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3910 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 11, NOVEMBER 2012

Energy-Efﬁcient Resource Allocation for

Heterogeneous Cognitive Radio Networks with

Femtocells

Renchao Xie, F. Richard Yu, Hong Ji, and Yi Li

Abstract—Both cognitive radio and femtocell have been con-

sidered as promising techniques in wireless networks. However,

most of previous works are focused on spectrum sharing and

interference avoidance, and the energy efﬁciency aspect is largely

ignored. In this paper, we study the energy efﬁciency aspect

of spectrum sharing and power allocation in heterogeneous

cognitive radio networks with femtocells. To fully exploit the

cognitive capability, we consider a wireless network architec-

ture in which both the macrocell and the femtocell have the

cognitive capability. We formulate the energy-efﬁcient resource

allocation problem in heterogeneous cognitive radio networks

with femtocells as a Stackelberg game. A gradient based iteration

algorithm is proposed to obtain the Stackelberg equilibrium

solution to the energy-efﬁcient resource allocation problem.

Simulation results are presented to demonstrate the Stackelberg

equilibrium is obtained by the proposed iteration algorithm and

energy efﬁciency can be improved signiﬁcantly in the proposed

scheme.

Index Terms—Cognitive radio, femtocell, energy efﬁciency,

Stackelberg game, Stackelberg equilibrium.

I. INTRODUCTION

APIDLY rising energy costs and increasingly rigid envi-

ronmental standards have led to an emerging trend of ad-

dressing “energy efﬁciency” aspect of wireless communication

technologies [1], [2]. In a typical wireless cellular network, the

radio access part accounts for up to more than 70 percent of

the total energy consumption [3]. Therefore, increasing the

energy efﬁciency of radio networks is very important to meet

the challenges raised by the high demands of trafﬁc and energy

consumption.

Cognitive radio technology, originally proposed to improve

the spectrum efﬁciency [4], can play an important role in

Manuscript receive d August 10, 2011; revised November 26, 2011 and

April 21, 2012; accepted July 31. 2012. The associate editor coordinating the

re view of this paper and approving it for publication was V. K. N. Lau.

R. Xie is with the Ke y Laboratory of Universal Wireless Communication,

Ministry of Education, Beijing University of Posts and Telecommunications,

Beijing, P.R. China, and also with the Dept. of Systems and Computer Eng.,

Carleton University, Ottaw a , ON, Canada.

F. R. Yu is with the Dept. of Systems and Computer Eng., Carleton

Univ ersity, Ottawa, ON, Canada (e-mail: Richard

yu@carleton.ca).

H. Ji, and Y. Li are with the Ke y Laboratory of Uni versal Wireless

Communication, Ministry of Education, Beijing University of Posts and

Telecommunications, Beijing, P.R. China.

This work was jointly supported by the State Key Program of National

Natural Science of China (Grant No. 60832009), the Natural Science Foun-

dation of Beijing, China (Grant No. 4102044), the National Natural Science

Foundation for Distinguished Young Scholar (Grant No. 61001115), the

National Natural Science Foundation of China (Grant No. 61101113), Huawei

Technologies Canada CO., Ltd., and the Natural Sciences and Engineering

Research Council of Canada.

Digital Object Identiﬁer 10.1109/TWC.2012.092112.111510

improving energy efﬁciency in radio networks [5]. In cog-

nitive radio networks, secondary users (SUs) can monitor the

surrounding radio environment, dynamically adapt transmis-

sion parameters, and opportunistically utilize the temporarily

unused spectrum resource licensed to primary users (PUs)

[6]. The cognitive abilities have a wid e range of pro perties,

including spectrum sensing and learning-empowered adaptive

transmission, which are beneﬁcial to improve the tradeoff

among energy efﬁciency, spectrum efﬁciency, bandwidth, and

deployment efﬁciency in wireless networks [3], [7], [8].

