Content uploaded by Hoang Dinh Thai
Author content
All content in this area was uploaded by Hoang Dinh Thai on Mar 18, 2015
Content may be subject to copyright.
180 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
QoS-Aware and Energy-Efficient
Resource Management in OFDMA Femtocells
Long Bao Le, Senior Member, IEEE, Dusit Niyato, Member, IEEE, Ekram Hossain, Senior Member, IEEE, Dong
In Kim, Senior Member, IEEE, and Dinh Thai Hoang
Abstract—We consider the joint resource allocation and admis-
sion control problem for Orthogonal Frequency-Division Multi-
ple Access (OFDMA)-based femtocell networks. We assume that
Macrocell User Equipments (MUEs) can establish connections
with Femtocell Base Stations (FBSs) to mitigate the excessive
cross-tier interference and achieve better throughput. A cross-
layer design model is considered where multiband opportunistic
scheduling at the Medium Access Control (MAC) layer and
admission control at the network layer working at different
time-scales are assumed. We assume that both MUEs and
Femtocell User Equipments (FUEs) have minimum average rate
constraints, which depend on their geographical locations and
their application requirements. In addition, blocking probability
constraints are imposed on each FUE so that the connections
from MUEs only result in controllable performance degradation
for FUEs. We present an optimal design for the admission control
problem by using the theory of Semi-Markov Decision Process
(SMDP). Moreover, we devise a novel distributed femtocell power
adaptation algorithm, which converges to the Nash equilibriumof
a corresponding power adaptation game. This power adaptation
algorithm reduces energy consumption for femtocells while still
maintaining individual cell throughput by adapting the FBS
power to the traffic load in the network. Finally, numerical results
are presented to demonstrate the desirable operation of the
optimal admission control solution, the significant performance
gain of the proposed hybrid access strategy with respect to
the closed access counterpart, and the great power saving gain
achieved by the proposed power adaptation algorithm.
Index Terms—Femtocell network, admission control, Markov
decision process, blocking probability, channel assignment.
I. INTRODUCTION
SMALL cell deployment and inter-cell interference mit-
igation have been recognized as the key techniques to
enhance the capacity of cellular wireless networks [1]. Due to
Manuscript received January 29, 2012; revised May 27 and August 02,
2012; accepted September 30, 2012. The associate editor coordinating the
review of this paper and approving it for publication is M. C. Gursoy.
This work was supported in part by the Natural Sciences and Engineering
Research Council of Canada (NSERC) under the Strategic Grant Program and
the MKE, Korea, under the ITRC support program supervised by the NIPA
(NIPA-2012-(H0301-12-1005)). This paper was presented in part at IEEE
International Conference on Communications (IEEE ICC’2012), Ottawa,
Ontario, Canada.
L. B. Le is with the Institut National de la Recherche Scientifique
-´
Energie, Mat´eriaux et T´el´ecommunications (INRS-EMT), Universit´edu
Qu´ebec, Montr ´eal, Qu´ebec, Canada (e-mail: long.le@emt.inrs.ca).
D. Niyato and D. T. Hoang are with Nanyang Technological University,
Singapore (e-mail: {dniyato, thdinh}@ntu.edu.sg).
E. Hossain is with University of Manitoba, Winnipeg, MB, Canada (e-mail:
Ekram.Hossain@ad.umanitoba.ca).
D. I. Kim is with Sungkyunkwan University (SKKU), Suwon, Korea (e-
mail: dikim@skku.ac.kr).
Digital Object Identifier 10.1109/TWC.2012.120412.120141.
minimal installation and operation costs, emerging femtocells
have been shown to be a viable technical solution for broad-
band wireless access in indoor environments [2]. However,
since femtocells may operate on the same frequency spectrum
as macrocells, mitigation of cross-tier interference is a very
significant research issue.
To enable spectrum sharing between macrocells and fem-
tocells in Orthogonal Frequency-Division Multiple Access
(OFDMA)-based two-tier networks, one of the three ac-
cess modes, namely, open, closed and hybrid access, can
be employed [3]-[7]. In the open access mode, the MUEs
are allowed to connect to either their own Macrocell BSs
(MBS) or FBSs. In contrast, in the closed access mode, only
certain users (subscribers) belonging to the so-called Closed
Subscriber Group are allowed to connect to each FBS. The
hybrid access mode balances the strengths and weaknesses of
the closed and open access modes. In a typical hybrid access
mode for OFDMA-based two-tier network, the FUEs can use
all available subchannels when there is no connected MUE.
However, limited spectrum access at each femtocell is granted
for MUEs which wish to establish connections. An efficient
admission control policy is required in this case to coordinate
spectrum sharing and admission control for both types of
users, which should strike a balance between achieving high
spectrum utilization and protecting QoS requirements for
FUEs. In this paper, we develop such a spectrum sharing
and admission control mechanism for OFDMA-based two-tier
networks.
There have been some recent works on resource allocation
and performance analysis of OFDMA-based femtocell net-
works. In [5], a static frequency assignment scheme based on
fractional frequency reuse was proposed considering the hand-
off, coverage, and interference aspects of femtocell networks.
In [8], a randomized frequency allocation strategy called F-
ALOHA was proposed and its area spectral-efficiency was
analyzed for OFDMA-based femtocell networks by using
stochastic geometry. Research studies in [9] suggested that
open access can provide a throughput gain of more than 300%
for CDMA-based femtocell networks whereas the throughput
performance of open and closed access modes for OFDMA
femtocells depends on user density. Moreover, the admission
control and handoff problem for femtocell networks was
studied by using simulations [4].
In [10], a hierarchical resource allocation framework for
OFDMA-based femtocell networks was proposed that includes
three control loops, namely, maximum power setting for FUEs,
1536-1276/13$31.00 c
2013 IEEE
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 181
target SINR assignment for FUEs, and instantaneous power
control to achieve these target SINR values. In [11], a dis-
tributed power control algorithm was proposed for femtocells
to maximize the sum-rate achieved by FUEs. In [12], to design
resource allocation algorithms, a game model was used, the
equilibria of which were shown to be fair and efficient. In [13],
a frequency scheduling algorithm based on spectrum sensing
was proposed for coexistence of MUEs and FUEs. In [14],
distributed admission control and spectrum allocation algo-
rithms were developed using reinforcement learning, which
are, however, unable to provide performance guarantees for
users of both network tiers.
There are existing works in the literature that investigated
the admission control problem based on Markov Decision Pro-
cess (MDP) and also the power control problem for traditional
one-tier CDMA wireless networks [16], [17], [21]. To the best
of our knowledge, the problem of optimal admission control
with quality-of-service (QoS) guarantee in multi-tier wireless
cellular networks, which is addressed in this paper, has not
been well investigated in the literature. The contributions of
this paper can be summarized as follows:
•We develop a mathematical model for joint resource
allocation and admission control design for dynamic
spectrum sharing in OFDMA-based two-tier femtocell
networks. This model considers the QoS requirements of
MUEs and FUEs in terms of average rates and blocking
probabilities in presence of both co-tier and cross-tier
interferences.
•We devise a cross-layer radio resource management
framework for femtocells with a multiband proportional-
fair scheduling scheme at the MAC layer and an ad-
mission control scheme at the network layer. Then, the
optimal admission control solution is obtained by using
the theory of Semi-Markov Decision Process (SMDP).
•For energy-efficient resource management, we propose a
novel distributed femtocell power adaptation algorithm
by using game theory. We prove that the proposed
femtocell power adaptation algorithm converges to the
Nash equilibrium (NE) of the game.
•We demonstrate the efficacy of the proposed admission
control scheme as well as the significant power saving
gains of the proposed power adaptation algorithm via
numerical studies.
The rest of this paper is organized as follows. In Section
II, we present the system model. The cross-layer resource
allocation and admission control framework is presented in
Section III. We present the distributed femtocell power adap-
tation algorithm in Section IV. Numerical results are presented
in Section V which is followed by conclusion in Section VI.
A summary of key notations is presented in Table I.
II. SYSTEM MODEL
We consider the downlink of a two-tier OFDMA-based
wireless network that employs Frequency-Division Duplexing
(FDD). There are Nsubchannels shared by MUEs and FUEs
for downlink communications1.Itisassumedthatthereare
1The structure of cross-tier interference in the uplink is quite different from
that in the downlink. Analysis of the uplink scenario is left for our future work.
2D
Macrocell
MBS
Femtocell
FBS
MUE
MBS
1
2
3
4
6
8
7
9
5
FUE
FUE
FUE
FBS
L=500m
Fig. 1. Two-tier femtocell network.
Jfemtocells sharing these Nsubchannels with Imacrocells.
We further assume that a hybrid access policy is employed
where MUEs can connect to a nearby FBS. This can happen
when MUEs suffer from undue cross-tier interference or they
can achieve better rates if connected with a nearby FBS. The
system model under consideration is illustrated in Fig. 1.
We assume that each subchannel can be assigned to at most
one FUE or MUE connecting to any FBS. Furthermore, we
assume a full spatial reuse where all subchannels are utilized
at each FBS. In addition, subchannels are assumed to be
allocated to macrocells in such a way that interference among
macrocells is properly controlled2. We consider the scenario
where users of both network tiers demand some minimum
average rates which are determined by their underlying appli-
cations and locations in the cell. In fact, location-dependent
QoS constraints can be imposed to balance user throughput
and fairness. For instance, cell-edge users may require a
minimum rate that is smaller than that of cell-center users
so that the total cell throughput is not severely compromised.
We assume that there are C1classes of FUEs and C2classes
of MUEs connecting to any FBS. In addition, it is assumed
that class-cMUEs and FUEs require their total average rates
to be at least R(mc)
min and R(fc)
min , respectively.
To illustrate these QoS constraints, let us assume that long-
term signal attenuation depends on the distance between users
and a BS symmetrically. Note however that this assumption
can be relaxed as long as detailed path-loss information in each
cell is available. The area around each FBS can be divided into
circular areas and users running the same application (e.g.,
voice or video) in each circular area can be imposed the same
minimum average rate requirement. Each such minimum rate
is mapped to one user class. We depict this QoS modeling
in Fig. 2 where the femtocell area is divided into cell-edge
and cell-center regions. In addition, there is a circular region
where MUEs inside that region would request to establish
connections with the underlying FBS (i.e., they switch their
2Examples of subchannel allocation schemes include fractional frequency
reuse and partial frequency reuse [15].
