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Pseudo-Handover Based Power and Subchannel
Adaptation for Two-tier Femtocell Networks
Hongjia Li, Xiaodong Xu, Dan Hu, Xin Chen, Xiaofeng Tao and Ping Zhang
Wireless Technology Innovation Institute
Key Laboratory of Universal Wireless Communication, Ministry of Education
Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China.
Email: lihongjia@mail.wtilabs.cn
Abstract—The two-tier femtocell network is comprised of
a central macrocell underlaid with shorter range femtocell
hotspots. Due to the universal frequency reuse, this kind of
new system architecture brings about urgent problems of the
interference management and the resource allocation. Motivated
by these problems, the following contributions are made in this
paper: 1) a novel joint power and subchannel allocation problem
for Orthogonal Frequency Division Multiple Access (OFDMA)
downlink based femtocells is formulated on the premise of
minimizing Femto BSs’ radiating interference; 2) a pseudo-
handover based scheduling information exchange method is
proposed to avoid the collision interference; 3) an iterative scheme
of subchannel allocation and power control is proposed to solve
the formulated problem, which is an NP-complete problem.
Through simulations and comparisons with three other schemes,
the proposed scheme shows better performance in reducing
interference and the Femto BS’s transmit power, and improving
the spectrum efficiency.
I. INTRODUCTION
Femtocell, as a green radio technique, processes characteris-
tics of lower power and superior indoor experience for users.
So a significant interest has focused on the femtocell, also
known as Home NodeB (HNB) or Home enhanced NodeB
(HeNB) in the 3GPP standardization [1] [2].
In two-tier femtocell networks, femtocells are underlaid in
the coverage of the macrocell, which brings many urgent
challenges to the architecture of current cellular systems.
The co-tier co-channel interference among femtocells and the
cross-tier co-channel interference between the femtocell tier
and the macrocell tier is one of the most urgent challenges.
Interference level splitting results in [2] show that the co-tier
interference and cross-tier interference have severe impact on
the capacity and coverage of femtocell networks.
In order to address the aforementioned problem, different
schemes have been proposed in the prior art. In [3]- [5], con-
tributions are made on the basis of the frequency partitioning
scheme, in which orthogonal frequency bands are allocated to
the femtocell tier and the macrocell tier respectively. However,
spectrum efficiency is the key problem of these schemes, and
hence the universal frequency reuse scheme [6] is preferable
both in the industry area and the research area.
In the universal frequency reuse scheme, how to avoid
interference through effective resource management and in-
terference management schemes are critical requirements for
the femtocell configuration. In [7], the authors utilize a time-
hopped CDMA scheme with universal frequency reuse in its
uplink system capacity analysis, which is in fact equivalent to
splitting the resource in the time domain instead of splitting it
in the frequency domain. In [8], the authors present a Dynamic
Frequency Planning (DFP) that takes Femto users (FUEs) as
Macro users (MUEs) to operate conventional resource allo-
cation. In [9], the authors proposed a decentralized resource
allocation scheme for the OFDMA downlink of the two-tier
femtocell networks, where each femtocell randomly selects a
subset of available OFDMA resources for transmission.
But many problems still need to be addressed:
1) Many schemes of prior literatures are on the basis of the
provision of co-tier and cross-tier information exchange, which
has potential benefits in allowing femtocells to take account
of uplink and downlink conditions at nearby the Macro Base
Station (MBS) and other Femto Base Station (FBSs) when
configuring power and resources to be used in uplink and
downlink [10]. But how to implement the information exchang-
ing procedure, considering the cost of overhead, the cross-tier
and co-tier synchronization and compatibility with LTE and
LTE-A systems, is not well discussed in prior works.
2) Available researches focus on improving the performance
of the overall system. In the femtocell networks, however, it is
important to improve the performance not only of the overall
system, but also of the specific non-CSG [10] MUEs which
are in the femtocell coverage.