Some works have been done to consider energy efﬁciency

in cognitive radio networks. In [9], the authors study the

hierarchy in energy games for cognitive radio networks. The

problem is to maximize the energy-efﬁciency for each selﬁsh

SU. The authors of [10] study the distributed power control

game to maximize the transmission energy-efﬁciency for SUs

in cognitive radio networks, where the problem of optimal

power control is formulated as a repeated game. Energy-

efﬁcient power control and receiver design in cognitive radio

networks are studied in [11], where a noncooperative power

control game for maximum energy efﬁciency for SUs is

proposed under the constraints of fairness and interference

threshold.

On the other hand, femtocell has been considered as a

promising technique, and has been integrated in current and

future radio access networks [12]. The authors of [13] study

the pr oblem of downlink power allocation to maximize the

capacity in a cellular network where a bi-level hierarchy exists.

Then the Stackelberg game model is used to formulate the

optimization problem and Stackelberg equilibrium is solved.

The distributed power allocation strategies for a spectrum-

sharing femtocell n etwork are considered in [14], and the

Stackelberg g ame is form ulated to jointly consider the utility

maximization of the macrocell and the femtocells. Due to its

short transmit-receive distance property, femtocell technique

can also reduce energy consumption, prolong handset battery

life, and increase network coverage [15], [16]. The problem

of energy efﬁciency for femtocell base station is studied in

[17], where a novel energy saving procedure is designed for

femtocell base stations. In [18], resource sharing and access

control in OFDMA femtocell networks are studied, where

users’ selﬁsh characteristics are considered and an incentive

mechanism is designed for subscribers to share the resource

of femtocell base stations.

Combining cognitive radio with femtocell can further im-

prove the system performance [19]–[22]. The smart cognitive

1536-1276/12$31.00

 2012 IEEE

XIE et al.: ENERGY-EFFICIENT RESOURCE ALLOCATION FOR HETEROGENEOUS COGNITIVE RADIO NETWORKS WITH FEMTOCELLS 3911

femtocell is considered in [20], where the tradeoff between the

macrocell throughput and the aggregate femtocell throughput

is studied. In [21], the problem of cross-tier interference in

autonomous femtocell networks is studied by using cognitive

radio technology to realize the cognitive radio resource man-

agement. And a strategic game is proposed to implement the

interference mitigation. The interference management for long

term evolution (LTE) networks with femtocells using cognitive

radio technology is investigated in [22]. Then based on a dis-

tributed architecture for LTE networks, the authors recommend

to use two game theoretical mechanisms to mitigate the co-

channel interference.

Although some works have been done for heterogeneous

cognitive radio networks with femtocells, most of previous

works are focused on spectrum sharing and interference avoid-

ance. Consequently, th e energy efﬁciency aspect in this setting

is largely ignored. In addition, most of previous works assume

that only the femtocell base station (FBS) has the cognitive

capability, without considering the cognitive capability of the

macrocell base station. In this paper, our work is different

from previous works. Some distinct features of this paper are

as follows.

• We focus on the energy efﬁciency aspect of spectrum

sharing and power allocation in heterogeneous cognitive radio

networks with femtocells. Since both cognitive radio and fem-

tocell are promising technologies to enable energy efﬁciency

in wireless networks, the interplay between them merits furthe r

research. We use bits/Hz per Joule, which is commonly used in

wireless networks [23], to measure the performance of energy

efﬁciency.

• To fully exploit the cognitive capability, we consider a

wireless network architecture in which both the macrocell and

the femtocell have the cognitive cap ability, which allows the

macrocell and femtocells to dynamic utilize the spectrum re-

source licensed to primary network and sense the surrounding

channel state in formation. This network architecture is ﬁrst

proposed in [19], which is of importance in practical cellular

femtocell networks, where the macrocell base stations can

sense the TV band.

• We formulate the energy-efﬁcient resource allocation

problem in heterogeneous cognitive radio networks with fem-

tocells as a Stackelberg game, which has been successfully

used in relay selection and power allocation problem s in co-

operative communication networks [24], among others. Then

a gradient based iteration algorithm is proposed to obtain

the Stackelberg equilibrium solution to the energy-efﬁcient

resource allocation problem.

