Manuscript received March 31, 2015; revised July 20, 2015.
This work was supported in part by the National Natural Science
Foundation of China under Grants No.61302105, 61302163; the Fundamental Research Funds for the Central Universities under Grant
No.13QN40. Corresponding author email: [email protected].
doi:10.12720/jcm.10.7.526-534
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Journal of Communications Vol. 10, No. 7, July 2015
©2015 Journal of Communications
Energy Supply-Demand Balance Based Resource
Allocation for Cellular Network with Smart Grid
Baogang Li and Xuewei Wang School of Electronic and Communication Engineering, North China Electric Power University, Baoding, 071003,
People’s Republic of China
Email: [email protected]; [email protected]
Abstract—Energy-efficient communications as one of the
promising technologies for 5G wireless communication systems
have gained great attention. This paper investigates the energy
aware resource allocation problem for the cognitive cellular
network under the smart grid environment. Considering the
Real-Time Pricing (RTP) model and the energy consumption
model of the small cell base station, a net bit transmission
benefit utility is designed. The optimization problem of
maximizing the net bit transmission benefit as a Mixed Integer
Programming (MIP) is put forward with the transmission rate
constraint. To simplify the complexity of MIP problem, the
subchannel allocation is processed based on the proportion of
quality of service requirement, meanwhile the barrier method
with BFGS algorithm is used to solve the power allocation.
Simulation results validate that, the proposed resource
allocation scheme can increase the net bit transmission benefit
and improve the energy supply-demand ratio; furthermore the
small cell base station cooperating with the smart grid is more
beneficial to the energy efficient design. Index Terms—Resource allocation, smart grid, energy supply-
demand, real-time pricing, mixed integer programming.
I. INTRODUCTION
Rapid wireless communication industry development
has led to a dramatic increase of energy consumption,
especially, energy consumption of cellular Base Stations
(BSs) in wireless networks accounts for more than 60%
[1]. The electricity bill has become a significant portion
of the operational expenditure of cellular operators.
Therefore, the rising energy costs and carbon footprint of
operating cellular networks have led to an emerging trend
of addressing Energy Efficiency (EE) for the base station
[2], [3].
Recently, green communications have received
considerable attention [4]-[11] which aim at enhancing
EE for the base station. In both downlink and uplink
cellular networks with Orthogonal Frequency Division
Multiple Access (OFDMA), Reference [4] studied the
energy-efficient resource allocation and developed a
suboptimal but low-complexity approach by exploring
the inherent structure and property of the energy-efficient
design. In the next-generation cellular networks,
Reference [5] provided an extensive overview of the
intelligent cooperation management techniques such as
switching cell, cell zooming, heterogeneous networks and
mobile operator cooperation. Under the statistical Quality
of Service (QoS) provisioning, Reference [6] formulated
the resource allocation problem as a maximization of
effective capacity based bits-per-joule capacity. For the
multicell OFDMA networks, Reference [7] investigated
the distributed power allocation by taking both the energy
efficiency and the intercell interference mitigation into
account. In order to realize the users’ fairness, Reference
[8] proposed a bisection-based optimal power allocation
to maximize EE and guarantee proportional data rates for
users in a downlink OFDM-based mobile communication
system. Considering the cognitive radio network,
Reference [9] investigated the power allocation as a
constrained fractional programming problem to maximize
the energy efficiency. Furthermore, Reference [10]
presented an in-depth mathematical analysis of the
maximization of energy efficiency by considering the
QoS. Reference [11] proposed a suboptimal two-step
power allocation algorithm to maximize the energy
efficiency based on OFDM-based frequency selective
channel of amplify-and-forward relay link.
On the other hand, the power grid as the energy
supplier of cellular networks is developing a new
infrastructure of smart grid. The smart grid integrates
more renewable energy sources such as the wind energy
source and the solar energy source to produce more
electrical energy. But these renewable energy sources
vary over time and the unpredictable weather, which are
highly intermittent in nature and often uncontrollable. So
the integration of the renewable energy resources into the
traditional power grid infrastructure is very difficult,
which easily result in the unbalance of energy supply and
demand.