3) Since Macrocell is the infrastructure of mobile commu-
nications, the service quality of MUEs should be guaranteed
as a priority, which means that femtocell should adjust its
resources, e.g., power and subchannels, to meet the macro
cellular link quality when its links interfere macro cellular
links.
This paper firstly formulates a novel resource allocation
problem, the objective of which is to minimize the co-tier and
cross-tier interference. Then, a co-tier and cross-tier schedul-
ing information exchange procedure based on the proposed
pseudo-handover method is designed, considering the cost
of overhead and compatibility. Finally, based on the pseudo-
handover information exchange scheme, this paper proposes an
iterative scheme to solve the formulated problem. Without loss
of generality, the rest of this paper focuses on the downlink and
IEEE WCNC 2011 - Network
978-1-61284-253-0/11/$26.00 ©2011 IEEE 1797
is organized as follows. Section II describes the system model
and the formulated problem. Section III depicts the proposed
scheme, together with important practical issues. Section IV
provides the setup of the simulation scenario and performance
results of the proposed scheme compared with three other
schemes. Finally, Section V wraps up the conclusion.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system bandwidth is divided into orthogonal sub-
carriers, which are in turn combined into Ngroups, known
as resource blocks or subchannel. The subchannel set shared
by the macrocell and femtocells is defined as Ncand the
bandwidth of each subchannel is equal to B.
In the following, femtocell kis taken as the femtocell
of interest to elaborate the proposed scheme. Define Nu
k
as the active FUEs in femtocell k. MUEs in the vicinity
of femtocell k can be interfered by the co-channel FUEs
camping on femtocell k, the set of which is defined as SM.
Correspondingly, the interference power received by any MUE
in set SMcan be represented as
ζcr (m, n)=n∈Nc
Pn
kˆgn
k, ¯m,∀¯m∈SM,(1)
where ˆgn
k, ¯mis the path gain from the FBS of femtocell k to
MUE ¯m(¯m∈SM) on subchannel n, and ˆgn
k, ¯mis set to zero if
¯m/∈SM;N0is the noise spectrum density; Pn
kis the transmit
power of the FBS of femtocell k on subchannel n.
Similarly, SFis defined as the set of co-channel FUEs
interfered by the FBS of femtocell k. Then, the interference
power received by any FUE in set SFcan be represented as
ζco ¯
k, n=n∈Nc
Pn
kˆgn
k,¯
k,∀¯
k∈SF,(2)
where ˆgn
k,¯
kis the path gain from the FBS of femtocell k to
the FUE ¯
k(¯
k∈SF) on subchannel n,andˆgn
k,¯
kis set to zero
if ¯
k/∈SF.
Therefore, considering minimizing the interference to neigh-
boring co-channel UEs (including MUEs and FUEs) and
satisfying the camped FUEs’ data rate requirements, i.e.,
Ri,i ∈Nu
k, the minimizing radiating interference problem
of femtocell k can be formulated as
min ζcr (¯m, n)+ζco ¯
k, n,∀¯m∈SM,∀¯
k∈SF
s.t. n∈Nc
iBlog (1 + ϑ(k, n)) ≥Ri,∀i∈Nu
k.
Pn
k≥0
(3)
As for (3), ϑ(k, n)is the Signal to Interference plus Noise
Ratio (SINR) of the FUE using the subchannel nin femtocell
k, which is represented as
ϑ(k, n)= Pn
kgn
k
In
k+BN0
,(4)
where gn
kis the path gain from the FBS of femtocell k to the
FUE using subchannel n; In
kis the interference power received
by the FUE using subchannel nin femtocell k, which contains
the interference from MBSs and the interference from FBSs
in its neighboring femtocells. Then, In
kcan be represented as
In
k=m∈ˆ
SM
Pn
mgn
m,k+f∈ˆ
SF
Pn
fgn
f,k,(5)
where ˆ
SMand ˆ
SFare sets of MBSs and FBSs that cause co-
channel interference to femtocell k, respectively; Pn
mand Pn
f
are the transmit powers of MBSs and FBSs on subchannel nin
set ˆ
SMand ˆ
SFrespectively; gn
m,k is the path gain from MBS
m(m∈ˆ
SM) to the FUE using subchannel nin femtocell k;
gn
f,k is the path gain from FBS f(f∈ˆ
SF) to the FUE using
subchannel nin femtocell k.