182 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
TAB L E I
SUMMARY OF KEY NOTATIONS
Notation Physical meaning
INumber of macrocells
JNumber of femtocells
NNumber of subchannels
WBandwidth of one subchannel
C1,C2Number of FUE/MUE service classes
R(fc)
min ,R(mc)
min Minumum required rate for class-cFUEs/MUEs
g(fc)
ijk ,g(fc)
ijk Channel gain from FBS/MBS jto class-cuser kin femtocell i
L(dijk )Path-loss over distance dijk
λ(f)
ic ,λ(m)
ic Arrival rate of class-cFUEs/MUEs in femtocell i
μ(f)
ic ,μ(m)
ic Servicerateofclass-cFUEs/MUEs in femtocell i
pi,p0Transmission power on each subchannel from FBS/MBS i
βiTransmission power ratio for femtocell i
Pmax
FBS ,Pmax
MBS Maximum transmission power of FBS/MBS
Γ(fc)
ik ,Γ(mc)
ik SINR of class-cFUE/MUE kin femtocell i
Γ(fc)
ik ,Γ(mc)
ik Average SINR of class-cFUE/MUE kin femtocell i
U(f)
ic ,U(m)
ic Set of class-cFUEs/MUEs in femtocell i
u(f)
ic ,u(m)
ic Number of class-cFUEs/MUEs in femtocell i
Δ(f)
ic ,Δ(m)
ic Set of subchannels allocated for class-cFUEs/MUEs in femtocell i
s(f)
ic ,s(m)
ic Number of subchannels allocated for class-cFUEs/MUEs in femtocell i
s(f)
ic ,s(m)
ic Required number of subchannels for class-cFUEs/MUEs in femtocell i
y(fc)
ik ,y(mc)
ik Equal Γ(fc)
ik /Γ(fc)
ik and Γ(mc)
ik /Γ(mc)
ik , respectively
fy(fc)
ik
(x),Fy(fc)
ik
(x)Probability density function and probability distribution function for y(fc)
ik
fy(mc)
ik
(x),Fy(mc)
ik
(x)Probability density function and probability distribution function for y(mc)
ik
r(fc)
ik ,r(mc)
ik Average rate achieved by class-cFUE/MUE kin femtocell i
r(fc)
ik ,r(mc)
ik Minimum average rate achieved by class-cFUE/MUE kin femtocell i
B(f)
ic ,B(m)
ic Blocking probability for class-cFUEs/MUEs in femtocell i
P(fc)
b,P(mc)
bTarget blocking probability for class-cFUEs/MUEs in femtocell i
a(f)
ic ,a(m)
ic Control action of class-cFUEs/MUEs in femtocell i
AxAdmissible action space for system state x
τx(a)Expected time until the next decision epoch when action ais taken
zxa Rate of choosing action ain state x
w(m)
ic ,w(f)
ic Weighting factors defining the cost function of the MDP formulation
Ti,TThroughput of femtocell iand total throughput
σStandard deviation of shadowing
δPower scaling factor
Pi,Fi(.)Power and payoff function of femtocell i
pxy(a)Transition probability from state xto state ygiven action abe taken
connections to the underlying FBS)3.
We assume that the distance from any user connecting with
FBS ito other FBS/MBS jcan be well approximated by the
distance from FBS ito FBS/MBS j. This assumption would
be valid because the size of a typical femtocell would be
much smaller than the distance between the BSs of either
tier. Let g(fc)
ijk and g(mc)
ijk be the channel gains on a partic-
ular subchannel from FBS jand MBS j, respectively, to a
particular class-cuser kof either tier who is associated with
femtocell i. For brevity, the subchannel index is omitted in
these notations. Channel gains are modeled considering path-
loss, shadowing, and Rayleigh fading. Specifically, we can
write g(xc)
ijk (xstands for for m)asg(xc)
ijk L(dijk )10η/10ω,
where L(dijk )represents the path-loss over the corresponding
distance dijk ,ηis a Gaussian-distributed random variable with
zero mean and standard deviation σ,andωrepresents the
short-term Rayleigh fading gain. In addition, we assume that
3MUEs typically achieve better average SINRs and higher transmission
rates when they enter this neighborhood and switch their connections to the
underlying FBS.
Switching boundary
for MUEs
Femtocell
boundary
Service-class
boundary for FUEs
FBS
Fig. 2. Location-dependent QoS classes and switching boundary for MUEs.
connection requests of class-cFUEs and MUEs in femtocell
i, which are assumed to follow Poisson processes, arrive with
rate λ(f)
ic and λ(m)
ic , respectively. The connection duration is
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 183
User Average Rate and
Required Bandwidth
Distributed
Opportunistic
Scheduling
Admission Control With
Rate and Blocking
Probability Constraints
Distributed Femtocell
Power Adaptation
Blocking
Probabilities
Cross-layer
Adaptation
Arrival and
Service Rates
Instantaneous CSI
and Co-tier/Cross-
tier Interference
Fig. 3. Cross-layer resource management model with time-scale separation.
assumed to be exponentially distributed with mean duration of
1/μ(f)
ic and 1/μ(m)
ic for class-cFUEs and MUEs, respectively.
III. CROSS -LAYER RESOURCE ALLOCATION AND
ADMISSION CONTROL FRAMEWORK
We consider a cross-layer joint resource allocation and
admission control framework for femtocells with the following
network functionalities. A distributed opportunistic scheduling
algorithm is assumed to be implemented at each FBS to exploit
the multiuser diversity at a small time-scale. Depending on the
channel dynamics observed by users in two tiers, the size of
a scheduling time slot is assumed to be designed accordingly.
In contrast, the admission controller operates at a larger time-
scale, which captures the system dynamics due to user arrivals
and departures. Also, we design a distributed power adaptation
algorithm that adapts the transmission power of FBSs to the
heterogeneous traffic distribution over the network for QoS-
aware and energy-efficient spectrum sharing between the two
network tiers.
The cross-layer model under consideration is illustrated in
Fig. 3. It is worth noting that we consider a dynamic network
model where users come and leave the network over time.
Therefore, traditional resource allocation algorithms developed
for a static and snapshot network model with fixed network
topology (i.e., fixed number of users with known locations)
cannot be applied to our setting.
We assume that the MBSs have maximum transmission
power of Pmax
MBS while the maximum allowable power of
FBSs is Pmax
FBS which is determined from outage probability
constraints for MUEs and will be described in Section III-C.
For simplicity, we assume that the MBSs and FBSs perform
uniform power allocation over the subchannels and FBS j
uses 0≤βj≤1fraction of its maximum power while
the MBSs use their maximum power for downlink commu-
nications4. These femtocell transmission power ratios βjwill
be employed by the distributed power adaptation algorithm
to be presented in Section IV. Therefore, the transmission
power on any subchannel for users connecting to FBS j
is pj=βjPmax
FBS /N and the transmission power from any
MBS on one subchannel is p0=Pmax
MBS/N . Given the power
4We do not consider resource allocation for the macrocell tier in this paper.
However, the proposed algorithms would be able to adapt to the potential
dynamic operations of the macrocells.
allocation for MBSs and FBSs, we present an opportunistic
scheduling algorithm and analyze its throughput performance
in the following.
A. Multi-band Opportunistic Scheduling
The signal-to-interference-plus-noise ratio (SINR) achieved
by class-cFUE kassociated with femtocell ion a particular
subchannel can be written as
Γ(fc)
ik =pig(fc)
iik
J
j=1,j=ig(fc)
ijk pj+I
j=1 g(mc)
ijk p0+N0
=pig(fc)
iik
J
j=1,j=ig(fc)
ijk pj+IN(fc)
ik
(1)
where N0denotes the noise power and recall that g(fc)
ijk and
g(mc)
ijk are the channel gains from FBS jand MBS jto class-c
FUE kin femtocell i, respectively. The first and second terms
in the denominator of (1) represent the total interference due
to other FBSs and MBSs, respectively. In addition, IN(fc)
ik =
I
j=1 g(mc)
ijk p0+N0denotes the total interference from MBSs
and the noise power. Similarly, the SINR achieved by class-c
MUE kconnecting with FBS ican be written as
Γ(mc)
ik =pig(mc)
iik
J
j=1,j=ig(fc)
ijk pj+I
j=1,j=jig(mc)
ijk p0+N0
=pig(mc)
iik
J
j=1,j=ig(fc)
ijk pj+IN(mc)
ik
(2)
where IN(mc)
ik =I
j=1,j=jig(mc)
ijk p0+N0and jiis the nearest
MBS of femtocell i. Here, we assume that subchannels allo-
cated to MUEs connected with FBS iare not assigned to other
MUEs connected with the nearest MBS of femtocell i. Hence,
in the second term in the denominator of (2) we exclude
the interference from this MBS in calculating the total noise
and interference power. For brevity, we omit the subchannel
index in the SINR notations Γ(fc)
ik and Γ(mc)
ik . We assume that
the SINR-proportional fair opportunistic scheduling algorithm
[20], [22] is employed on each subchannel5. In particular,
time is divided into equal-size time slots and scheduling
decisions are made in each time slot for all subchannels.
Because the time slot interval is very small (e.g., typically
few milliseconds) compared to the user dwelling time, the
opportunistic scheduling algorithm operates over a small time-
scale. Note that a particular user of either tier can be scheduled
to transmit on multiple subchannels in each time slot.
Let U(m)
ic and U(f)
ic denote the sets of class-cMUEs and
FUEs in femtocell iand their cardinalities are denoted as
u(m)
ic =|U(m)
ic |and u(f)
ic =|U(f)
ic |, respectively. In addition, let
Δ(f)
ic and Δ(m)
ic be the sets of subchannels allocated for class-c
FUEs and MUEs in femtocell i, respectively. We assume that
these sets are determined to meet the average rate requirements
and they are only updated when the numbers of active users
5Consideration of the proportional fair scheduling in the cross-layer model
would be quite natural given that it has been adopted in practical wireless
standards [20], [22]. Moreover, the framework considered in this paper can
be readily extended to other scheduling schemes.