An intuitive way to tackle the unbalance of energy
supply and demand is that, energy should be consumed or
stored once produced. When production exceeds
consumption, the surplus energy should be stored
immediately, but the storage capacity is limited for the
present technology [12], [13]. Therefore, the Demand-
Side Management (DSM) may be more feasible for this
problem where the dynamic price can be used to adjust
the consumed electricity. The dynamic pricing of DSM
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includes critical peak pricing, time-of-use pricing and
Real-Time Pricing (RTP), which is used to improve the
reliability of the power grid by dynamically changing or
shifting the electricity consumption.
Hence, from the energy supply and demand point of
view, only considering energy efficiency in the cellular
network may not be enough [3]. The wireless cellular
network should change the consumed energy quantity
according to the dynamic pricing, which can generate
more or less bit transmission benefit meanwhile balance
the energy supply and demand of smart grid. Thus BSs
should cooperate with the smart grid to manage the
energy consumption.
To the best of our knowledge, there are only limited
works on energy aware issues with smart grid in wireless
cellular networks so far. Reference [14] studied the
optimizing green energy utilization with both the
traditional power grid and green energy in cellular
networks. Reference [15] reviewed recent energy
efficient advances made at specific point within the
communications cycle such as components, network
operation and topology, by incorporating renewable and
alternative energy into base stations. Reference [16]-[18]
formulated the cellular network and multiple power
retailers as a two-level Stackelberg game for the
coordinated multipoint communications and the cognitive
mobile network with small cells. Reference [19] studied
the energy efficient resource allocation in OFDMA
systems powered by hybrid renewable energy. As an
important interaction parameter between power grid and
BS, the dynamic pricing model should have more effect
on the energy-aware design. But the problem of energy
efficient design for BS with the electricity price model
has not been studied based on the energy supply and
demand, which can be more conducive to energy saving
and hence the main focus of this paper.
In this paper, we show that how to design energy
aware resource allocation with the influence of electricity
bill model under the smart grid environment. Firstly,
based on the energy supply and demand, the net bit
transmission benefit metric is put forward with the RTP
model for the cognitive cellular. Secondly, under the
influence of the energy supply’s fluctuation in smart grid
and the interference constraint of Licensed Cellular Base
Station (LCBS), a mixed integer programming problem
(MIP) of the allocation for power and subchannel is
designed. Thirdly, to reduce the computational
complexity of MIP, the QoS based subchannel allocation
algorithm and the efficient barrier method with BFGS
(B_BFGS) algorithm for the power allocation are
described. In addition, some discussions about the
complexity and the realization of proposed algorithms are
given.
The rest of this paper is organized as follows. In
Section II, the system model is described. In Section III,
the energy aware optimization problem is given. In
Section IV, the simplified QoS based subchannel
allocation algorithm and the joint of barrier method with
BFGS algorithm for MIP are proposed. The discussion
and the realization for the proposed algorithm are given
in Section V. Numerical results are provided in Section
VI. Finally, we summarize the paper with some
concluding remarks in Section VII.
II. SYSTEM MODEL
We assume there are several service regions, which are
powered by the smart grid with individual RTP. In each
service region, there are multiple electricity users
including one cognitive cellular system. All electricity
users are connected to the electricity supplier through the
network communication system of the smart grid. The
cognitive cellular system contains one licensed cell with
M Primary Users (PUs) and multiple cognitive cells with
Secondary Users (SUs). The SUs share the spectrum
licensed by the PUs via the Cognitive Cellular Base
Stations (CCBSs). All CCBSs are connected to the LCBS
over a broadband connection, such as the Digital
Subscriber Line (DSL). In the scenario considered by this
paper, the CCBSs are deployed sparsely, so that the
mutual interference between the CCBSs is negligible.
The system model is shown in the Fig. 1.
The other
electricity
devices
Service Region of
Smart Grid
LCBS
CCBS
PU
PU
SUSU
SU
Traditional
Energy
Renewable
Energy
Smart Grid
+
CCBS
The electricity supplier...
RTP, energy consumption
informationelectricity
Fig. 1. The system model
The system is operated in a time-slotted manner, which
is assumed with unit time slot. At each time slot, multiple
CCBSs can use the same subchannel as the PU in each
service region, and then each CCBS assigns one most
appropriate user to each subchannel. We only
demonstrate the situation of one CCBS in the service
region, because we mainly focus on how the decisions in
the CCBS are affected by the supply’s fluctuation of
smart grid and the interference constraint of licensed cell
base station. The model also can be extended to multiple
CCBSs situations using various techniques, such as dual
decomposition technique or game theory.