In essence, the formulated problem (3), which is to min-
imize the interference radiated from every femtocell, is to
jointly allocate subchannel and power according to the FUEs’
data rate requirements. However, to obtain the optimal solu-
tions is restricted by the following reasons:
1) Because SM,SF,ˆgn
k, ¯mand ˆgn
k,¯
kin (3) is hard to be
acquired by the FBS of femtocell k, the interference to its
neighboring victims is difficult to be known the FBS of
femtocell kin practice;
2) (3) is an NP-complete combinatorial problem [11], which
cannot be solved in polynomial time.
Therefore, the PHO based power and subchannel adaptation
scheme is proposed and introduced in Section III.
III. PSEUDO-HANDOVER BASED POWER AND
SUBCHANNEL ADAPTATIO N SCHEME
A. Pseudo-Handover based Scheduling Information Exchange
As shown in Fig.1, FUE (2,2) and MUE 1, which are
non-CSG (Closed Service Group) users of femtocell 1, lie
in the coverage of FBS1. If FBS1 allocates subchannels
occupied by FUE (2,2) or MUE1, collision interference can
jam the communication of them. In order to avoid the collision
interference, FBS1 should find out occupied subchannels of
the non-camping UEs in its coverage at first. Therefore,
we propose the Pseudo-Handover based scheduling-message
exchanging method.
Fig. 1. Collision interference scenario.
Fig.2 shows an applicable femtocell architecture compatible
with the LTE-Advanced system, where an intermediate entity
called Femto gateway (GW) is located between FBSs and
the mobile Core Network (CN). It connects the FBSs and
CN through wired way. The interfaces between FBSs and
Femto GW, and the interface between Femto GW and MME/S-
GW [12] are all S1 interface [12]. In one MBS coverage
area, X2 interface [12] exists between Femto GW, which can
be seen as a ”virtual” MBS, and the MBS. Seen from the
femtocell architecture, the Pseudo-Handover is executed in
the Radio Access Network (RAN), not referring to Mobility
1798
Management Entity (MME), which is de facto a significantly
reduced version of the regular handover procedure.
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Fig. 2. An applicable femtocell architecture.
As same as the regular handover procedure [13], UEs
start searching for femtocells when they are in their vicinity.
However, because femtocells only provide services to their
CSG users, performing a handover in the two-tier femtocell
networks is not always a possible option. This feature can be
utilized to execute a control plane handover for co-tier and
cross-tier scheduling information exchanges.
As shown in Fig.3, the cross-tier Pseudo-Handover proce-
dure is presented. When any MUE or FUE steps into the
coverage of its non-camping femtocell, i.e., the Received
Signal Strength (RSS) of a neighboring cell pilot plus a given
threshold stronger than the RSS of the serving cell pilot, the
UE judges whether it is in the CSG according to the received
Physical Cell Identity (PCI) and Cell Global Indicator (CGI)
from the FBS [13]. If it is a CSG user, the regular handover is
triggered; or else, the pseudo-handover is triggered as shown
in Fig.3. In the procedure of pseudo-handover, every FBS sets
up and maintains the table containing the IDs of non-CSG
interferers (hereafter, we call them pseudo-handover users) and
their scheduling messages, which are obtained in the process
of Pseudo-Handover.
Seen from Fig.3, FBSs do not provide data services for
pseudo-handover user, but complete handover initialization
procedure plus scheduling information exchanges in the con-
trol plane. As indicated by Fig.3, the procedure of the pseudo-
handover ends in the Femto GW, and does not refer to the
MME/S-WG to minimize the cost of overhead.
