Efficient Resource Allocation Algorithm with Rate ... · Efficient Resource Allocation Algorithm...

Efficient Resource Allocation Algorithm with Rate

Requirement Consideration in Multicarrier-Based

Cognitive Radio Networks

Ling Zhuang, Lu Liu, Kai Shao, Guangyu Wang, and Kai Wang Chongqing Key Laboratory of Mobile Communication

Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

Email: {zhuangling, shaokai}@cqupt.edu.cn; {liulucqupt, wkcqupt}@163.com; [email protected]

Abstract—In this paper, we present an efficient downlink

resource allocation algorithm with rate requirement

consideration in multicarrier-based cognitive radio (CR)

networks. The algorithm is divided into two steps aiming to

maximize the downlink capacity of the network under the total

power, the interference introduced to the primary users (PUs)

and the transmission rate of the secondary users (SUs)

constraints. The transmission rate requirement is considered by

ensuring the allocated number of subcarriers satisfies the

required number of subcarriers for every SU within the

subcarrier assignment step and turning the minimum

transmission rate threshold constraints into the minimum power

constraint on each subcarrier within the power allocation step.

Simulation results demonstrate that the proposed algorithm

provides a good guarantee of transmission rate requirement and

prove that filter bank multicarrier (FBMC) has higher efficiency

than orthogonal frequency division multiplexing (OFDM) in CR

networks.

Index Terms—Cognitive radio, multicarrier, rate requirement,

resource allocation

I. INTRODUCTION

Spectrum scarcity crisis exists for many wireless

applications, but investigations show that many licensed

frequency bands are far underutilized [1]. Cognitive

Radio (CR), a technique first introduced by Mitola [2], is

considered as a promising method to solve the spectrum

efficiency problem, in which unlicensed secondary users

(SUs) are allowed to use the licensed frequency bands

without causing a harmful interference to the licensed

primary users (PUs).

The multicarrier technique is a hot topic in 5G

communication systems [3] and has been suggested as a

promising candidate for CR systems due to its flexibility

in allocating resources among different SUs. Orthogonal

frequency division multiplexing (OFDM) is the common

transmission technique in current CR systems.

Nevertheless, with the large side lobes of its filter

frequency response, the OFDM-based CR system suffers

Manuscript received October 10, 2014; revised January 29, 2015. This work was supported by Sino-Finland Cooperation Project (No.

1018) and Chongqing Municipal Education Commission Project (No. KJ1400437).

Corresponding author email: [email protected].

from considerable amount of interference to the PUs [4].

Moreover, inserting the cyclic prefix (CP) in each OFDM

symbol decreases the system total capacity. As a

candidate for the physical layer in the future 5G

communications systems, filter bank multicarrier (FBMC)

can overcome the spectral leakage problem without any

CP extension by decreasing the side lobes of each

subcarrier, which leads to small interference to the PUs

and high efficiency [5].

In multicarrier-based CR systems, the resource

allocation problem is an attractive research issue and

many algorithms have been proposed with different

degree of success. In [6], the author focused on

maximizing the downlink capacity of the CR system

while keeping the interference induced to the PU bands

below the prespecified thresholds, but the total power

constraint was not considered and the optimal solution

obtained by the Lagrange method had a high

computational complexity. In order to reduce the

complexity, some suboptimal algorithms were proposed

to maximize the total system capacity under both total

power and interference introduced to the PUs constraints

[7]-[9], but the complexity still remained high. In [7], two

kinds of subcarriers were considered, the underlay

subcarriers and the overlay subcarriers. The equal amount

of power was allocated on each underlay subcarrier and

the overlay subcarriers were allocated power according to

a ladder profile. The proposed algorithm in [8] started

with an initial power allocation step, where an initial

power level was allocated to the subcarriers according to

four different criteria and then the subcarrier allocation

problem was formulated as a multiple-choice knapsack

problem. In [9], based on the structure of solutions that

were obtained through the Lagrangian duality, a

distributed algorithm was proposed, which only required

some limited cooperation among primary and secondary

networks while offering optimum performance. In [10],

an algorithm called PI algorithm was presented, where

the subcarriers were assigned based on the best channel

gain criterion, the interference constraints were converted

into the maximum power constraint on each subcarrier

and the optimization problem was solved using the

concept of the conventional water-filling with lower

complexity. However, the minimum transmission rate

Journal of Communications Vol. 10, No. 1, January 2015

16©2015 Engineering and Technology Publishing

doi:10.12720/jcm.10.1.16-23

constraint for each SU was not taken into consideration in

the algorithms proposed in [6]-[10].