In each service region, assuming that the other
electricity users include all the electricity users except the
CCBS, which have their own independent rule of energy
consumption and are not related to RTP. Thus the energy
consumption of the other electricity users can be denoted
as Lu, which is modeled as a constant for simplicity in
this paper. The fluctuation influence analysis of the other
electricity users to the service region is similar to the
following energy supply’s fluctuation.
The renewable energy sources integrated by the smart
grid are highly intermittent and often uncontrollable,
which easily result in the energy supply’s fluctuation of
the smart grid. In order to balance the fluctuation
effectively with RTP, the electricity supplier can provide
a scheduled power consumption capacity for each service
region, which is denoted as t
SL . Different from the given
generation rule of the renewable energy sources in some
studies [13], [14], [19], the scheduled power consumption
capacity for each service region fluctuates with the
generation capacity of the renewable energy, traditional
energy and the energy demand, which is not the focus of
this paper. Denote the renewable energy induced by the
harvested fluctuation as t
HE for this service region in the
time slot t. Due to the energy causality, the harvested
energy cannot be consumed before its arrival [20].
Thus for simplicity, the fluctuation rule of scheduled
power consumption capacity for each service region in
each time slot is modeled as follows
t t t
S G HL E E (1)
where t
GE is the average power consumption capacity of
the traditional grid is this service region.
For the dynamic pricing, considering that the CCBS is
affected by the energy supply’s fluctuation of smart grid
and the interference constraint of LCBS in the service
region, we assume that the energy consumed by the
CCBS can influence the RTP in terms of its quantity,
which can produce scale effect with much more CCBSs
in practice. In a discrete time slot, applying the principle
of congestion pricing in IP networks to the DSM [21], the
RTP is related to the energy supply-demand ratio of this
service region and the benchmark price of electricity
supplier, which can be defined as follows
t
t t
S
LP
L
(2)
where α is the benchmark price of electricity supplier,
which is a constraint factor that can control the general
level of the electricity price. γ is an incentive factor,
which can control the sensitivity of the price to the real-
time energy demand. Lt is the real-time power consumed
by this service region, including the considered CCBS
and other electricity users. So Lt can be modeled as
t
t b uL L L (3)
where t
bL as the power consumption of CCBS contains
the transmission power, the circuit energy consumption
incurred by signal processing and active circuit blocks in
the active mode of transmitter. Without loss of generality,
the associated circuit power consumption is modeled as a
constant LC [22]. Thus the energy consumption model of
CCBS t
bL and the energy consumption model of the
service region Lt can be expressed respectively as
, ,
1 1
K Nt t t
b k n k n C
k n
L l L
(4)
, ,
1 1
K Nt t
t k n k n C u
k n
L l L L
(5)
where ,
t
k nl is the power allocated to the nth subchannel
used by the kth SU, k=1, 2,…, K. K is the number of SUs
in each service region.,
t
k n can be either 1 or 0 informing
whether the subchannel n is occupied by the kth SU or
not.
Assuming that the SUs have the lowest rate
requirements Rk,min. The whole available bandwidth W is
divided into N OFDM subchannels for the cognitive radio
(CR) network, and the bandwidth of each subchannel is
W/N, which spans from f0 + (n-1)W/N to f0 + nW/N in the
nth subchannel with the starting frequency f0. Assume the
mth PU’s nominal band ranges from fm to fm + Bm, where
fm and Bm are the mth PU’s starting frequency and
bandwidth.
We assume that the CCBS has perfect knowledge of
channel state information between the transmitter of the
CCBS and the receivers of the SUs, as well as between
the transmitter of the CCBS and the receivers of the PUs.
The channel state information can be collected through
channel reciprocity between uplink and downlink. The
scenario with the imperfect channel state information will
be considered in the future paper. When the CCBS
transmits information over the nth subchannel with unit
transmission power, the interference introduced to the
mth PU is [23]
0
0
( 1/2) /
, ,( 1/2) /
( )m m
m
f B f n W NSP
n m n mf f n W N
I f df
(6)
where ,n m is the power gain from the CCBS to the
receiver of the mth PU over the nth subchannel. ( )f is
the power spectrum density (PSD) of OFDM signal with
( )f = T ((sin πfT)/(πfT) )2, where T is the OFDM
symbol duration. To ensure the performance of the PUs,
the interference introduced to the PUs must be carefully
controlled in a tolerable range.