184 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
u(m)
ic and u(f)
ic change. The SINR-proportional fair opportunis-
tic scheduling algorithm operates on a particular subchannel
v∈Δ(f)
ic as follows. FBS ichooses FUE k∗that achieves
the largest ratio Γ(fc)
ik (t)/Γ(fc)
ik for transmission in time slot t
on this subchannel, i.e., k∗argmaxk∈U(f)
ic
Γ(fc)
ik (t)/Γ(fc)
ik
where recall that Γ(fc)
ik (t)and Γ(fc)
ik are the instantaneous
and average SINR of FUE kon the underlying subchannel,
respectively. Similar operations are applied for subchannels in
Δ(m)
ic to schedule MUEs in the sets U(m)
ic .
Now, we determine the average rate achieved by a par-
ticular FUE k∈U(f)
ic on one particular subchannel. To-
ward this end, we need to describe the probability distri-
bution of Γ(fc)
ik (t)/Γ(fc)
ik . It was shown in [19], [20] that
the composite variability of g(fc)
ijk due to Rayleigh fading
and lognormal shadowing can be approximated by a single
lognormal distribution. In addition, it is well-known that
a sum of lognormally-distributed random variables can be
represented by a single lognormal distribution [23], [32]. Also,
the ratio of two lognormally-distributed random variables is
lognormally distributed. Therefore, y(fc)
ik =Γ
(fc)
ik (t)/Γ(fc)
ik
can be approximated by a lognormally-distributed random
variable whose mean and standard deviation can be calculated
as in [20]. Then, the average rate achieved by FUE k∈U(f)
ic
on a particular subchannel can be written as follows6:
r(fc)
ik =W∞
0
log 1+y(fc)
ik Γ(fc)
ik
×⎧
⎪
⎨
⎪
⎩
j∈U(f)
i,c ,j=k
Fy(fc)
ij
(x)⎫
⎪
⎬
⎪
⎭
fy(fc)
ik
(x)dx (3)
where Wis the bandwidth of one subchannel; fy(fc)
ik
(x)and
Fy(fc)
ik
(x)represent the probability density function and prob-
ability distribution function of y(fc)
ik , respectively. Similarly,
the average rate achieved by MUE k∈U(m)
ic on a particular
subchannel can be written as follows:
r(mc)
ik =W∞
0
log 1+y(mc)
ik Γ(mc)
ik
×⎧
⎪
⎨
⎪
⎩
j∈U(m)
ic ,j=k
Fy(mc)
ij
(x)⎫
⎪
⎬
⎪
⎭
fy(mc)
ik
(x)dx (4)
where y(mc)
ik =Γ
(mc)
ik (t)/Γ(mc)
ik ;fy(mc)
ik
(x)and Fy(mc)
ik
(x)
represent the probability density function and probability
distribution function of y(mc)
ik , respectively.
B. QoS Constraints
It can be verified that the average rate r(fc)
ik calculated in (3)
decreases with the path-loss L(diik )for given power allocation
and channel gain parameters. Moreover, r(fc)
ik decreases with
the number of class-cFUEs u(f)
ic because the proportional-fair
6Assuming that the long-term channel gains on different subchannels are the
same and the typical user dwelling time is much larger than a scheduling time
slot, the average rates achieved by a particular user on different subchannels
are the same.
scheduling allows equal long-term time-shares among users
[18], [20] and each subchannel in Δ(f)
ic is shared by u(f)
ic
FUEs. Recall that class-cMUEs and FUEs require their total
average rates to be at least R(mc)
min and R(fc)
min , respectively. To
determine the minimum number of subchannels to meet the
minimum rate requirement, we consider the worst user with
minimum L(diik)(or maximum diik ) for each service class c
in femtocell i. That is, the femtocell iis located at the edge
of the corresponding service class for symmetric path-loss.
Let r(fc)
iand r(mc)
ibe the minimum rates achieved by any
class-cFUE and MUE, respectively. These minimum rates can
be calculated by using (3) and (4) for the corresponding worst
users. Let s(f)
ic =|Δ(f)
ic |and s(m)
ic =|Δ(m)
ic |be the numbers of
subchannels allocated for class-cFUEs and MUEs in femtocell
i, respectively. To maintain the rate requirements for FUEs
and MUEs of each service class, we impose the following
constraints7:
R(fc)
min ≤s(f)
ic ×r(fc)
i(u(f)
ic )(5)
R(mc)
min ≤s(m)
ic ×r(mc)
i(u(m)
ic )(6)
where we explicitly describe the dependence of r(fc)
iand
r(mc)
ion u(f)
ic and u(m)
ic , respectively. These constraints ensure
that the minimum rate requirements are satisfied by any class-
cuser. From these inequalities, we require that the numbers
of subchannels allocated for class-cMUE and FUE satisfy
s(f)
ic ≥R(fc)
min
r(fc)
i(u(f)
ic )s(f)
ic u(f)
ic (7)
s(m)
ic ≥R(mc)
min
r(mc)
i(u(m)
ic )s(m)
ic u(m)
ic .(8)
Therefore, the rate constraints in (5) and (6) hold if the
following constraints for femtocell iare satisfied:
N≥
C1
c=1
s(f)
ic u(f)
ic +
C2
c=1
s(m)
ic u(m)
ic ,∀i=1,2,...,J.
(9)
This constraint means that the number of available sub-
channels should be large enough to support the required
minimum rates for all service classes. This constraint will be
used for admission control design. Since the MUEs degrade
the performance of the FUEs connecting to the same FBS,
the FUEs must be satisfactorily protected. Toward this end,
we assume that a class-cFUE has the maximum tolerable
blocking probability of P(fc)
b.LetB(f)
ic denote the blocking
probability of class-cFUEs in femtocell i. Then, the blocking
probability constraints can be written as follows:
B(f)
ic ≤P(fc)
b,∀i, c. (10)
The admission control and channel assignment should be
performed in such a way that they can satisfy the channel and
blocking probability constraints in (9) and (10), respectively.
7Since the average rates achieved by any user on different subchannels are
the same, only the number of subchannels allocated to a particular service
class impacts the achievable average rates of its users. Note, however, that we
have exploited the channel dynamics to enhance the user throughput through
employing the proportional fair scheduling.
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 185
C. Maximum Power Constraints Under Closed and Hybrid
Access
Let dMU be the radius of the circular area centered around
each FBS where MUEs inside this region will connect with the
corresponding FBS under the proposed hybrid access scheme.
Also, let dFbe the radius of the coverage area of any femtocell.
We consider both closed and hybrid access strategies and
derive the corresponding maximum power constraints for
FBSs so that MUEs which are connected with MBSs and close
to FBSs are protected from excessive cross-tier interference.
Specifically, it is required that the transmission powers of
FBSs must be smaller than some maximum value so that
outage probability of MUEs is smaller than a desirable value.
Toward this end, let us consider a particular MUE kthat
connects with a nearby MBS and FBS iis its closest FBS.
Let h(m)
ik be the channel gain between the considered MUE k
and its connecting MBS. Then, we can express the SINR of
this MUE kas
γ(m)
ik =p0h(m)
ik
J
j=1 g(fc)
ijk pj+I
j=1,j=jig(mc)
ijk p0+N0
=p0h(m)
ik
J
j=1 g(fc)
ijk pj+IN(mc)
ik
.(11)
Note that all femtocells including femtocell icreate cross-tier
interference for the considered MUE k. In addition, MUEs
are not allowed to connect with nearby FBSs under the closed
access. To calculate the maximum allowable power for FBSs
under the closed access, we impose the outage probability
constraints for the worst MUE kwhose distance from FBS
iis exactly dF.Letγ0be the target SINR of the considered
MUE kthen the outage probability constraint can be expressed
as
Pr γ(m)
ik (dF)<γ
0<P
(m)
o(12)
where γ(m)
ik (dF)denotes the SINR of the MUE whose distance
to the nearest FBS is dFand P(m)
orepresents the target
outage probability. The LHS of this inequality denotes the
outage probability for the considered MUE. Recall that γ(m)
ik
can be modeled as a lognormally distributed random variable
with mean and standard variation (in dB) of μmand ηm,
respectively, which can be calculated as in [20]. The outage
probability in the left hand side of (12) can be expressed as
[20]
Pr γ(m)
ik (dF)<γ
0=1−1
2erfc 10 log10 γ0−μm
√2ηm(13)
where erfc(x)denotes the complementary error function,
defined as erfc(x)= 2
√π∞
xexp(−y2)dy. Then, we assume
that the transmission power of any FBS is constrained by
a common maximum value Pmax
FBS so that outage probability
constraints in (12) are satisfied for neighboring MUEs of all
femtocells. This kind of outage probability constraints has
been considered in several recent works [27], [28]. For the
proposed hybrid access, any MUE whose distance from the
nearest FBS is less than dMU will connect with the FBS.
Therefore, the outage probability constraints in this case can
be expressed as
Pr γ(m)
ik (dMU)<γ
0<P
(m)
o.(14)
The outage probability in (14) can be calculated as in (13) with
the corresponding mean and standard deviation values. And
the maximum transmission power Pmax
FBS of all FBS under the
hybrid access can be calculated so that the outage probability
constraints in (14) are satisfied. The maximum transmission
power Pmax
FBS under either access scheme is assumed to be
estimated by FBSs during a network startup phase.
D. SMDP-Based Distributed Admission Control in Femtocells
Given the considered physical and network layer models,
admission control is performed at the network layer con-
sidering user dynamics at the call level. It turns out that
admission control can be performed separately in each cell,
which enables distributed implementation. We will present
and analyze the performance of an optimal admission control
scheme for a particular femtocell i. In fact, we can formulate
the admission control problem as an SMDP [33].
We proceed by describing the state and action spaces for
the underlying SMDP. The decision epochs of the underlying
SMDP are arrival and departure instants of either FUE or MUE
in the considered femtocell i. We define a general system state
at decision epoch tas follows:
x(t)u(f)
i1(t),...,u
(f)
iC1(t),u
(m)
i1(t),...,u
(m)
iC2(t)(15)
where recall that u(f)
ic (t)and u(m)
ic (t)are the numbers of class-
cFUEs and MUEs at decision epoch t, respectively. Then, the
state space Xis defined as follows:
X{x:constraint (9) holds}.(16)
At each decision epoch when the system changes its state, an
admission control action is determined for the next decision
epoch. In fact, an admission control action is only taken for
a newly arriving user of either type. At a departure instant of
any connection, state transition occurs and no action is needed.