In this paper, an efficient resource allocation algorithm

with rate requirement consideration in downlink

multicarrier-based CR systems is presented to maximize

the downlink capacity of the CR system while keeping

the total power and the interference induced to the PU

bands below the prespecified thresholds with the

consideration of the transmission rate of the SUs

constraints as well. The algorithm is divided into two

phases and the minimum transmission rate limit is

considered in both phases. The subcarriers to SUs

assignment is performed first according to the required

number of subcarriers for every SU using the proposed

RS algorithm. Then the power is allocated to the different

subcarriers using the proposed PIR algorithm, where the

minimum transmission rate constraints are transformed

into the minimum power constraint on each subcarrier

and the optimization problem is solved efficiently with

the modified “cap-limited” water-filling to reduce the

computational complexity. The efficiency of the proposed

algorithm will be investigated in both OFDM and FBMC-

based CR systems. The rest of this paper is organized as

follow. Section II presents the system model and

formulates the problem. The subcarrier and power

allocation algorithms are developed in Section III.

Simulation results are provided to evaluate the

performance of the proposed algorithm in Section IV.

Finally, Section V concludes the paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

Consider the downlink of a multiuser multicarrier-

based CR network. The CR system’s frequency spectrum

is equally divided into K subcarriers each being assigned

a f bandwidth, where L PUs are in the licensed bands

and the others are the unlicensed bands. All subcarriers

are shared by M SUs, which means the SUs can use both

the unlicensed bands and the licensed PU bands.

Assume that each subcarrier goes under frequency flat

fading gains and the instantaneous fading gains are

perfectly known at the CR system. The transmission rate

of the kth subcarrier kR , the transmit power emitted by

the kth subcarrier kP , and the channel gain kh are related

via the Shannon capacity formula and is given by

2

2 2log 1

k k

k

k

P hR

(1)

where 2

k is the sum of the additive white Gaussian noise

(AWGN) variance and the interference introduced by PUs

on the kth subcarrier, which is assumed to be equal on

each subcarrier. In turn, given a transmission rate kR , the

required transmit power kP can be expressed as follows:

2

2

2 1kR

k

k

k

Ph

(2)

B. Modeling of Interference to Primary Users

The interference of the lth PU band introduced by the

kth subcarrier with unit transmission power l

kIF can be

written as [4]

22

2

( )k l

k l

d B

l l

k k k

d B

IF g f df

(3)

where kd is the spectral distance between the kth

subcarrier and the center frequency of the lth PU band, lB

is the bandwidth occupied by the lth PU, l

kg is the

channel gain between the kth subcarrier and the lth PU

band, ( )k f is the power spectrum density (PSD) of the

kth subcarrier and can be written as

2

( ) ( )k kf H f (4)

where ( )kH f is the frequency response of ( )kh n , which

denotes the shaping filter on the kth subcarrier. The

expression of ( )kH f depends on the used multicarrier

technique.

If an OFDM-based CR system is assumed, the

prototype filter ( )h n can be chosen as the rectangular

window with the length T K C in number of samples,

where K is the number of subcarriers and C is the length

of the CP in number of samples. Hence we get

1

2

1

( ) 2 cos 2T

kr

kH f T T r r f

K

(5)

If an FBMC-based CR system is assumed, the

prototype filter can be chosen as ( )h n with 0,1,...,n W ,

where W NK and N is the length of each polyphase

components (overlapping factor). Assuming that (0)h is

zero, and ( )h n have even symmetry around ( 2)h W [11],

we get

2 1

1

( ) 2 cos 22 2

W

kr

W W kH f h h r r f

K

(6)

C. Problem Formulation

The optimization objective is to maximize the total

capacity of the CR system under the total transmit power, the

interference introduced to the PUs and the transmission

rate of SUs constraints. The constrained optimization

problem can be formulated as follows:

,

2

. ,

, 2 21 1

1: max log 1k m

M Kk m k m

k mP

m k k

P hOP a

(7)

subject to

,m 0,1 , ,ka k m , (8)



,1

1, 1,2,...,M

k mm

a k K

(9)

, ,1 1

M K

k m k m Tm k

a P P

(10)

, 0, ,k mP k m (11)

, ,1 1

, 1,2,...,M K

l l

k m k m k thm k

a P IF I l L

(12)

2

, ,

, 2 21

log 1 , 1,2,...,K

k m k m m

k m thk k

P ha R m M

(13)

where ,k ma denotes the subcarrier allocation indicator, i.e.