Let ,
t
k nr denotes the transmission rate of the nth
subchannel used by the kth SU, we have
2
, ,
, 2
0
log 1( / )
t t
k n k nt
k n PS
k
l hWr
N N W N I
(7)
where ,
t
k nh is the channel gain from the CCBS to the kth
SU’s receiver over the nth subchannel. N0 is the PSD of
additive white Gaussian noise and Γ is the SNR gap. For
an uncoded multilevel quadrature amplitude modulation,
Γ related to a given Bit-Error-Rate (BER) requirement
with Γ =−ln(5BER)/1.5 as derived in [24]. PS
kI is the
interference caused by the PUs’ signals to the kth SU,
which can be measured by the receivers of SUs [25].
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is
III. THE PROBLEM FORMULATION
Generally, energy efficiency is defined as the
transmission rate per unit of the consumed power with the
unit of bit/Joule. In this paper, we utilize the energy
aware performance criterion to measure the structure,
which is to consider the energy cost during transmissions
with the unit of bit/s [26]. The CCBS produces the bit
transmission benefit by transmitting the information to
many SUs; meanwhile the power consumption cost
should be taken into account. Thus the energy aware
performance criterion is adopted to measure the bit
transmission benefit in the rest of this paper. In the
discrete time slot, the energy aware utility function of the
CCBS called the net bit transmission benefit can be
represented as
, ,
1 1
K Nt t t t
E k n k n t b
k n
u r PL
(8)
where the front part represents the bit transmission
benefit and the latter part represents the energy cost of the
CCBS. In order to be unified with the bit transmission of
front part in Equation (6), Pt as an energy price parameter
is with the unit of bit/s/W.
We try to maximize the bit transmission benefit and
minimize the energy cost, by allocating the subchannels
and the power appropriately. The concerned problem is
formulated as
, ,
2
, ,
, 2,
1 1 0
max log 1( / )t t
k n k n
t tK N
k n k nt t
k n t bPSl
k n k
l hWP L
N N W N I
, , ,min
1
. . 1 , 1,2, ,N
t t
k n k n k
n
s t C r R k K
, ,
1 1
2K N
t t
k n k n total
k n
C l L
(9)
,3 0, 1,2, , , 1,2, ,t
k nC l n N k K
, , ,
1 1
4 , 1, ,K N
t t SP th
k n k n n m m
k n
C l I I m M
,5 0,1 , 1,2, , , 1,2, ,t
k nC n N k K
,
1
6 1, 1,2, ,K
t
k n
k
C n N
where Ltotal is the transmission power limit of the CCBS, th
mI is the interference threshold of the mth PU. C1
guarantees the minimal rate requirements of the SUs, C2
is the constraints on transmission power budget. C4
contains the interference constraints of the PUs. C5 and
C6 guarantee that one subchannel can be only allocated to
one SU.
Note that (9) defines a mixed integer programming
(MIP) problem that involves both binary variables
,
t
k n and real variables ,
t
k nl for optimization. The main
difficulty lies in the integer constraint of C5. An intuitive
way to tackle them is TS) method [27],
which simply relaxes the integer variables into real ones.
But it still suffers from non-convex problem and is
generally infeasible for the problem (9).
IV. THE SIMPLIFIED MIP SOLUTION
A. The QoS Based Subchannel Allocation
Through analyzing the structure of the MIP problem
(9), it’s easy to conclude that the capacity increases
linearly with bandwidth, but only logarithmically with
power. Meanwhile considering the importance of channel
diversity for the throughput, the subchannels should be
allocated to individual SUs firstly based on the proportion
of QoS requirement and fairness by ignoring the allocated
power for simplify.
We introduce a subchannel allocation factor πk for the
kth SU, by rounding the proportion of QoS requirement
for each SU which is defined as
,min
1,min 2,min ,min
max ,1k
k
K
R Nround
R R R
(10)
It is easily concluded from Equation (10) that, higher
rate requirement has bigger subchannel allocation factor
and one subchannel is allocated to each SU at least. The
channel condition, the interference to the PU and the
power constraint will be considered in the stage of power
allocation. Therefore, the subchannels can be allocated
through the following three steps.
-First step. Initialization:
Calculate the subchannel allocation factor πk according
to Equation (10).
-Second step. Allocation Body:
Check whether πk is equal to 0 for the kth SU;
Yes, one subchannel is allocated for the kth SU, πk=πk -
1;
No, turn to the (k+1)th SU, and continue until that the
subchannels are allocated to all the SUs.