We define a general action aat decision epoch tas
a(t)a(f)
i1(t),...,a
(f)
iC1(t),a
(m)
i1(t),...,a
(m)
iC2(t)(17)
where a(f)
ic (t)and a(m)
ic (t)denote the admission control ac-
tion when an arrival occurs for class-cFUEs and MUEs in
femtocell i, respectively, which are defined as follows:
a(f)
ic =1,if a newly arriving FUE is admitted
0,otherwise (18)
a(m)
ic =1,if a newly arriving MUE is admitted
0,otherwise.(19)
The action state space can be defined as A=
a:a∈{0,1}C1+C2. Given these system and action state
spaces, we can determine the transition probabilities for the
underlying embedded Markov chains based on which the
optimal solution can be obtained (see Appendix A). Let B(f)
ic
and B(m)
ic be the blocking probabilities for class-cFUEs and
186 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
MUEs, respectively, which can be calculated from the SMDP-
based admission control solution presented in Appendix A.
Then, we can calculate the achievable call throughput of
femtocell ias follows:
Ti=
C1
c=1
(1 −B(f)
ic )λ(f)
ic +
C2
c=1
(1 −B(m)
ic )λ(m)
ic (20)
where we have taken blocked arrivals into consideration. Fi-
nally, the total network throughput achieved by all femtocells
can be calculated as T=J
i=1 Ti. The admission control
framework developed in this section will be used in the design
of a femtocell power adaptation algorithm in the next section.
IV. DISTRIBUTED POWER ADAP TATION ALGORITHM
High transmission power at an FBS may severely degrade
the performance of other highly-loaded femtocells and macro-
cells because of excessive inter-cell and cross-tier interference.
To address this issue, we develop an efficient power adaption
mechanism by using game theory8. The proposed power
adaptation algorithm aims to adapt transmission powers of
FBSs to spatial traffic load over the network [31]9. Therefore,
it is only activated when the traffic load described by user
arrival rates changes.
Femtocell Power Adaptation Game (FPAG):
•Players: JFBSs.
•Strategies: Each FBS ican select its total transmission
power Pi∈[0,Pmax
FBS ](the transmission power ratio βi
for FBS iis in [0,1]) to maximize its payoff.
•Payoffs: Fi(Pi,P
−i)for each FBS iis Fi(Pi,P
−i)=
−Pi,whereP−i[P1,...,P
i−1,P
i+1,...,P
J]denotes
a vector containing transmission powers of other FBSs
excluding FBS i.
It is assumed that all FBSs are required to satisfy the
channel and blocking probability constraints in (9) and (10),
respectively, while maximizing their payoffs. In addition, we
require that each FBS ithat wishes to reduce its transmission
power must satisfy the following blocking probability con-
straints for their MUEs
B(m)
ic ≤P(mc)
b,1≤c≤C2(21)
given that these constraints are satisfied when the maximum
power Pmax
FBS is used. Here P(mc)
bs are some predetermined
values. These additional constraints ensure that satisfactory
performance in terms of blocking probabilities is achieved for
users of both network tiers while the payoffs of all the FBSs
are maximized.
Remark 1: We assume that only FBSs participate in the power
adaptation game. In general, this formulation can be readily
extended to the scenario where MBSs are also players of
the game. However, MBSs are typically inter-connected by
high-speed links, which enable them to achieve certain global
8In general, femtocell owners would be interested in maximizing their own
benefits while maintaining required QoS for their users. Therefore, use of
non-cooperative game theory in designing the power adaptation algorithm for
femtocells arises quite naturally.
9The related research topics including design of FPGA, power circuitry,
and sleep mode strategies are other aspects of cross-layer design in attaining
the energy efficiency, which are out of the scope of this paper.
objectives. Investigation of power control issues for MBSs are,
therefore, beyond the scope of this paper.
One important concept in game theory is the Nash equilib-
rium (NE), which is defined in the following.
Definition 1: A transmission power vector P∗is called the NE
of the FPAG if for each FBS i,Fi(P∗
i,P∗
−i)≥Fi(Pi,P∗
−i),
∀Pi∈[0,Pmax
FBS ].
In the following, we develop a femtocell power adaptation
algorithm that converges to the NE of the FPAG. In particular,
FBSs, whose required blocking probability constraints are still
maintained, decrease their transmission powers by a factor δ<
1iteratively. Toward this end, we present some preliminary
results that characterize the system behavior under these power
scaling operations.
Proposition 1: Given the channel gains for all users, we have
the following properties:
1) For any FUE and MUE, whose FBS scales down power,
the SINR given in (1) and (2) decreases;
2) For any FUE and MUE, whose FBS does not scale down
power, the SINR given in (1) and (2) increases.
Proof: To prove the first property of this proposition, let
us consider the SINR on any subchannel achieved by a class-c
FUEs associated with FBS iwhich scales down power by a
factor δ.LetΩbe the set of FBSs which scale down their
transmission powers excluding FBS iin the current iteration.
Then, we can rewrite the SINR of FUE ias follows:
Γ(fc)
ik =δp(p)
ig(fc)
iik
j∈Ωg(fc)
ijk δp(p)
j+j/∈Ωg(fc)
ijk p(p)
j+IN(fc)
ik
=p(p)
ig(fc)
iik
j∈Ωg(fc)
ijk p(p)
j+j/∈Ωg(fc)
ijk
p(p)
j
δ+IN(fc)
ik
δ
≤p(p)
ig(fc)
iik
j∈Ωg(fc)
ijk p(p)
j+j/∈Ωg(fc)
ijk p(p)
j+IN(fc)
ik
(22)
where p(p)
j=βjPmax
FBS /N is the transmission power on any
subchannel in femtocell jin the previous iteration. The last
inequality in (22) holds because δ<1. It can be observed that
the quantity in the right hand side of (22) is indeed the SINR of
class-cFUEs in femtocell iin the previous iteration. Similarly,
we can prove the decrease of SINR of MUEs. Therefore, the
first property stated in the proposition holds.
The second property in the proposition can be proved
similarly. In particular, for any FBS which does not scale
down power, the received powers of its FUEs remain the same.
However, the total received interference can only decrease due
to the decreases in transmission powers of some other FBSs.
The results in Proposition 1 describe how the power
updates of FBSs impact the SINRs of users in the network.
We now state further results on the average rates achieved by
the opportunistic scheduling scheme under power adaptation.
Proposition 2: We have the following results for the aver-
age rates achieved by the SINR-proportional fair scheduling
scheme:
1) For any FUE and MUE whose FBS scales down power,
the average rate given in (3) and (4) decreases;
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 187
2) For any FUE and MUE whose FBS does not scale down
power, the average rate given in (3) and (4) increases.
Proof: From Proposition 1, for any FUE and MUE
whose connecting FBS scales down the transmission power,
its average SINR and rate in each scheduled slot decreases.
In addition, one important principle of the proportional fair
scheduling is that it allows equal long-term time shares among
competing users on each subchannel [18], [20]. Therefore, for
the fixed number of users of either type (i.e., FUEs or MUEs)
in a particular service class, each user is asymptotically
scheduled for the same fraction of time. Since the average
rate of each user in each scheduled slot decreases with the
decreasing FBS transmission power, its long-term average rate
decreases. Therefore, the first property in Proposition 2 holds.
The second property can be proved similarly by using the fact
that the average SINR and rate achieved by any FUE or MUE
in each scheduled slot increases in this case.
According to (7) and (8), the number of subchannels
required to support certain target minimum rates can increase
or decrease if the average rates of the corresponding user class
decrease or increase, respectively. In turn, the channel require-
ments for different user classes impact the channel constraint
in (9) and the corresponding admission control performance.
Because we are interested in the throughput performance at
the network layer, the impacts of power adaptation on the
admission control performance must be characterized. Let
ui=u(f)
i1,...,u
(f)
iC1,u
(m)
i1,...,u
(m)
iC2be the vector whose
elements represent the number of users of different classes
and let si=s(f)
i1,...,s
(f)
iC1,s
(m)
i1,...,s
(m)
iC2be the required
numbers of subchannels to support the minimum rate require-
ments in (7) and (8), respectively.
Definition 2: A vector siis said to dominate another vector
s
iwritten as sis
iif we have s(f)
ic ≥s
(f)
ic ,c =1,...,C
1,
s(m)
ic ≥s
(m)
ic ,c =1,...,C
2, and there is at least one strict
inequality in these inequalities.
We are ready to state an important result that describes the
interaction of the physical and network layer performance of
the proposed cross-layer design model.
Proposition 3: Consider the performance of the SMDP-
based optimal admission control described in Section III.C
under two different channel requirement vectors siand s
i
where sis
i.LetB(f)
ic ,B(m)
ic and B
(f)
ic ,B
(m)
ic be the
optimal blocking probabilities that are attained with the two
different channel requirement vectors siand s
i, respectively.
Suppose that arrival rates are sufficiently high so that B(f)
ic =
B
(f)
ic =P(fc)
b,1≤c≤C1under the SMDP-based admission
control10. Then, we have B
(m)
ic ≤B(m)
ic .
Proof: Let us rewrite the cost function Fπin (29) for a
particular stationary policy πas
Fπ=
C1
c=1
w(f)
ic B(f)
ic +
C2
c=1
w(m)
ic B(m)
ic (23)
where recall that B(f)
ic and B(m)
ic denote the blocking proba-
bilities of class-cFUEs and MUEs, respectively.
10As will be seen in the numerical results, these probability constraints for
FUEs are met with equality for sufficiently large arrival rates.
Let π∗denote the optimal policy of the system with the
channel requirement vector siand let B(f)
ic and B(m)
ic be
the optimal blocking probabilities achieved by this optimal
policy for FUEs and MUEs, respectively. Refer to Appendix
A for further details on how to calculate the optimal ad-
mission control solution for a given channel requirement
vector. Suppose we apply this policy π∗for another system
with the channel requirement vector s
i. Since we assume
sis
i, such policy utilization can maintain the subchannel
constraint in (9) and the achievable blocking probabilities
satisfy B
(f)
ic =B(f)
ic =P(fc)
b(the second equality holds due
to the assumption of the proposition) and B
(m)
ic =B(m)
ic .
Now, let us compare the blocking probabilities B
(m)
ic
obtained above with the blocking probabilities B
(m)
ic attained
by the optimal solution for the system with the channel
requirement vector s
i.WemusthaveB
(m)
ic ≤B
(m)
ic since
B
(m)
ic is due to the optimal policy for the system with the
channel requirement vector s
i. Therefore, we have B
(m)
ic ≤
B
(m)
ic =B(m)
ic . This completes the proof of the proposition.