Furthermore, the only difference between the cross-tier
Pseudo-Handover and co-tier Pseudo-Handover is that infor-
mation transmission between FBS and Femto GW is through
S1 interface, whereas information transmission between MBS
and Femto GW is through X2 interface.
B. Subchannel and Power Adaptation Scheme
Having received the scheduling message, the FBS can find
out subchannels which are being used by pseudo-handover
users, and delete these subchannels from its candidate sub-
channel set Ncto construct a new candidate subchannel set
ˆ
Nc. So the collision interference to UEs in the coverage of
femtocells is avoided, which means the main interference to
MUEs in SMand FUEs in SFis eliminated. Long distance
or bad link qualities between the remainder UEs in SMor SF
and their interferers, i.e., ˆgn
k, ¯mand ˆgn
k,¯
k, makes the interference
between them relatively small. So the strength of interference
Fig. 3. Procedure of cross-tier pseudo-handover.
radiated by FBSs depends on their transmit power allocated
to each subchannel. According to above analysis, we ignore
ˆgn
k, ¯mand ˆgn
k,¯
kin (3), and reconstruct (3) as a minimum
transmit power problem as (6), which is also an NP-complete
combinatorial problem. To solve the problem, we propose a
two-phase iterative subchannel and power allocation scheme.
According to (3), when the transmit power of every sub-
channel is given, the subchannel allocation depends on the
FUEs’ data rate requirements (i.e., Ri), and every FUE’s
SINR of every subchannel, which in turn influences the
strength of the FBS’s radiating interference of each subchan-
nel. Therefore, in the subchannel allocation phase, a modified
proportional fair scheme is proposed, which takes into account
Riand FUEs’s SINR.
In the power control phase, utilizing the subchannel al-
location result from the first phase, a modified water-filling
algorithm is proposed to minimize each FBS’s total transmit
power.
The main procedure of the iterative subchannel and power
allocation scheme is as:
1) Initialize the power allocation of one FBS by distributing
the total power randomly among the different subchannels in
ˆ
Nc;
2) For the given power allocation, the subchannel allocation
is optimized by the scheme in Subsection C;
3) For the given subchannel assignment, the power alloca-
tion is optimized by solving the problem in Subsection D;
4) Iterate steps 2) and 3) until the resource allocation
convergence, i.e., n∈ˆ
Nc
i
i∈Nu
k
|Pn
k(t)−Pn
k(t−1)|≤ε,whereε
is the convergence threshold and tis iteration index, which is
omitted for analysis convenience.
C. Subchannel Allocation Phase
In this phase, the interference power received by different
FUEs on different subchannels is taken into consideration,
which is reported to FBSs by FUEs. Define gn
i,k and In
i,k as
the link quality of FUE i and the interference power received
by FUE i using subchannel n in femtocell k, respectively.
The subchannel allocation scheme is provided in Table I.
1799
TAB L E I
SUBCHANNEL ALLOCATION SCHEME
Initialize: Set n=0,n∈ˆ
Ncand ˆ
Nc
i=φ, i ∈Nu
k,wherenis the
index of subchannels in ˆ
Nc;ˆ
Nc
iis the FUE i’s subchannel set and
i∈Nu
k
ˆ
Nc
i=ˆ
Ncis satisfied after the subchannel allocation is
completed; Nu
kis the active FUE set of femtocell k. The transmit
power is randomly allocated for the first iteration.
(1) Given transmit power Pn
k,FBSkcalculates the service rate gains
for for all FUE i(in Nu
k) on subchannel n:
∇An
i=B
Rilog21+ Pn
kgn
i,k
In
i,k ,∀i∈Nu
k;
(2) FBS kcalculates the sum of the current service rate gain of for all
FUEs (in Nu
k) on subchannel n:
Si=m∈ˆ
Nc
i
B
Rilog21+ Pm
kgm
i,k
Im
i,k+BN0,∀i∈Nu
k;
(3) Assign subchannel nto the FUE according to the rule:
i∗=argmin
i∈Nu
kmax j∈Nu
k
j=i
|(Si+∇Ai)−Sj|;
(4) Update the FUE i∗’s subchannel set as ˆ
Nc
i∗=ˆ
Nc
i∗∪n;
(5) Exclude subchannel nfrom ˆ
Ncas ˆ
Nc=ˆ
Nc−n;
(6) Consider the next sub-channel in ˆ
Nc, i.e., n=n+1, and go back
to Step (1) until ˆ
Ncis empty.