-Third step. Judgment:
If there are any subchannels left, then continue the
allocation process from the second step;
Or else, the subchannel allocation process stops.
Finally, denote the set of subchannels allocated to the
kth SU as Ωk, the concerned MIP problem (9) is
transformed to
,
2
, ,
2
1 0
max log 1( / )t
k nk
t tK
k n k n t
t bPSl
k n k
l hWP L
N N W N I
, ,min. . 1 , 1,2, ,k
t
k n k
n
s t C r R k K
,
1
2k
Kt
k n total
k n
C l L
(11)
,3 0, , 1,2, ,t
k n kC l n k K
, ,
1
4 , 1, ,k
Kt SP th
k n n m m
k n
C l I I m M
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Journal of Communications Vol. 10, No. 7, July 2015
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the Time-Sharing (
B. The Joint of Barrier Method with BFGS Algorithm
When the subchannel allocation is given, the main
difficulty of binary variables is solved, thus we only need
to solve the power allocation among subchannels to
maximize the bit transmission benefit while keeping the
lowest energy cost. By analyzing the problem (11), the
standard convex optimization techniques can be applied
to obtain the global optimal solution generally [28], but
the complexity always is high. In this part, we develop an
efficient barrier method with BFGS algorithm based on
the Armijo search for the optimal power allocation.
In the barrier method, we define a logarithmic barrier
function firstly. The barrier function of (11) is as follows
2 , ,min 2 ,
1 1
2 , 2 , ,
1 1 1
( ) log log
log log
k k
k k
K Kt t
t k n k total k n
k n k n
K M Kt th t SP
k n m k n n m
k n m k n
r R L l
l I l I
l
(12)
where 1 2, , ,t t t
Nl l ll . Notice that the subscript k is
omitted now as it is fixed for a given subchannel
assignment. Denote
2
, ,
2
1 0
( ) log 1( / )
k
t tK
k n k n t
t t bPSk n k
l hWy P L
N N W N I
l
Then by introducing parameter v, which decides the
accuracy of the approximation, the objective problem (11)
is converted into a sequence of unconstrained
minimization problems
min ( ) ( ) ( )t
v t tvy l l l (13)
Since function ( )t
v l is convex and twice continuously
differentiable, (13) has a unique optimal solution. The
optimal solution of (11) can be approximated by solving
the unconstrained minimization problem. As v increases,
the approximation becomes more and more accurate to
the optimal solution of the original problem [28].
Particularly, each unconstrained minimization problem
with the given v can be solved by Newton method.
Denote the Hessian matrix and the gradient of ( )t
v l
respectively as follows
2 ( )t
vG l
( )t
vg l
Further to reduce the computational difficulty of the
Hessian matrix, the BFGS algorithm based on the Armijo
search can be applied to solve the unconstrained
minimization problem [29]. BFGS correction for Hessian
matrix approximation has faster convergence and
superlinear convergence rate. The efficient joint of the
barrier method and the BFGS algorithm is denoted as
B_BFGS algorithm in Algorithm 1. During the iteration,
assume offset qj=lj+1-lj, gradient difference fj=gj+1-gj,
Hessian matrix can be approximated by the symmetric
positive definite matrix as
1
, 0,
, 0
T
j j j
T T
j j j j j j j T
j j jT T
j j j j j
A f q
A A q q A f fA f q
q A q f q
(14)
Algorithm 1: The B_BFGS algorithm
0. The barrier method part:
1. Initialization
2. Find feasible point l0, v := v(0) > 0, tolerance є > 0, μ > 1
3. Outer loop
4. Centering step: compute l*(v) derived by problem (13)
5. The BFGS algorithm part:
6. Initialization
7. Starting point l0, (0,1) , (0,0.5) , A0=G(l0),
8. termination error value 0 1 , : 0j
9. Inner loop
10. Compute gj, quit if j
g , output lj;
11. else compute j jA d g , get
jd ;
12. Denote minimum nonnegative integer sj meet
13. ( ) ( )s s T
j j j
t t
v j v jd g d l l ,
14. Denote js
ja , 1j j j j
a d l l ;
15. Compute Aj+1 by (14), : 1j j ;
16. Update: l *(v) = lj.
17. Stopping criterion: (N +K+M+ 1)/v < є.
18. Increase: v := μv
V. THE DISCUSSION AND REALIZATION OF THE
PROPOSED ALGORITHM
A. Optimality Discussions and Complexity Analysis
In the stage of subchannel allocation, to remove the
integer constraints of the MIP problem, the proposed
simplified solution ignores the power constraint for
simplicity only considering the QoS requirement and
fairness of the SUs. In the stage of power allocation, the
proposed B_BFGS algorithm makes use of the BFGS
correction for Hessian matrix approximation. So the
simplified solution and algorithm are suboptimal for the
original optimization problem.