The results in Proposition 2 and Proposition 3 establish
the foundation to develop the power adaptation algorithm.
Specifically, we can allow lightly-loaded FBSs to reduce their
transmission powers, which in turn increases the blocking
probabilities of their users as long as the resulting blocking
probabilities satisfy the constraints in (10) and (21). The
reduction of transmission powers in lightly-loaded FBSs will
increase transmission rates for femtocells with high traffic
load. This can potentially decrease channel requirement vector
sifor other highly-loaded femtocell i. This can result in an
improvement in blocking probabilities and the total throughput
in these highly-loaded femtocells.
The proposed power adaptation algorithm is described in
details in Algorithm 1. In steps 3-5, each FBS in set Af
attempts to reduce its transmission power by a factor δ. Param-
eter P(mc)
bin (21) is introduced to maintain the performance
of MUEs connecting with lightly-loaded FBSs. When multiple
femtocells scale down their powers at the same time there
may be a subset of these femtocells failing to maintain their
blocking probability requirements (i.e., constraints (10) and
(21)). In steps 7-9 of Algorithm 1, the femtocells which fail to
maintain their blocking probability requirements scale up their
powers by a factor 1/δ to do so. There are subtle interactions
among femtocells after step 9. Specifically, the power scale-
up of femtocells in steps 7-9 may make other femtocells
violate their blocking probability requirements. This is because
a larger transmission power of any femtocell results in higher
interference and therefore lower transmission rates for users in
other femtocells. In steps 10-15 of Algorithm 1, any violating
femtocell scales up its transmission power to maintain its
blocking probability requirement. This is performed until
the blocking probability requirements in all femtocells are
satisfied.
The proposed algorithm can be implemented in a distributed
fashion because each FBS only needs to know the average
rates achieved by its FUEs and MUEs of different classes.
This can be attained by letting FUEs and MUEs of all classes
188 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
Algorithm 1 FEMTOCELL POWER ADAP TATION
1: Initialization: Each FBS uses its maximum power for
downlink communications. Moreover, each FBS calculates
its admission control performance using the analytical
model presented in Section III.C.
2: Let Afbe the set of active femtocells who can maintain
its blocking probability requirements in (10) and (21).
3: for each FBS iin Afdo
4: FBS iscales down its transmission power by a factor
δ<1(i.e., FBS iperforms the following update: βi:=
δβiand transmits with power βiPmax
FBS ).
5: end for
6: Each FBS re-calculates its admission control solution
based on the current perceived SINRs of its user classes
where additional constraints (33) are imposed for each
FBS iif constraints in (21) for FBS ihold in the previous
iteration.
7: for each FBS jwhich scales down its transmission power
in the current iteration and cannot maintain the blocking
probability constraints in (10) or (21) do
8: FBS jscales up the transmission power by a factor 1/δ
(i.e., go back to the previous power level).
9: end for
10: while there are any femtocells which scale up their
transmission power do
11: Each FBS re-calculates its admission control solution
based on the current perceived SINRs of its user classes
where additional constraints in (33) are imposed for
each FBS iif constraints in (21) for FBS ihold in the
previous iteration.
12: for each FBS jwhich scales down its transmission
power in the current iteration and cannot maintain the
blocking probability constraints in (10) or (21) do
13: FBS jscales up the transmission power by a factor
1/δ (i.e., go back to the previous power level).
14: end for
15: end while
16: Update the set Afto contain all femtocells who suc-
cessfully maintain their blocking probability requirements
in (10) and (21) after power scale-down in the current
iteration or those that fail to do so Kiterations before
where Kis a predetermined number.
17: Go to step 2 until convergence.
to feedback the estimated mean and standard variation of the
lognormally distributed variables representing their SINRs to
each FBS i, which are used to calculate the average rates and
channel requirement vector si. The channel requirement vec-
tors are used to calculate the admission control performance
for users of both tiers in each femtocell. The convergence of
Algorithm 1 is stated in the following theorem.
Theorem 4: We have the following results for Algorithm 1:
1) The blocking probability requirements in (10) and (21)
are satisfied at the end of each iteration.
2) Algorithm 1 converges to an equilibrium.
3) If δis sufficiently close to 1 then the achieved equilib-
rium tends to the NE of the FPAG.
Proof: Note that the interference received by any FUEs
and MUEs does not increase over iterations; therefore, if a
femtocell goes back to its power level in the previous iteration
their blocking probability constraints must be satisfied. Also,
since the blocking probability requirements of all lightly-
loaded femtocells are satisfied in the first iteration and there is
a finite number of femtocells, the inner loop corresponding to
steps 10-15 of Algorithm 1 must terminate in a finite number
of sub-iterations (bounded by the number of femtocells).
Therefore, the blocking probability requirements in (10) and
(21) for all femtocells are satisfied at the end of each iteration
(i.e., after step 15). Hence, we have completed the proof for
the first property of this theorem.
We now prove the convergence of Algorithm 1. In each
iteration, each femtocell either utilizes the same power level
as in the previous iteration or scales down its power by
a factor δ<1in Algorithm 1. Recall that the power
adaptation operations performed in Algorithm 1 can maintain
the blocking probability constraints (10) and (21) for all
femtocells in any iteration (the first property of the theorem).
In order to maintain these constraints, the average achieved
rates of associated users must be strictly larger than zero (since
the blocking probabilities of any user class tend to one if the
average achieved rate of that user class tends to zero (i.e.,
zero service rate)). Since each FUE and MUE receive non-
zero total noise and interference power from other MBSs,
the transmission power of any FBS must be strictly larger
than zero to achieve non-zero average rates for its associated
users. This implies that Algorithm 1 must converge to an
equilibrium at which no femtocell can scale down its power
further.
Finally, we prove that the achieved equilibrium tends to the
NE of the FPAG for δsufficiently close to 1 by contradiction.
Specifically, suppose that the achieved equilibrium is not
a NE. Then there must exist an FBS which can increase
its payoff or slightly decrease its transmission power while
still maintaining the constraints in (10) and (21) given the
transmission powers of other FBSs. However, this contradicts
to the fact that Algorithm 1 cannot decrease the transmission
power of any FBS further at the equilibrium. Therefore, the
achieved equilibrium must be close to the NE of the FPAG if
δis sufficiently close to 1.
Let β∗
i,i=1,...,J be the femtocell transmission power
ratios obtained by Algorithm 1 at convergence. Then, we
can calculate the power saving with respect to the maximum
allowed transmission power as follows:
Sp= 100 ×JPmax
FBS −J
i=1 β∗
iPmax
FBS
JPmax
FBS
= 100 ×J−J
i=1 β∗
i
J.
(24)
One may want to compare the admission control performance
at the equilibrium attained by Algorithm 1 with that achieved
by using the maximum power. We characterize these results
in the following theorem.
Theorem 5: We have the following results for the equilibrium
achieved by Algorithm 1.
1) Throughput reduction ΔTiof a lightly-loaded fem-
tocell i, which scales down its transmission power,
can be upper-bounded as ΔTi≤C1
c=1 P(fc)
bλ(f)
ic +
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 189
C2
c=1 P(mc)
bλ(m)
ic .
2) Let siand s
ibe channel requirement vectors of a
particular highly-loaded femtocell iunder maximum
power and at the equilibrium attained by Algorithm 1.
Suppose the arrival rates of the considered femtocell are
sufficiently large such that the constraints in (10) are
met with equality when the maximum power is used. In
addition, assume that we have s
i≺si. Then, Algorithm
1results in better throughput for the considered femto-
cell icompared to that achieved by using the maximum
power.
Proof: The first result of this theorem can be proved
by noting that a lightly-loaded femtocell ionly decreases
its transmission power as long as the blocking probability
constraints in (10) and (21) are still satisfied. Using the fact
that the blocking probabilities for FUEs and MUEs are upper-
bounded by P(fc)
band P(mc)
b, respectively, the upper-bound
in throughput reduction can be obtained by consulting the
throughput formula in (20).
The second result of this theorem can be proved by using
the results in Proposition 3. In particular, the blocking prob-
abilities for FUEs and MUEs decrease under Algorithm 1
because we have s
i≺si. Therefore, the second result follows
by using these results and the throughput formula in (20).
Remark 2: The power adaptation operations can be imple-
mented asynchronously without impacting its convergence. In
fact, in the arguments employed to prove the convergence
of Algorithm 1 we do not impose any restriction on the
number of femtocells that scale down transmission powers
in any iteration. Therefore, the convergence holds for both
synchronous and asynchronous power updates. Moreover, the
choice of parameter δin Algorithm 1 impacts the tradeoff
between convergence speed and the transmission powers at
the equilibrium. In particular, fast convergence can be achieved
by smaller δat the cost of larger transmission powers at the
equilibrium.
Remark 3: Let us define λtot =C1
c=1 λ(f)
ic +C2
c=1 λ(m)
ic .
Suppose we choose P(fc)
b=P(mc)
b=Pb; then, the throughput
loss of a lightly-loaded femtocell ipresented in Theorem 5
can be rewritten as ΔTi≤Pbλtot.Sinceλtot is bounded
in stable systems we can achieve any desirable throughput
loss by choosing Pbsufficiently small. This implies that the
NE achieved by Algorithm 1 indeed results in better energy
efficiency for the femtocell network with improved throughput
for highly-loaded femtocells and negligible throughput loss
for lightly-loaded femtocells. Therefore, the achieved NE is a
desirable operating point.
Remark 4: Although the NE may not be very efficient
compared to certain globally optimal solution, choosing NE
as an operating point for the femtocells can be justified
by the following facts. Firstly, femtocells’ owners would
be typically selfish and only interested in optimizing their
own benefits. Hence, NE would be an appropriate solution
concept that enables us to realize this expectation. Secondly,
the proposed power adaptation algorithm (i.e., Algorithm 1),
which converges to the NE of the underlying game, can be
implemented in a distributed manner. This is very desirable
as backhaul links over which signaling information can be ex-
changed typically have limited capacity. Thirdly, development
of a distributed algorithm to reach a certain globally optimal
solution for the considered multi-layer resource allocation and
admission control problem seems to be non-tractable. In fact,
it has been well-known that the utility maximization problem
for multicell OFDMA setting even under the static scenario
(i.e., fixed number of users without dynamic user arrival
and departure) is NP-hard and very complex to solve up to
optimality [29]. Therefore, formulating the power adaption as
a game where we can reach the NE in a distributed manner
would be a natural design approach for the femtocell network.
