sarily yield the network-wide configuration optimized from
the SINR perspective. Indeed, Table III shows that MaxPwr
optimization configures relatively high transmit power to the
femto BS indices including 20, 22, 24, and 26, which are
located at the same floor.
V. CONCLUSION
We formulated the femtocell network optimization problems
with constraints on the inbuilding coverage and the interfer-
ence given to the outdoor users for two different objectives.
The MaxPwr and MaxCap problems aim to maximize the
capacity of the target indoor area by maximizing the sum of
femto BSs’ transmit power and by maximizing the sum of ap-
proximated cell capacity respectively. Through the numerical
results based on a widely used channel model, we verified the
benefit of the femtocell network and analyzed the solutions
obtained for each optimization objective. Our results show
the theoretical performance bound by network optimization in
such an environment. As future work, we plan to develop low
complexity algorithms and tackle the network-wide throughput
optimization problem considering the intracell and network-
wide fairness policy.
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