The rest of this paper is organized as follows. In Section II,

the system model is given, and the Stackelberg game model is

formulated. In Section III, the Stackelberg equilibrium solution

is p resented. Simulation results are presented and discussed in

Section IV. Finally, we conclude this study in Section V.

II. S

YSTEM DESCRIPTION

In this section, the heterogeneous cognitive radio network

with femtocells is presented. Then the problem of spectrum

sharing and resource allocation for energy-efﬁcient communi-

cations is formulated as a three-stage Stackelberg game.

MSU

PBS

FSU

FBS

MSU

Fig. 1. System model for femtocell-based cognitive radio networks (PBS:

primary base station; PU: primary user; w

: spectrum resource from primary

network l; MSU: macrocell secondary user; FBS: femtocell base station; FSU:

femtocell secondary user).

A. System Model

Consider a communication system that consists of primary

networks and a femtocell-based heterogeneous cognitive radio

network, as shown in Fig. 1. The primary n etworks may

operate on the different frequency spectrum.In this case, we

will not consider the interference among the primary networks.

Each primary network can offer a spectrum selling price and

sell part of spectrum resource to the heterogeneous cognitive

radio network with femtocells to earn additional proﬁt. In

the heterogeneous cognitive radio network, there are m ultiple

macro secondary users (MSUs), a cognitive base station (BS),

multiple femtocells, and multiple femtocell secondary users

(FSUs). The cognitive BS and femtocells have the cognitive

capability and can sense the channel state information [25].

Then the cognitive BS allocates the spectrum resource bought

from the primary networks to femtocells or MSUs directly

based on the channel quality condition to maximize its rev-

enue. In each femtocell, there is a femtocell base station (FBS)

to provide service for FSUs, where the FBS is connected to

the cognitive BS over a broadband connection, such as cable

modem or digital subscriber line (DSL). The whole system is

operated in a time-slotted manner, and the primary networks

and the femtocell-based cognitive radio network are assumed

to be perfectly synchronized. To simplify the analysis of the

problem, without loss generality, we assume that there is only

one FSU serviced by the FBS in each time slot.

Under this framework, we assume that there are L primary

networks. Each primary network l is willin g to offer a spec-

trum selling price c

and sell its part spectrum resource w

of total spectrum W

to the heterogeneous cognitive radio

network to maximize its proﬁt. The cognitive BS can buy

the spectrum resource w

from primary network l depending

on the spectrum p rice. Then the cognitive BS allocates the

spectrum w

to the femtocells or MSUs directly to gain its

revenue. Here, we assume that each femtocell and MSU are

accessed in the form of frequency division multiple access

(including OFDMA), and in each time slot they could only

be allocated one spectrum resource bought from a certain

primary network. Assume there are K

tot

femtocells and I

tot

MSUs directly served by the cognitive BS in th e heteroge-

3912 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 11, NOVEMBER 2012

FBS

Fig. 2. Three-stage Stackelberg game modeling (FBS: femtocell base station;

: spectrum resource from primary network l; c

: spectrum selling price from

primary network l; η

: energy efﬁciency in femtocell k for spectrum resource

; x

∈{0, 1} is the spectrum allocation index, where x

=1means

that the spectrum bought from primary network l is allocated to femtocell k,

otherwise x

=0).

neous cognitive radio network. Usually the total number of

femtocells and MSUs requesting to connect to the cognitive

BS is larger than the total number of spectrum resource bought

from the L primary networks, i.e., (K

tot

+ I

tot

) ≥ L.Dueto

the limited spectrum resource bought from primary networks,

we assume that there are at most L out of (K

tot

+ I

tot

)

femtocells and MSUs that can be accessed to the cognitive

BS in each time slot, which can be realized by scheduling

and admission control. Under this assumption, without loss

generality, we assume there are K femtocells and I MSUs

accessed to the cognitive BS, where K + I = L. In each

time slot, when a certain spectrum w

is used by a fem tocell,

the aim of the femtocell is to maximize its energy-efﬁcient

communications by allocating its power. Similarly, when the

spectrum is used by MSUs, the cognitive BS performs the

energy-efﬁcient power allocation.