Remark 5: We can calculate the energy efficiency for the
proposed hybrid access scheme in terms of energy per bit [24],
[25], [26]. Assume that users of each service class transmit
data at the required minimum rates, i.e., class-cMUEs and
FUEs transmit at rates R(mc)
min and R(fc)
min , respectively. Let
N(fc)
iand N(mc)
ibe the average numbers of class-cFUEs
and MUEs connected with FBS i. Then, we can calculate the
average numbers of bits transmitted by FBS iin one second
as
Si=
C1
c=1
N(fc)
iR(mc)
min +
C2
c=1
N(mc)
iR(fc)
min .(25)
Recall that FBS itransmits at the power level Pi=βiPmax
FBS .
Therefore, we can calculate the overall energy efficiency of
all femtocells as
E=J
i=1 Pi
J
i=1 Si
=J
i=1 βiPmax
FBS
J
i=1 C1
c=1 N(fc)
iR(mc)
min +C2
c=1 N(mc)
iR(fc)
min .
This implies that we can calculate the energy efficiency if
we can calculate N(fc)
iand N(mc)
ifor a given power usage
profile of all femtocells (i.e., βifor all femtocells i=1,...,J)
and an admission control policy. Unfortunately, it seems non-
tractable to find closed-form expressions of N(fc)
iand N(mc)
i
for the proposed optimal admission control policy. However,
we can quantify the performance gain of the proposed power
adaptation algorithm (i.e., Algorithm 1) in terms of energy
efficiency with respect to the scenario where the maximum
transmission power Pmax
FBS is used if we can calculate the ratio
of Stot =J
i=1 C1
c=1 N(fc)
iR(mc)
min +C2
c=1 N(mc)
iR(fc)
min
under these two power usage profiles (i.e., S1
tot/S2
tot where
S1
tot and S2
tot denote the values of Stot under the two power
usage profiles, respectively).
We can argue that the values of Sto t are approximately the
same under these two power usage profiles. In fact, Algorithm
1only scales down powers of lightly-loaded femtocells to the
extent that the blocking probabilities of all associated MUEs
and FUEs are below the predetermined small target block-
ing probabilities. In addition, any femtocell having higher
average service rate compared to other femtocells reduces its
transmission power. Since the interference decreases with the
transmission power, all femtocells would have roughly the
same “service rates” under both power usage profiles. Since
the energy efficiency given in (26) is inversely proportional to
Stot, which is approximately the same under both power usage
190 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
profiles, the performance gains in terms of power saving and
energy efficiency are approximately the same.
V. N UMERICAL RESULTS
We present numerical results to illustrate the performance
of the proposed admission control and power adaptation
algorithms. The network setting is shown in Fig. 1 where there
are 9 femtocells located at the edge of the central macrocell in
a cluster of macrocells. The distance between two neighboring
femtocells is 120m. We assume there are 2 classes of FUEs
in each femtocell where class-one and class-two FUEs are
located in the inner and outer circular regions whose radii
from the corresponding FBS are 15m and 30m, respectively.
To calculate the required number of subchannels for FUEs of
each class (i.e., s(f)
i,c in (7)), we consider the worst case where
FUEs are located on the boundary of the corresponding inner
and outer regions (i.e., distances from these worst class-1 and
class-2 FUEs to their FBS are 15m and 30m, respectively).
Moreover, we assume that MUEs will attempt to connect
with a nearest FBS when they enter a circular area whose
radius is 40m from the underlying FBS. To calculate the rate
requirements for MUEs in (8), we also assume the worst case
where MUEs are located on the boundary of this circular area.
We calculate the long-term channel gains based on the
corresponding distance. We assume that the distance dij from
BS jto MUEs or FUEs associated with femtocell ican be
approximated by the distance from BS jto FBS i. Also, the
path-loss in dB corresponding to dijk is calculated as [15]:
L(dijk ) = [44.9−6.55 log10 (hBS)] log10 (dij k )+34.46
+5.83 log10 (hBS) + 23 log10 (fc/5) + nijk Wijk
where hBS is the BS height, which is chosen to be 25m and
10m for MBSs and FBSs, respectively (i.e., depending on
whether BS jin this loss calculation corresponds to MBSs
or FBSs); fcis the carrier frequency in GHz which is set to
2 GHz. In addition, Wijk is the wall loss, and nijk denotes
the number of walls. For communications from an FBS to its
associated FUEs, we choose Wijk =5dB (i.e., indoor light
walls) and nijk =1; for communications from an FBS to
an indoor FUE connected with a different FBS, we assume
Wijk = 12dB and nij k =2; for other cases we assume
Wijk = 12dB and nijk =1. The path loss in the linear scale
corresponding to L(dijk )in dB is 10L(dij k)/10 .
Other system parameters are set as follows: FUEs’ and
MUEs’ average service time μ(f)
i,c =μ(m)
i,c =1minute,
∀i, c; arrival rates for all FUEs and MUEs are chosen to
be the same (i.e., λ(f)
i,c =λ(m)
i,c ,∀i, c); maximum power
of an MBS Pmax
MBS = 80W; weighting factors in (29) are
w(m)
i,c =w(f)
i,c =1(∀i, c); standard deviation of shadowing
σ= 8dB; power scaling factor for Algorithm 1 δ=0.9;total
number of available subchannels N=6; and parameter Kin
step 16 of Algorithm 1 is chosen as K=3. Moreover, the
minimum required rate for MUEs is R(m1)
min /W =6b/s/Hz;
the minimum required rates for class-1 and class-2 FUEs are
R(f1)
min /W =10b/s/Hz and R(f2)
min /W =4b/s/Hz, respectively.
The target blocking probabilities used in Algorithm 1 are
chosen as P(mc)
b=P(fc)
b= 0.05, ∀c;targetSINRofMUEsis
γ0=3dB; and target outage probability for MUEs in (12) is
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Arrival rate (users/min)
Blocking probability
Class−1 FUE
Class−2 FUE
Class−1 MUE
Fig. 4. Blocking probabilities in femtocell 1 when all FBSs use their
maximum allowed power.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Arrival rate (users/min)
Blocking probability
Class−1 FUE
Class−2 FUE
Class−1 MUE
Fig. 5. Blocking probabilities in femtocell 2 when all FBSs use their
maximum allowed power.
P(m)
o=0.15. We assume that the noise power and interference
power from MBSs except the closest MBS of femtocell ifor
SINR calculations in (1) and (2) are negligible compared to the
interference powers from femtocells and the closest MBS. By
using the techniques presented in Section III.C, the maximum
allowable powers of each FBS for which we can still maintain
the target outage probability of the MUEs P(m)
o=0.15 are
Pmax
FBS =3.5mW and Pmax
FBS =1.5mW for the hybrid and closed
access strategies, respectively.
Fig. 4 and Fig. 5 show the blocking probabilities achieved
by the optimal admission control versus arrival rates in femto-
cells 1 and 2, respectively, as all FBSs use their maximum al-
lowable transmission power under the hybrid access, which is
equal to Pmax
FBS =3.5mW to meet the target outage probability
P(m)
o=0.15. These figures confirm that the QoS requirements
of FUEs in terms of blocking probabilities are always satisfied.
As the network becomes congested, blocking probabilities of
FUEs reach the target values (i.e., P(fc)
b= 0.05) while the
blocking probability of MUEs increases slowly, and then it
increases sharply before the system becomes unstable (i.e.,
it is not possible to support the target blocking probabilities
of FUEs). In addition, the blocking probability of MUEs in
Fig. 4 is much larger than that in Fig. 5 since users connecting
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 191
0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
3.5
4
Arrival rate (users/min)
Femtocell call throughput (users/min)
Hybrid access
Closed access
Fig. 6. Call throughput of femtocell 2 under the closed and proposed hybrid
access strategies.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
−0.5
0
0.5
1
1.5
2
2.5
Arrival rate (users/min)
Call throughput (users/min)
Femto, Rmin
(f2)/W=4
Macro, Rmin
(f2)/W=4
Femto, Rmin
(f2)/W=6
Macro, Rmin
(f2)/W=6
Fig. 7. Call throughput of FUEs and MUEs in femtocell 2 under different
minimum rate constraints.
with FBS 1 receive relatively stronger interference from the
nearest MBS compared to users connecting with FBS 2. This
confirms the results in Proposition 3.
In Fig. 6, we plot the average call throughput achieved by
all FUEs in femtocell 2 versus the arrival rate under the closed
and proposed hybrid access strategies. This figure shows that
the proposed hybrid access strategy achieves significantly
higher call throughput than that due to the closed access
strategy when the arrival rate is high. This performance gain
comes from the fact that the maximum allowable transmission
power of FBSs under the hybrid access is considerably larger
than that under the closed access (Pmax
FBS =3.5mW and
Pmax
FBS =1.5mW, respectively). Hence, even though FBSs
must reserve some bandwidth for connecting MUEs under the
hybrid access, the overall throughput achieved by FUEs is still
higher than that under the closed access. The proposed hybrid
access is, therefore, the win-win strategy for users of both
network tiers.
To demonstrate the impacts of minimum rate requirements
on the spectrum sharing between users of both tiers, we show
the call throughputs achieved by FUEs and MUEs versus the
arrival rate for femtocell 2 in Fig. 7 for R(f2)
min /W =4b/s/Hz
and R(f2)
min /W =6b/s/Hz while rate requirements for other
0 5 10 15 20 25
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Iteration
Transmission power ratio βi
Femto 1
Femto 2
Femto 3
Femto 7
Femto 8
Femto 9
Fig. 8. Convergence of transmission power ratios under Algorithm 1.
0.2 0.25 0.3 0.35 0.4 0.45 0.5
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
λ0 (users/min)
Average call throughput (users/min)
Without power adaptation, NL=3
With power adaptation, NL=3
Without power adaptation, NL=6
With power adaptation, NL=6
Fig. 9. Average throughput per femtocell with and without power adaptation.
user classes are R(m1)
min /W =6b/s/Hz and R(f1)
min /W =10
b/s/Hz. As is evident from this figure, while the call throughput
achieved by FUEs remains almost the same, the call through-
put of MUEs becomes much smaller in the high arrival rate
regime as R(f2)
min /W increases from 4 b/s/Hz to 6 b/s/Hz. This
means the proposed hybrid access strategy enables MUEs
to appropriately exploit the radio resources beyond what is
needed to support the required QoSs of FUEs.