D. Power Control Phase
In the power control phase, the FBS minimizes the transmit
power of the allocated subchannels according to FUEs’ data
rate requirements. Since each FUE’s subchannel set in femto-
cell k(i.e., ˆ
Nc
i) is determined in the subchannel allocation
phase, this phase solves the following power-minimization
problem for every FUE with inequality constraints:
min n∈ˆ
Nc
iPn
k,∀i∈Nu
k
s.t. n∈ˆ
Nc
iBlog2(1 + ϑ(k, n)) ≥Ri,∀i∈Nu
k.
Pn
k≥0,∀n∈ˆ
Nc
i
(6)
FBS ksolves this problem by each FUE iindependently. a
and bnare referred to as Lagrange multipliers. Deriving the
Lagrange function of (6) and substituting ϑ(k, n)by (4), we
have
L(Pn
k,a,b
n)=n∈ˆ
Nc
iPn
k
+an∈ˆ
Nc
iBlog 1+ gn
kPn
k
In
k+BN0−Ri−n∈ˆ
Nc
ibnPn
k.
(7)
Then, the necessary and sufficient conditions for optimality
are given by the Karush-Kuhn-Tucker (KKT) conditions:
Pn
k=a
bn−1B−In
k+BN0
gn
k
,(8)
bnPn
k=0,∀n∈ˆ
Nc
i.(9)
Equation (8) denotes a water-filling system when all bn
are zero. Assuming bnare non-zero, a modified water-filling
algorithm for FUE i in femtocell k is performed in Table II
and power allocation for other FUEs can follow the same way.
It is noticed from the power allocation algorithm that
more transmission power is assigned to the subchannel which
experiences less interference or better link gain, while no
TAB L E I I
POWER ALLOCATION ALGORITHM
Initialize: Define the power allocation set for FUE i in femtocell k as
Pn
i,k=Pn
k|n∈ˆ
Nc
i;seta=0.
(1) Calculate the transmit power for all items in Pn
i,kas
Pn
k=−aB −In
k+BN0gn
k;
(2) If any item (i.e., Pn
k)inPn
i,kis less than zero, set Pn
k=0;
(3) According to current Pn
i,k, current FUE i’s data rate is calculated
as n∈ˆ
Nc
i
Blog (1 + ϑ(k, n)).
(4) If n∈ˆ
Nc
i
Blog (1 + ϑ(k, n)) <R
i, decrease athe predefined
step size and return to Step (1). Or else, the power allocation of FUE i
is completed.
transmission power is allocated to the subchannel, (i.e., the
subchannel is turned off), which experiences heavy interfer-
ence caused by cross-tier or co-tier interference from MBSs
or neighboring FBSs.
IV. PERFORMANCE EVA L U AT I O N
In this section, system level simulations are performed to
evaluate the performance of the proposed scheme, comparing
with three other schemes.
A. Simulation Environment and Assumptions
An OFDMA cellular system with 7macrocell, i.e., one ring
case, is considered. MUEs and houses which have an area
of 20 ×20 m2are randomly dropped within each macrocell.
Moreover, every house owns only one FBS which randomly
dropped in the house and serves 4FUEs. Taken their home
FBS as the circle center, FUEs are randomly dropped in a
circle with the radius of 10 meters. FBSs are connected to
one Femto GW in every macrocell.
In the macrocell tier, all the available subchannels are
transmitted with equivalent power according to [14] and the
scheduler for the MBS is proportional fair resource allocation.
