Energy Supply-Demand Balance Based Resource Allocation for ...

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

526

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

527



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].

528


©2015 Journal of

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

529



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

530



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=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

531



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


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


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

532



app:ds:and

app:ds:demand

app:ds:and

app:ds:and

app:ds:and

app:ds:supply

app:ds:and

app:ds:demand

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

)



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.

REFERENCES

[1] M. A. Marsan, L. Chiaraviglio, D. Ciullo, and M. Meo, “Optimal

energy savings in cellular access networks,” in Proc. IEEE ICC,

Dresden, 2009, pp. 1-5.

[2] D. Feng, C. Jiang, G. Lim, et al., “A survey of energy-efficient

wireless communications,” IEEE Commun. Survey & Tutorials,

vol. 15, no. 1, pp. 167-178, 2013.

[3] Z. Hasan, H. Boostanimehr, and V. K. Bhargava, “Green cellular

networks: a survey, some research issues and challenges,” IEEE

Commun. Surveys & Tutorials, vol. 13, no. 4, pp. 524-540, 2011.

[4] C. Xiong, G. Y. Li, S. Zhang, Y. Chen, and S. Xu, “Energy-

efficient resource allocation in OFDMA networks,” IEEE Trans.

on Commun., vol. 60, no. 12, pp. 3767-3778, 2012.

[5] A. Mohammed, H. N. Rosdiadee, and I. Mahamod, “A review on

intelligent base stations cooperation management techniques for

greener LTE cellular networks,” Journal of Communications, vol.

9, no. 12, pp. 937-945, 2014.

[6] A. Aijaz, X. Chu, and A. H. Aghvami, “Energy efficient design of

SC-FDMA based uplink under QoS constraints,” IEEE Wireless

Commun. Letters, vol. 3, no. 2, pp.149-152, 2014.

[7] Z. Ren, S. Chen, B. Hu, and W. Ma, “Energy-efficient resource

allocation in downlink OFDM wireless systems with proportional

rate constraints,” IEEE Trans. on Vehicular Technology, vol. 63,

no. 5, pp. 2139-2150, 2014.

[8] Z. Fei, C. Xing, N. Li, and J. Kuang, “Adaptive multiobjective

optimisation for energy efficient interference coordination in

multicell networks,” IET Commun., vol. 8, no. 8, pp. 1374-1383,

2014.

[9] M. Naeem, K. Illanko, A. Karmokar, A. Anpalagan, and M.

Jaseemuddin, “Optimal power allocation for green cognitive radio

533



app:ds:of

app:ds:supply

app:ds:and

app:ds:demand

fractional programming approach,” IET Commun., vol. 7, no. 12,

pp. 1279-1286, 2013.

[10] T. O. Ting, S. F. Chien, X. Yang, and S. Lee, “Analysis of quality-

of-service aware orthogonal frequency division multiple access

system considering energy efficiency,” IET Commun., vol. 8, no.

11, pp. 1947-1954, 2014.

[11] Y. Chen, X. Fang, and Y. Zhao, “Energy-efficient adaptive power

allocation in orthogonal frequency division multiplexing-based

amplify-and-forward relay link,” IET Commun., vol. 7, no. 15, pp.

1676-1687, 2013.

[12] F. Genoese, M. Genoese, and M. Wietschel, “Occurrence of

negative prices on the German spot market for electricity and their

influence on balancing power markets,” in Proc. International

Conference on the European Energy Market, Madrid, 2010, pp. 1-

6.

[13] M. Nicolosi, “Wind power integration and power system

flexibility-an empirical analysis of extreme events in Germany

under the new negative price regime,” Energy Policy, vol. 38, no.

11, pp. 7257-7268, 2010.

[14] T. Han and N. Ansari, “On optimizing green energy utilization for

cellular networks with hybrid energy supplies,” IEEE Trans. on

Wireless Commun., vol. 12, no. 8, pp. 3872-3882, 2013.

[15] H. An, A. Ashwin, T. Thomas, et al., “Green communications: A

call for power efficient wireless systems,” Journal of

Communications, vol. 6, no. 4, pp. 340-351, 2011.

[16] S. Bu, F. R. Yu, Y. Cai, and X. P. Liu, “When the smart grid

meets energy-efficient communications green wireless cellular

networks powered by the smart grid game,” IEEE Trans. on


[17] S. Bu, F. R. Yu, and Y. Qian, “Energy-efficient cognitive

heterogeneous networks powered by the smart grid,” in IEEE

Infocom, Turin, 2013, pp. 980-988.

[18] S. Bu and F. R. Yu, “Green cognitive mobile networks with small

cells for multimedia communications in the smart grid

environment,” IEEE Trans. on Vehicular Technology, vol. 1, no. 1,

pp. 1-12, 2014.

[19] D. W. K. Ng, E. S. Lo, and R. Schober, “Energy-efficient resource

allocation in OFDMA systems with hybrid energy harvesting base

station,” IEEE Trans. on Wireless Commun., vol. 12, no. 7, pp.

3412-3427, 2013.

[20] J. Gong, S. Zhou, and Z. Niu, “optimal power allocation for

energy harvesting and power grid coexisting wireless

communication systems,” IEEE Trans. on Commun., vol. 61, no. 7,

pp. 3040-3049, 2013.

[21] F. Zhong, “A distributed demand response algorithm and its

application to PHEV charging in smart grids,” IEEE Trans. on

Smart Grid, vol. 3, no. 3, pp. 1280-1290, 2012.

[22] G. Miao, N. Himayat, and G. Li, “Energy-efficient link adaptation

in frequency-selective channels,” IEEE Trans. on Commun., vol.

58, no. 2, pp. 545-554, 2010.

[23] S. M. Almalfouh and G. L. Stuber, “Interference-aware radio

resource allocation in ofdma-based cognitive radio networks,”

IEEE Trans. on Vehicular Technology, vol. 60, no. 4, pp. 1699-

1713, 2011.

[24] A. J. Goldsmith and S. G. Chua, “Variable-rate variable-power

MQAM for fading channels,” IEEE Trans. Commun., vol. 45, no.

10, pp. 1218-1230, 1997.

[25] P. Setoodeh and S. Haykin, “Robust transmit power control for

cognitive radio,” Proc. of the IEEE, vol. 97, no. 5, pp. 915-939,

2009.

[26] E. Jorswieck, H. Bophe, and S. Naik, “Energy-aware utility

regions multiple access pareto boundary,” IEEE Trans. on


[27] M. Ge and S. Wang, “Fast optimal resource allocation is possible

for multiuser OFDM-Based cognitive radio networks with

heterogeneous services,” IEEE Trans. on Wireless Commun., vol.

11, no. 4, pp. 1500-1509, 2012.

[28] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge

University Press, 2004.

[29] W. Sun and Y. X. Yuan, Optimization Theory and Methods,

Springer, 2006.

[30] G. Debreu, “A social equilibrium existence theorem,” in Proc. Nat.

Acad. Sciences, 1952, no. 38, pp. 886-893.

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.

534



Energy Supply-Demand Balance Based Resource Allocation for ...

Documents