We show the evolutions of the femtocell transmission
power ratios βifor different femtocells under the synchronous
power updates which demonstrate the convergence of Al-
gorithm 1 in Fig. 8. There are NL= 6 lowly-loaded
femtocells (femtocells 1 to 6) with λ(f)
i,c =λ(m)
i,c =0.2
users/min and the arrival rates of the remaining 3 highly-
loaded femtocells are λ(f)
7,c ,λ
(f)
8,c ,λ
(f)
9,c =[λ0,3λ0,4.5λ0]
where λ0=0.3users/min. To keep the figure readable,
we only show the transmission power ratios for 6 femto-
cells. In Fig. 9, we illustrate the average call throughput
per femtocell achieved by the optimal admission control
scheme with and without the power adaptation algorithm (i.e.,
Algorithm 1) where the arrival rates of NLlowly-loaded
femtocells (femtocells 1 to NL) are fixed at λ(f)
i,c =λ(m)
i,c
= 0.2 users/min and the arrival rates of the remaining highly-
loaded femtocells are varied by using a parameter λ0. Here,
the arrival rates of highly-loaded femtocells are chosen as
192 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
0.2 0.25 0.3 0.35 0.4 0.45 0.5
20
25
30
35
40
45
50
55
60
λ
0
(users/min)
Power saving (%)
NL=3
NL=6
Fig. 10. Power saving due to femtocell power adaptation.
λ(f)
4,c ,λ
(f)
5,c ,...,λ
(f)
9,c =[λ0,3λ0,4.5λ0,λ
0,3λ0,4.5λ0]and
λ(f)
4,c ,λ
(f)
5,c ,λ
(f)
6,c =[λ0,3λ0,4.5λ0]for NL= 3, 6, respec-
tively. This figure shows that the proposed power adaptation
algorithm can indeed maintain the average throughput for
different values of arrival rates in the highly-loaded femtocells.
In fact, Algorithm 1 slightly increases the average throughput
for some values of arrival rates. The increase of throughput
in highly-loaded femtocells is offset by slight decrease of
throughput in other lightly-loaded femtocells. Therefore, the
average throughput per femtocell remains almost the same for
different values of arrival rates.
Finally, we present the power saving achieved by Algo-
rithm 1 with the parameter λ0in Fig. 10 when the numbers
of lowly-loaded femtocells are NL= 3 and 6. This figure
confirms that significant power saving can be achieved by the
proposed power adaptation algorithm when λ0is small, which
are about 50%and 60%for λ0=0.2users/min and NL=3
and 6, respectively. Moreover, when the arrival rates of highly-
loaded femtocells become larger, the power saving drops to
about 22%and 41%for NL=3andNL= 6, respectively.
In fact, the power saving for NL= 6 is larger than that for
NL= 3 with high arrival rates because most of the power
saving comes from the reduction in transmission powers of
lightly-loaded femtocells.
VI. CONCLUSION
We have considered the cross-layer resource allocation
and admission control problem for OFDMA-based femtocell
networks. Specifically, we have developed a unified model
that captures co-tier and cross-tier interference as well as rate
and blocking probability requirements for users of both tiers.
Moreover, we have presented a novel distributed power adap-
tation algorithm, which has been proved to converge to the NE
of the corresponding power adaptation game. Via numerical
studies, we have demonstrated the desirable performance of
the optimal admission control scheme in maintaining the QoS
requirements for FUEs and optimally using the spectrum
resources. Finally, it has been confirmed that a significant
power saving can be achieved by the proposed joint admission
control and power adaptation algorithm.
APPENDIX A
SMDP-BASED ADMISSION CONTROL
Given the system and action state spaces described in
Section III.C, we are particularly interested in the admissible
action space Axfor a given system state x. In fact, Ax
comprises all possible actions that do not result in transition
into a state that is not allowed (i.e., not in allowable state
space Xin (16)). In addition, if x=0, then it is required that
action a=0is excluded from Axto prevent the system to be
trapped in the zero state forever. Let e(f)
ic (e(m)
ic ) be a vector
of dimension C1+C2, which is of the same size as that of
the general state vector x(t)having all zeros except the one at
the same position of x(f)
ic (x(m)
ic ) in (15). Then, we can write
Axas follows:
Axa∈A:a(f)
ic =0if x+e(f)
ic /∈X;
a(m)
ic =0if x+e(m)
ic /∈X;and a=0if x=0
.(26)
We now analyze the dynamics of this SMDP, which is charac-
terized by the state transition probabilities of the Markov chain
obtained by embedding the system at arrival and departure
instants. Specifically, we will determine transition probability
pxy(a)from state xto state ywhen action ais taken. Toward
this end, let τx(a)denote the expected time until the next
decision epoch after action ais taken at system state x. Then,
τx(a)can be calculated as the inverse of the cumulative arrival
and departure rate with blocked arrivals taken into account. In
particular, τx(a)can be calculated as follows [16], [33]:
τx(a)=C1
c=1
λ(f)
ic a(f)
ic +
C1
c=1
μ(f)
ic u(f)
ic +
C2
c=1
λ(m)
ic a(m)
ic
+
C2
c=1
μ(m)
ic u(m)
ic −1
(27)
for a∈Ax. We are now ready to calculate transition
probability pxy (a)of the underlying embedded Markov chain.
This can be done by noting that the probability of a certain
event (e.g., connection arrival and departure) is equal to the
ratio between the rate of that event and the total cumulative
event rate 1/τx(a). Therefore, the transition probability pxy(a)
can be determined as follows:
pxy(a)=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
λ(f)
ic a(f)
ic τx(a),if y=x+e(f)
ic
λ(m)
ic a(m)
ic τx(a),if y=x+e(m)
ic
μ(f)
ic u(f)
ic τx(a),if y=x−e(f)
ic
μ(m)
ic u(m)
ic τx(a),if y=x−e(m)
ic
0,otherwise
(28)
where for simplicity we omit user index iin both τx(a)and
pxy(a). In the following, we formulate the optimal admission
control problem using the above description of the underlying
SMDP.
We formulate the admission control problem by defining a
cost function as the weighted sum of blocking probabilities.
In particular, we are interested in minimizing the following
LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 193
cost function:
min
zxa≥0
C1
c=1
w(f)
ic
x∈X
a∈Ax
(1 −a(f)
i,c )zxaτx(a)
+
C2
c=1
w(m)
ic
x∈X
a∈Ax
(1 −a(m)
ic )zxaτx(a)(29)
where zxa denotes the rate of choosing action ain state
x;w(m)
ic >0and w(f)
ic >0are weighting factors control-
ling the desired performance tradeoff. In this cost function,
B(f)
ic =x∈Xa∈Ax(1 −a(f)
ic )zxaτx(a)and B(m)
ic =
x∈Xa∈Ax(1 −a(m)
ic )zxaτx(a)express the blocking prob-
abilities of class-cFUEs and MUEs, respectively, where
zxaτx(a)represents the probability that action ais taken for
a given system state x.
In addition, we impose blocking probability constraints for
FUEs as follows:
B(f)
ic =
x∈X
a∈Ax
(1 −a(f)
ic )zxaτx(a)≤P(fc)
b,1≤c≤C1.(30)
Moreover, we impose other standard constraints for an MDP
as follows [33]:
a∈Ay
zya −
x∈X
a∈Ax
pxy(a)zx,a =0,∀y∈X(31)
x∈X
a∈Ax
zxaτx(a)=1 (32)
which describe the balance equation and the normalization
condition, respectively [33]. The optimal admission control
policy can be obtained as follows. We calculate optimal z∗
xa by
solving the linear program (29)-(32). Then, we can determine
an optimal randomized admission control policy as follows:
for each system state xthe probability of choosing action
a∈Axcan be calculated as θx(a)=z∗
xaτx(a)/az∗
xaτx(a).
These probabilities can be calculated offline and applied
for online admission control for different system states. In
the above model, we do not impose blocking probability
constraints for MUEs. However, these additional constraints
can be easily added to the model. Specifically, if P(mc)
bis the
maximum tolerable blocking probability for class-cMUEs,
then additional blocking probability constraints can be written
as
B(m)
ic =
x∈X
a∈Ax
(1 −a(m)
ic )zxaτx(a)≤P(mc)
b,
1≤c≤C2.(33)
Then, we can calculate optimal z∗
xa by solving the linear pro-
gram (29)-(32), (33), and find the optimal admission solution
accordingly. This calculation is indeed used in Algorithm 1.
REFERENCES
[1] G. Boudreau, J. Panicker, N. Guo, R. Wang, and S. Vrzic, “Interference
coordination and cancellation for 4G networks,” IEEE Commun. Mag.,
vol. 44, no. 4, pp. 74–81, Apr. 2009.
[2] D. Lopez-Perez, A. Valcarce, G. de la Roche, and J. Zhang, “OFDMA
femtocells: a roadmap on interference avoidance,” IEEE Commun. Mag.,
vol. 47, no. 9, pp. 41–48, Sep. 2009.
[3] G. d. l. Roche, A. Valcarce, D. Lopez-Perez, and J. Zhang, “Access
control mechanisms for femtocells,” IEEE Commun. Mag., vol. 48, no.
1, pp. 33–39, Jan. 2010.
[4] D. Lopez-Perez, A. Valcarce, A. Ladanyi, G. d. l. Roche, and J. Zhang,
“Intracell handover for interference and handover mitigation in OFDMA
two-tier macrocell-femtocell networks,” EURASIP J. Wireless Commun.
Netw., 2010.
[5] I. Guvenc, M. R. Jeong, F. Watanabe, and H. Inamura, “A hybrid
frequency assignment for femtocells and coverage area analysis for
cochannel operation,” IEEE Commun. Lett., vol. 12, no. 12, pp. 880–
882, Dec. 2008.
[6] D. T. Ngo, L. B. Le, and T. Le-Ngoc, “Distributed Pareto-optimal power
control for utility maximization in femtocell networks,” IEEE Trans.
Wireless Commun., vol. 11, no. 10, pp. 3434–3446, Oct. 2012.
[7] D. T. Ngo, L. B. Le, T. Le-Ngoc, E. Hossain, and D. I. Kim, “Distributed
interference management in two-tier CDMA femtocell networks,” IEEE
Trans. Wireless Commun., vol. 11, no. 3, pp. 979–989, Mar. 2012.