The main simulation parameters are listed in Table III, which
are obtained from [14] [15]. According to [15], the path loss
model covers the following 5 links:
1) MBS to outdoor MUE:
PL =15.3+37.6log10 R, (10)
2) MBS to indoor UE (including the MUE and the FUE):
PL =15.3+37.6log10 R+Low ,(11)
3) FBS to indoor UE (including the MUE and the FUE):
PL =38.46 + 20log10R+0.7dindoor,(12)
4) FBS to outdoor MUE:
PL =max(15.3+37.6log10R, 38.46 + 20log10R)
+0.7dindoor +Low,(13)
5) FBS to FUE inside a different house:
PL =max(15.3+37.6log10R, 38.46 + 20log10R)
+0.7dindoor +2×Low,(14)
1800
where Ris the distance between the BS and the UE; dindoor
is the shortest indoor distance from BS to UE; Low is the
penetration loss of outdoor wall for the house. Obviously, R
equals dindoor in (12).
TABLE III
SYSTEM SIMULATION PARAMETERS
Parameter Value
Cell Parameters
Cell Radius 500m
Total MBS transmit power 43dBm
Frequency reuse factor 1
Channel Model
Shadowing standard deviation 8dB
Auto-correlation distance of shadowing 50m
Fast fading SCME
OFDMA Parameters
Carrier frequency 2000MHz
Bandwidth 10MH
Subcarrier spacing 15KHz
FFT size 1024
Number of subchannels 50
Number of subcarriers per subchannel 12
Traffic Model Full buffer
B. Comparison Schemes
Comparison scheme 1-the proposed scheme without PHO:
The proposed scheme does not operate the PHO based colli-
sion interference avoidance.
Comparison scheme 2-the random allocation scheme [9]:
Each femtocell randomly selects a subset of subchannel for
transmission. The fraction of radio resources per transmission
interval accessible by each femtocell is set as 60%.
Comparison scheme 3-the scheme based on reuse 3: The
system frequency reuse factor is 3, and the femtocell tier
can only use 2/3 frequency spectrum that is not allocated to
its local macrocell. The transmit power of each femtocell is
controlled according to its FUEs’ data rate requirements.
C. Simulation Results
The simulation results in Fig.4, 5 and 6 are obtained as there
are 50 femtocells randomly distributed in every macrocell and
the data rate requirements of all FUEs are randomly assigned
within the value set {100kbps,150kbps,...,10Mbps}.
Fig.4 shows the Cumulative Distribution Function (CDF)
of MUEs’ SINRs. Since the collision interference to MUEs is
avoided by the PHO method, the proposed scheme remarkably
improves the MUEs’ SINR performance, where MUEs’ SINRs
increase 3.8dB and 11.85dB on average compared with the
proposed scheme without PHO and the random allocation
scheme, respectively. Although there is no cross-tier inter-
ference in the scheme based on reuse 3 due to orthogonal
subchannels allocation to the femtocell tier and the macrocell
tier, MUEs’ SINR of the proposed scheme is only 2.3dB
lower on average. This is mainly due to the effectiveness of
the subchannel allocation and power control algorithm in the
proposed scheme.
−30 −20 −10 0 10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR[dB]
C.D.F
The proposed scheme
The proposed scheme without PHO
Random allocatoin scheme
Scheme based on Reuse 3
Fig. 4. CDF of MUEs’ SINR.
Fig.5 shows the CDF of FBSs’ transmit power. Because
the proposed scheme minimizes every FBS’s radiating inter-
ference, the signal transmit power to meet the given SINR
requirement (i.e., the data rate requirement) is reduced. There-
fore, the FBS’s transmit power of the proposed scheme is
1.1dB and 0.84dB less than that of the random allocation
scheme and that of the proposed scheme without PHO on av-
erage. Compared with random allocation scheme, the proposed
scheme without PHO brings 0.35dB gain, which demonstrates
the effectiveness of the resource allocation scheme of the
proposed scheme. In addition, since the scheme based on reuse
3 avoids the cross-tier interference at the cost of low spectrum
efficiency, the transmit power of it is 0.6dB less than that of
the proposed scheme.