The computational complexity can be counted roughly
as follows. The original convex optimization problem (9)
with 2𝑁K variables and (2NK+N+K+M+1) constraints is
simplified as problem (11) with 𝑁 variables and
(N+K+M+1) constraints. Meanwhile the B_BFGS
algorithm also reduces the computational complexity of
Hessian matrix.
B. The Realization for One CCBS
In this scenario, the CCBS acts as the only power users
to adjust the fluctuation of energy supply and demand in
the smart grid. There are two methods to realize the
energy efficient resource allocation and the adjustment of
energy supply and demand. One is that the variation rules
of energy consumed by other electricity users and the
scheduled power consumption information LS reflecting
the supply’s fluctuation information can be conveyed to
the CCBS, so that the proposed simplified solution can be
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©2015 Journal of Communications
performed in the CCBS, and the RTP is obtained to adjust
the energy supply and demand during the process of
resource allocation. It is straightforward and ideal, but
may be only suitable to the scenario of only one CCBS.
The other method is that, the RTP is decided by the
electricity supplier, under the circumstance that the RTP
information and the energy consumption information are
conveyed between the CCBS and the electricity supplier.
Multiple iterative processes are needed in this method,
which is similar to the scenario of multiple CCBSs below.
C. The Realization for Multiple CCBSs
When there are multiple CCBSs as the main electricity
users in the service region, the electricity supplier and
CCBSs are connected through the network
communication system, which can deliver the energy
consumption information and the RTP calculated by the
electricity supplier according to the energy supply and
demand. Because the utility function of every CCBS is
private, it could not be conveyed to the electricity
supplier. Therefore this is a distributed mechanism for
two-stage energy allocation. The first stage is the energy
allocation for multiple CCBSs, and the second stage is
the energy allocation for the SUs in each small cell. The
two stages interact with each other to maximize the
individual net bit transmission benefit utility, which make
it more complex. For simplicity the power load and price
forecasting mechanism is not considered temporarily in
this paper.
In practice, the relation of the electricity supplier and
multiple CCBSs can also be seen as a Stackelberg game.
We can easily get the twice derivation of t
Eu in (8), which
prove the utility function t
Eu is a concave function and
there is at least one Nash equilibrium [30]. The proposed
iterative algorithm can be implemented to obtain the
Stackelberg equilibrium. In each time slot, the working
process is as follows:
The electricity supplier of the smart grid first offer an
initial electricity price according to (2) and broadcast
the information, where the supply-demand ratio of
this service region is set as 1.
Multiple CCBSs receive the price information, each
CCBS performs its energy-efficient subchannel and
power allocation according to (9), then broadcast its
energy consumption information.
Based on the received energy consumption
information of every CCBS and the supply’s
fluctuation information of the smart grid, the
electricity supplier updates the electricity price
according to (2) and broadcast the information. Then
repeat steps (b), the iteration stops until the prices
converge or meet the termination criteria.
The termination criteria for the proposed iterative
algorithm can be set as
1i i
t tP P (15)
where parameter ω is set to a small value, such as 1%.
The best response of the electricity supplier i
tP at
iteration i is the electricity price based on the energy
supply and demand. In this way, the smart grid and
CCBSs can effectively balance the energy supply and
demand, meanwhile maximize the net bit transmission
benefit under the given electricity price.
VI. NUMERICAL RESULTS
In this section, some brief numerical results are
presented regarding the energy aware criterion
performance of one CCBS with RTP in order to validate
the proposed solution. We compare the proposed solution
with the optimal algorithms: TS method. The solution of
the TS method is an upper bound of the original problem
(9). The upper bound is generally infeasible and can only
be approached by feasible solutions of the problem (9).