[8] V. Chandrasekhar and J. G. Andrews, “Spectrum allocation in tiered
cellular networks,” IEEE Trans. Commun., vol. 57, no. 10, pp. 3059–
3068, Oct. 2009.
[9] P. Xia, V. Chandrasekhar, and J. G. Andrews, “Open vs. closed access
femtocells in the uplink,” IEEE Trans. Wireless Commun.,vol.9,no.
10, pp. 3798–3809, Dec. 2010.
[10] J.-H. Yun and K. G. Shin, “Adaptive interference management of
OFDMA femtocells for co-channel deployment,” IEEE J. Sel. Areas
Commun., vol. 29, no. 6, pp. 1225–1241, June 2011.
[11] M.-S. Kim, H. W. Je, and F. A. Tobagi, “Cross-tier interference miti-
gation for two-tier OFDMA femtocell networks with limited macrocell
information,” in Proc. 2010 IEEE GLOBECOM.
[12] C.-H. Ko and H.-Y. Wei, “On-demand resource-sharing mechanism
design in two-tier OFDMA femtocell networks,” IEEE Trans. Veh.
Technol., vol. 60, no. 3, pp. 1059–1071, Mar. 2011.
[13] M. E. Sahin, I. Guvenc, M.-R. Jeong, and H. Arslan, “Handling CCI
and ICI in OFDMA femtocell networks through frequency scheduling,”
IEEE Trans. Consumer Electron., vol. 55, no. 4, pp. 1936–1944, Nov.
2009.
[14] S. Namal, K. Ghaboosi, M. Bennis, A. B. MacKenzie, and M. Latva-
Aho, “Joint admission control &interference avoidance in self-
organized femtocells,” in Proc. 2010 Asilomar Conf. Signals, Syst.
Comput.
[15] M. Rahman and H. Yanikomeroglu, “Enhancing cell-edge performance:
a downlink dynamic interference avoidance scheme with inter-cell
coordination,” IEEE Trans. Wireless Commun., vol. 9, no. 4, pp. 1414–
1425, Apr. 2010.
[16] J. Choi, T. Kwon, Y. Choi, and M. Naghshineh, “Call admission control
for multimedia services in mobile cellular networks: a Markov decision
approach,” in Proc. 2000 IEEE Int. Symp. Comput. Commun.
[17] S. Singh, V. Krishnamurthy, and H. V. Poor, “Integrated voice/data call
admission control for wireless DS-CDMA systems,” IEEE Trans. Signal
Process., vol. 50, no. 6, pp. 1483–1495, June 2002.
[18] P. Viswanath, D. Tse, and R. Laroia, “Opportunistic beamforming using
dumb antennas,” IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1277–1294,
June 2002.
[19] A. M. D. Turkmani, “Probability of error for M-branch macroscopic
selection diversity,” IEE Proc. I Commun. Speech Vision, vol. 139, no.
1, pp. 71–78, Feb. 1992.
[20] H. Fu and D. I. Kim, “Analysis of throughput and fairness with downlink
scheduling in WCDMA networks,” IEEE Trans. Wireless Commun.,vol.
5, no. 8, pp. 2164–2174, Aug. 2006.
[21] D. I. Kim, E. Hossain, and V. K. Bhargava, “Downlink joint rate and
power allocation in cellular multi-rate WCDMA systems,” IEEE Trans.
Wireless Commun., vol. 2, pp. 69–80, Jan. 2003.
[22] C. J. Chen and L. C. Wang, “A unified capacity analysis for wireless
systems with joint multiuser scheduling and antenna diversity in Nak-
agami fading channels,” IEEE Trans. Wireless Commun., vol. 54, no. 3,
pp. 469–478, Mar. 2006.
[23] N. B. Mehta, J. Wu, A. F. Molisch, and J. Zhang, “Approximating a sum
of random variables with a lognormal,” IEEE Trans. Wireless Commun.,
vol. 6, no. 7, pp. 2690–2699, July 2007.
[24] G. Miao, N. Himayat, G. Y. Li, and S. Talwar, “Distributed interference-
aware energy-efficient power optimization,” IEEE Trans. Wireless Com-
mun., vol. 10, no. 4, pp. 1323–1333, Apr. 2011.
[25] M. C. Gursoy, D. Qiao, and S. Velipasalar, “Analysis of energy effi-
ciency in fading channels under QoS constraints,” IEEE Trans. Wireless
Commun., vol. 8, no. 8, pp. 4252–4263, Aug. 2009.
[26] D. Qiao, M. C. Gursoy, and S. Velipasalar, “Energy efficiency in the
low-SINR regime under queueing constraints and channel uncertainty,”
IEEE Trans. Wireless Commun., vol. 59, no. 7, pp. 2006–2017, July
2011.
[27] X. Chu, Y. Wu, D. Lopez-Perez, and X. Tao, “On providing downlink
services in collocated spectrum-sharing macro and femto networks,”
194 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013
IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4306–4315, Dec.
2011.
[28] W. C. Chung, T. Q. S. Quek, and M. Kountouris, “Throughput opti-
mization, spectrum allocation, and access control in two-tier femtocell
networks,” IEEE J. Sel. Areas Commun., vol. 30, no. 3, pp. 561–574,
Apr. 2012.
[29] Z. Q. Luo and S. Zhang, “Dynamic spectrum management: complexity
and duality,” IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp.
57–73, Feb. 2008.
[30] 3GPP TR V0.0.9, “Overview of 3GPP Release 11,” Jan. 2012. Available:
http://www.3gpp.org
[31] Z. Niu, “TANGO: traffic-aware network planning and green operation,”
IEEE Wireless Commun., vol. 18, no. 5, pp. 25–29, 2011.
[32] G. L. Stuber, Principles of Mobile Communication. Kluwer Academic,
1996.
[33] M. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic
Programming. Wiley, 1994.
Long Bao Le (S’04-M’07-SM’12) received the
B.Eng. (with Highest Distinction) degree from Ho
Chi Minh City University of Technology, Vietnam,
in 1999, the M.Eng. degree from Asian Institute
of Technology, Pathumthani, Thailand, in 2002, and
the Ph.D. degree from the University of Manitoba,
Winnipeg, MB, Canada, in 2007.
From 2008 to 2010, he was a postdoctoral re-
search associate with Massachusetts Institute of
Technology, Cambridge, MA. Since 2010, he has
been an assistant professor with the Institut National
de la Recherche Scientifique (INRS), Universit´eduQu´ebec, Montreal, QC,
Canada, where he leads a research group working on cognitive radio and
dynamic spectrum sharing, radio resource management, network control and
optimization.
Dr. Le is a member of the editorial board of IE E E COMMUNICATIONS
SURVEYS AND TUTORIALS and IEEE WIRELES S COMMUNICATIONS LET-
TERS. He has served as technical program committee co-chairs of the Wireless
Networks track at IEEE VTC2011-Fall and the Cognitive Radio and Spectrum
Management track at IEEE PIMRC2011. He is a Senior Member of the IEEE.
Dusit Niyato (M’09) received the BE degree from
King Mongkuts Institute of Technology Ladkrabang
(KMITL), Bangkok, Thailand in 1999, and the PhD
degree in electrical and computer engineering from
the University of Manitoba, Canada, in 2008. He
is currently an assistant professor in the School
of Computer Engineering at the Nanyang Techno-
logical University, Singapore. His research interests
are in the area of radio resource management in
cognitive radio networks and broadband wireless
access networks. He is a member of the IEEE.
Ekram Hossain (S’98-M’01-SM’06) is a Full Pro-
fessor in the Department of Electrical and Com-
puter Engineering at University of Manitoba, Win-
nipeg, Canada. He received his Ph.D. in Elec-
trical Engineering from University of Victoria,
Canada, in 2001. Dr. Hossain’s current research
interests include design, analysis, and optimization
of wireless/mobile communications networks, cog-
nitive radio systems, and network economics. He
has authored/edited several books in these areas
(http://www.ee.umanitoba.ca/∼ekram). Dr. Hossain
serves as the Editor-in-Chief for the I EEE COMMUNICATIONS SURVEYS
AND TUTORIALS (for the term 2012-2013) and an Editor for IEEE Wireless
Communications. Previously, he served as the Area Editor for the I EE E
TRANSACTIONS ON WIRELESS COMMUNICATIONS in the area of “Resource
Management and Multiple Access” from 2009-2011 and an Editor for
the IEEE TRANSACTIONS ON MOBI LE COMPUTING from 2007-2012. Dr.
Hossain has won several research awards including the University of Manitoba
Merit Award in 2010 (for Research and Scholarly Activities), the 2011 IEEE
Communications Society Fred Ellersick Prize Paper Award, and the IEEE
Wireless Communications and Networking Conference 2012 (WCNC’12)
Best Paper Award. He is a registered Professional Engineer in the province
of Manitoba, Canada.
Dong In Kim (S’89-M’91-SM’02) received the
Ph.D. degree in electrical engineering from the
University of Southern California, Los Angeles, in
1990.
He was a tenured Professor with the School
of Engineering Science, Simon Fraser University,
Burnaby, BC, Canada. Since 2007, he has been with
Sungkyunkwan University (SKKU), Suwon, Korea,
where he is currently a Professor with the School of
Information and Communication Engineering. His
research interests include wireless cellular, relay
networks, and cross-layer design.
Dr. Kim has served as an Editor and a Founding Area Editor of Cross-
Layer Design and Optimization for the IEE E TRANSACTIONS ON WIRELESS
COMMUNICATIONS from 2002 to 2011. From 2008 to 2011, he served as the
Co-Editor-in-Chief for the Journal of Communications and Networks. He is
currently an Editor of Spread Spectrum Transmission and Access for the
IEEE TRANSACTIONS ON COMMUNICATIONS and the Founding Editor-in-
Chief for the I EEE W IRELESS COMMUNICATIONS LETTERS.
Dinh Thai Hoang received his Bachelor degree
in Electronics and Telecommunications from Hanoi
University of Technology (HUT), Vietnam in 2009.
From 2010 to 2012 he worked as a research assistant
at Nanyang Technological University (NTU), Singa-
pore. He has received the NTU research scholarship
and he is currently working toward his Ph.D. degree
in School of Computer Engineering, NTU under
Professor Dusit Niyato’s supervision. His research
interests include cooperative networked systems, and
resource allocation for wired and wireless networks.