Based o n the discussion above, we can formulate the prob-

lem of resource allocation for energy-efﬁcient communications

in the heterogeneous cognitive radio n etwork as a three-stage

Stackelberg game problem.

B. Problem Formulation

In this subsection, we formulate the energy-efﬁcient re-

source allocation problem as a three-stage Stackelberg game,

as shown in Fig. 2 , which consists of leaders and followers.

Here, we view the up-stage as the leaders that move ﬁrst,

then down-stage as the followers that move subsequently

by observing the leaders’ strategies. Therefore, in Stage I,

the primary networks are the leaders, and multiple primary

networks offer the spectrum selling price c

to the cognitive

BS. In Stage II, the cognitive BS, as the follower in Stage

I, decides to buy the spectrum size w

from primary network

l depending on the price c

offered by primary network l.

Next, the cognitive BS, as the leader in Stage II, allocates

the spectrum to FBSs or MSUs dir ectly, and performs power

allocation for the MSUs to gain its revenue. The FBSs in stage

III performs power allocation for FSUs. Based on the above

analysis, we know that each stage’s strategy will affect other

stages’ strategies, and the leaders should take the followers’

actions into account when deciding their strategies. Therefore,

to formulate the three-stage Stackelberg game model, we can

use the backward induction method as follows.

When femtocell k obtains spectrum resource w

from the

cognitive BS, the FBS aims to maximize energy efﬁciency in

power allocation, which can be expressed as

log





+ p

, (1)

where p

denotes the additional circuit power consumption

of devices during transmissions [26] (e.g., digital-to-analog

converters, ﬁlters, etc), which is independent to the data

transmission power. h

and p

are the channel gain and power

allocation on spectrum w

for FBS k, respectively. σ

is the

additive Gaussian white noise with zero mean and unit varia-

tion. In (1), bits/Hz per Joule is used as the energy efﬁciency

metric, which is commonly used in wireless networks [23],

[27]. In our work, we assume that the channels are ﬁxed over

the time-period of interest. This simplifying assumption has

been commonly adopted by the game-theoretic studies in the

communication literature [14]. To improve energy efﬁciency,

less energy should be used to transmit more information data.

Based on (1), the aim of FBS k is to maximize its utility given

spectrum w

, which can be expressed as follows.



l=1

(ς

− c



l=1

(ς

− c

) x

(2)

where w

is the spectrum resource bought from primary

network l, ς

is the revenue for FBS k,andc

is the cost

charged by the cognitive BS due to the allocated spectrum.

∈{0, 1} is the spectrum allocation index, where x

means that the spectrum bought from primary network l

is allocated to FBS k;otherwisex

=0. As the energy

efﬁciency criterion is used, the ﬁrst term denotes the revenue

gained from the FSU for energy efﬁcient transmission, and

the second term denotes the cost charged by the cognitive

BS for using the spectrum resource. Here, we have ς

Otherwise, the FBSs will not request to access.

When the FBSs ﬁnish the energy-efﬁcient power allocation,

there is feedback information to the cognitive BS. For the

cognitive BS, the aim is to buy the size of spectrum from

primary networks and allocate them to the FBSs or MSUs

directly to maximize its revenue. Here, we notice that the

cognitive BS also does the energy-efﬁcient power allocation

for MSUs when the spectrum is allocated to MSUs, which

is similar to (1). If we assume that spectrum demand for

cognitive BS from the prim ary networks is satisﬁed the linear

demand structure, we can use the following quadratic utility

function [28] for the cognitive BS.

(w)=



l=1





k=1



i=1



−





l=1

+2θ



q=l



−



l=1

(3)

where w = {w

, ..., w

} denotes the spectrum bought

from primary networks, η

is the energy-efﬁcient transmission

parameter for MSUs, ξ

is the cost paid by MSUs to the

cognitive BS, c

is the price offered by primary network l,and

θ ∈ [−1, 1] is the spectrum substitutability parameter. θ =1

means that the FBSs or MSUs can switch among the spectrum;

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