We consider the downlink of cognitive cellular
coexisting with a licensed cellular in each service region,
which is powered by the smart grid. Assume that only
one CCBS’s energy fluctuates with RTP. The benchmark
price is α=4Mbits/s/W [25], LC=0.25W [22], Lu=10W, t
GE is set as 10.65W, the harvested energy follows non-
negative uniform distribution with mean 20dBm [20].
There are 2 PUs and 8 SUs randomly distributed in the
square region in a 3 × 3km area. The path loss exponent
is 4 and the variance of shadowing effect is 10dB. The
channel gains h and g are modeled as independent,
identically distributed Rayleigh random variables with an
average of 0 dB. Assume there is 20MHz available
bandwidth, which is divided into 64 OFDM subchannels.
Suppose the noise power is 10-13
W, Rk,min = 6Mbit/s. All
results are average of 50 samples during 1000s.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8160
170
180
190
200
210
220
Transmission Power Limit (W)
Avera
ge N
et
Bit T
ransm
issio
n B
enefit
(Mbits/s
)
γ=0 for proposed solution
γ=1 for proposed solution
γ=2 for proposed solution
γ=2 for TS
Fig. 2. The net bit transmission benefit utility against transmission power limit for different incentive factor
Fig. 2 depicts the net bit transmission benefit utility
versus transmission power limit for different incentive
factor γ of RTP. The interference thresholds of all PUs
are set to 5× 10-12
W. At the beginning, the net bit
transmission benefit increase quickly with the increase of
transmission power limit, but then the growth of net bit
transmission benefit is slowed with the sufficient
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Journal of Communications Vol. 10, No. 7, July 2015
©2015 Journal of Communications
transmission power limit. That is because the CR system
outage can be reduced for more Ltotal, the net bit
transmission benefit achieves the optimum under a
certain consumed power of CCBS. For the same Ltotal, the
net bit transmission benefit is bigger for higher γ, because
γ can control the sensitivity of the price to the real-time
demand. For γ =0, it is a fixed uniform price; for γ =1or 2,
the RTP has more effect on the consumed power of
CCBS and the net bit transmission benefit with the
electricity bill. In addition, when γ= 2, the proposed
heuristic solution achieves more than 98% of the TS
method, which indicates our proposed heuristic method
performs quite well for the considered problem.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8130
140
150
160
170
180
190
200
210
Transmission Power Limit (W)
Avera
ge N
et
Bit T
ransm
issio
n B
enefit
(Mbits/s
)
LC=0.25W
LC=0.35W
Fig. 3. The net bit transmission benefit utility for different circuit power
Fig. 3 depicts the net bit transmission benefit utility
against the transmission power limit for different circuit
power. Under the energy supply’s fluctuation of smart
grid, the CCBS with LC=0.25W can gain more net bit
transmission benefit than that with LC=0.35W. That is
because with lower circuit power, the more power can be
used to transmit information for the same electricity bill.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Transmission Power Limit(W)
Lb/L
tota
l
γ=0
γ=1
γ=2
Fig. 4. Lb / Ltotal vs. transmission power limit
Fig. 4 depicts Lb/Ltotal versus transmission power limit
for different incentive factor γ. When Ltotal is lower than
0.65W, Lb/Ltotal is 1 for all γ. That is because in order to
meet the QoS of SUs, lower Lb is inevitably work out,
which means Lb is equal to Ltotal. But when Ltotal is higher
than 0.65W, Lb/Ltotal is reduced to lower than 1. During
this stage, the consumed power does not necessarily lead
to a higher net bit transmission benefit for the higher
electricity bill cost. So on average the optimized Lb is not
necessarily equal to Ltotal, especially for high values of
Ltotal. From the figure we also observe that, the curve of
Lb/Ltotal decline lastly and higher for γ=2 than γ=1. That is
because higher γ can control the price easily with lower
price and more energy consumption, to balance the
energy supply and demand meanwhile result in higher net
bit transmission benefit.
We can define the ratio of the energy supply and
demand which can evaluate the RTP’s influence to the
smart grid through the energy consumption of CCBS
more precisely. It is defined as follows
, ,
1 1100%
K Nt t
k n k n C u
k n
t t
S
l L L
L
(16)
Fig. 5 illustrates the ratio of the energy supply and
demand against the transmission power limit for different
available bandwidth. When the transmission power limit
is below 0.4W, the adjustment effect is affected by the
power budget LS, which is also observed in the Fig.4.