−5 0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Transmit Power per FBS [dBm]
C.D.F
The proposed scheme
The proposed scheme without PHO
the scheme based on reuse 3
Random allocation scheme
Fig. 5. CDF of FBSs’ Transmit Power.
Fig.6 shows the CDF of the reciprocal of co-tier interference
power received by FUEs. Compared to the random allocation
scheme, the proposed scheme without PHO and the scheme
based on reuse 3, the proposed scheme decreases the FUE’s
co-tier interference by 9.92dB,10.68dB and 17.58dB on
average, respectively. In addition, it can be seen from the figure
that the scheme based on reuse 3 suffers the greatest co-tier
interference, which is mainly due to the fact that it has only
2/3 available subchannels set, which can be reused among
1801
femtocells in one macrocell.
−20 0 20 40 60 80 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Reciprocal of co−tier intereference power received by FUE [dBm]
C.D.F
The proposed scheme
The proposed scheme without PHO
Random allocation scheme
Scheme based on reuse 3
Fig. 6. CDF of the reciprocal of co-tier interference power received by FUEs.
Fig.7 depicts the average throughput per FUE varying with
the number of femtocells. The simulation method to obtain
the result is that all FUEs’ data rate requirements are equally
increased until the average throughput cannot be improved any
more. Seen from the figure, with the number of femtocells in-
creasing, the average throughput per FUE decreases for all the
four schemes due to the growth of interference. However, the
proposed scheme is more robust to the growth of interference
than the other schemes. As the number of femtocell is less than
30, the average throughput of the proposed algorithm without
PHO can reach throughput performance of the proposed
scheme. However, with the number of femtocells increasing,
more collision interference deteriorates its performance. As for
the scheme based on reuse 3, when the number of femtocells
is below 40, orthogonal subchannel allocation between two
tiers has its advantage. However, since its available subchannel
set is limited, the average throughput per FUE falls sharply
when the number of femtocells exceeds 80. As for the random
allocation scheme, only 60% of the system frequency resource
can be used by each femtocell makes its average throughput
lowest when the number of femtocell is less than 60.How-
ever, when the number of femtocells exceeds 60, its average
throughput declines more slowly due to the frequency hopping
characteristic of this scheme.
In addition, the convergence speed is irrelative to the
number of femtocells, and the iteration is within 8to 13 as the
proposed iterative scheme converges in 95% femtocells. Due to
the limited number of FUEs in one CSG femtocell, the iterative
calculation burden of the proposed scheme is released. Hence,
the proposed algorithm is suitable for the femtocell context.
V. C ONCLUSION
In this paper, we have constructed a problem of minimizing
the co-tier and the cross-tier interference, the essence of
which is a problem of joint resource allocation. The PHO
based subchannel and power adaptation scheme is proposed to
solve the problem. Performance evaluation results show that
minimizing the interference radiated by each FBS is in turn
0 20 40 60 80 100 120 140 160
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
The number of Femtocells
Average throughput [b/s/Hz]
The proposed scheme
The proposed scheme without PHO
Random allocation scheme
Scheme based on reuse 3
Fig. 7. Average throughput per FUE varying with the number of femtocells.
beneficial to reduce every FBS’s own required transmit power
and improve its FUEs’ throughput. With comparison with
three other schemes, the proposed scheme is better in reducing
interference and the FBS’s transmit power, and improving the
spectrum efficiency. The optimality of the constructed problem
and the performance evaluation of the PHO scheme will be
completed in our future work.
ACKNOWLEDGMENT
Key Project of Beijing Municipal Science &Technology
Commission (No. D08080100620802), International Cooper-
ation and Exchanges Project (No. S2010GR0902) and NSFC
Project (No. 60872048, No. 60772112).
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