During this stage, the ratios of the energy supply and
demand increase with the increase of the transmission
power limit. When the transmission power limit is above
0.4W, its influence to the adjustment effect is eliminated,
where the adjustment effect reach 98% for W=25MHz
and 99.3% for W=20MHz. The ratio of the energy supply
and demand is more close to 1 for W=20MHz than that
for W=25MHz, which is because the less available
bandwidth lead to more energy consumed for the CCBS,
so the adjustment to the balance of the energy supply and
demand is more remarkable.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
Transmission Power Limit (W)
Ratio o
f E
nerg
y S
upply
and D
em
and (
×100%
)
W=20MHz
W=25MHz
Fig. 5. Ratio of the energy supply and demand
Fig. 6 shows the net bit transmission benefit utility
against the interference threshold of the PU, for the
different benchmark price. The transmission power limit
of the CCBS is 0.4W and the incentive factor γ=1. It is
shown that the net bit transmission benefit increases
quickly in the beginning part of the interference threshold,
but changes little from the interference threshold of
40×10-12
W. The reason is that the lower interference
threshold induces more frequent outage of the CR system.
It also can be seen that higher α can decrease the net bit
transmission benefit of the CR system, which can be
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Journal of Communications Vol. 10, No. 7, July 2015
©2015 Journal of Communications
explained that higher α has bigger electricity bill with the
same consumed power.
5 15 25 35 45 55 65 75210
215
220
225
230
235
240
The Interference Threshold of PU(×10-12W)
Avera
ge N
et
Bit T
ransm
issio
n B
enefit
(Mbits/s
)
α=16
α=4
Fig. 6. The net bit transmission benefit utility against the interference threshold
10 20 30 40 50 60 70 80 90 10020
30
40
50
60
70
80
Random instance
Num
ber
of
itera
tions
γ=2
γ=1
Fig. 7. The convergence vs. random instance
0 10 20 30 40 50 60 70 80198
200
202
204
206
208
210
212
Number of iterations
The N
et
Bit T
ransm
issio
n B
enefit
(Mbits/s
)
γ=1 for proposed solution
γ=2 for proposed solution
Fig. 8. The system performance versus the number of iterations
We investigate the convergence of the proposed
B_BFGS method. As discussed in the proposed solution,
the computational load mainly lies in the number of
iterations for the proposed B_BFGS method. From Fig. 7,
we observe that the number of iterations varies in a
narrow range, while the average number of iterations is
about 47 with γ=2 and 53 with γ=1. That is because
higher incentive factor can have more effect on the
adjustment so as to reach its equilibrium quickly.
Similarly, the system performance versus the number of
iterations of the proposed algorithm is also given in Fig. 8.
With the increasing iteration number, the net bit
transmission benefit utility curve goes to a fixed value.
We conservatively conclude that the proposed B_BFGS
method is effective and efficient.
VII. CONCLUSIONS
In this paper, the net bit transmission benefit metric in
cognitive cellular system is proposed with the RTP of
smart grid. A simplified power and subchannel allocation
optimization problem and an efficient B_BFGS algorithm
based on the Armijo search are designed. The simulation
results imply that, the cooperation of cellular base station
and smart grid can be positive to influence the power
consumed by the CCBS, and the RTP of smart grid is
favor of the balance of energy supply and demand. In the
future, a general framework of spectral efficiency and
energy efficiency and the tradeoff between energy
efficiency and spectral efficiency of the cellular network
with joint energy harvesting and grid power supply will
be our future work.
ACKNOWLEDGMENT
The authors would like to thank the reviewers for their
detailed reviews and constructive comments. This work
was supported in part by the National Natural Science
Foundation of China under Grants No.61302105,
61302163; the Fundamental Research Funds for the
Central Universities under Grant No.13QN40.
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Baogang Li was born in Hebei Province,
China, in 1980. He received the Ph.D. degree
from Beijing University of Posts and
Telecommunications of China (BUPT),
Beijing, in 2012. He is now with School of
Electronic and Communication engineering,
North China Electric Power University of
China. His research interests include cognitive
wireless networking, mobile communication
and green networking.
Xuewei Wang received the Bachelor degree
from Hebei Normal University of China,
Shijiazhuang, in 2014. She is now studying for
the Master degree in the North China Electric
Power University of China. Her research
interests include mobile and cellular networks,
network optimization and energy efficient
networking.
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Journal of Communications Vol. 10, No. 7, July 2015
©2015 Journal of Communications
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