, 1k ma only if the kth subcarrier is allocated to the mth

SU. Inequality (9) ensures that each subcarrier can be

allocated to one SU at most. ,k mP is the transmit power on

the kth subcarrier, ,k mh is the channel gain from the base

station to the mth SU on the kth subcarrier, PT is the total

SUs power budget, l

thI is the interference threshold of the

lth PU, and m

thR is minimum transmission rate limit of the

mth SU.

III. DOWNLINK SUBCARRIER AND POWER ALLOCATION

The optimal solution for the combinatorial

optimization problem OP1 has a high computational

complexity which grows exponentially with the input size.

The problem is solved in two steps to reduce the

computational complexity, where in the first step, the

subcarriers are assigned to the SUs and then the power is

allocated to these subcarriers in the second step. Once the

subcarriers assignment is complete, the multiuser

multicarrier system can be viewed virtually as a single

user multicarrier system which makes the optimization

problem computationally simpler.

A. Subcarrier Assignment

As proved in [12], the CR system can obtain the

maximum transmission rate in downlink if the subcarriers

are assigned to the SU with the best channel gain on that

subcarrier, however, it will lead to the situation that some

SUs cannot reach to the required transmission rate. In this

section, we present a subcarrier assignment algorithm, in

which the subcarriers are assigned by jointly considering

the channel gain and the subcarrier requirement of each SU.

22

2log 1m

m th m mK R P h

is the estimated

number of subcarriers required for the m th SU, where

m TP P K is the average power allocated to each

subcarrier of the mth SU, ,1

K

m k mkh h K

is the average

channel gain on each subcarrier for the mth SU, and 2 2

k is the AWGN variance. In the Requirement-

based Subcarrier (RS) assignment algorithm, referred to as

RS algorithm, the subcarriers are assigned successively

based on the best channel gain criterion in [12] and if the

number of subcarriers allocated to the mth SU mK satisfies

the subcarrier requirement of that SU mK , the subcarriers

assignment for it will stop. When the subcarrier

requirement is met for every SU, the remaining subcarriers

are allocated according to the previous criterion. The

implementation of the RS algorithm is described in Table I.

B. Power Allocation

By subcarrier assignment, the values of the subcarrier

allocation indicator ,k ma are determined and hence for

notation simplicity, single user notation can be used. The

channel gain on the kth subcarrier kh is determined as

follows:

, ,1

M

k k m k mm

h a h

(14)

It can be assumed that each subcarrier belongs to the

closest PU band and only introduces interference to it

according to the fact mentioned in [4] that most of the

interference of the PU bands is caused by cognitive

transmission on the subcarriers which are in the PU bands

as well as directly adjacent to the PU bands. And hence

the optimization problem OP1 in (7) can be reformulated

as follows:

2

2 21

2 : max log 1k

Kk k

Pk k

P hOP

(15)

subject to

1

K

k Tk

P P

, (16)

0, 1,2,...,kP k K , (17)

, 1,2,...,l

l l

k k thk K

P IF I l L

, (18)

2

2 2log 1 , 1,2,...,

m

k k m

thk K k

P hR m M

, (19)

where lK denotes the set of the subcarriers belong to the

lth PU band and mK denotes the set of the subcarriers

assigned to the m th SU.

TABLE I: RS ALGORITHM

1. Initialize , 0, ,k ma k m

2. for 1k to 1

M

mmK

do

*

,arg max k mm

m h , *,1

k ma , * * 1

m mK K

if * *m mK K

let *,0, 1,2,...,

k mh k K

end if

end for

3. for 1

1M

mmk K

to K do

*

,arg max k mm

m h , *,1

k ma

end for



Theorem 1: The solution to the optimization problem

OP2 is given by

2

*

2

1 m kk l

l k k

PIF h

(20)

where max(0, )x x and , , 1,2, ,l l L , ,m

1,2,...,m M are the Lagrange multipliers for (16),

(18), (19), respectively. Three Lagrange multiplies can be

obtained based on interior point method with a complexity 3( )O K [13].

Proof: See Appendix.

The optimal solution is computationally complex so

that it is unsuitable for practical wireless communication

systems, and hence a low complexity algorithm will be

proposed. If the total power and the transmission rate

constraints are ignored, applying the Lagrange multiplier

method, the optimal solution can be written as

2

2

1IF kk IF l

l k k

PIF h

(21)

where , 1,2,...,IF

l l L is the Lagrange multiplier for

(18) and can be calculated by substituting (21) into

l

IF l l

k k thk K

P IF I

to get

22

l

lIF

ll l

th k k kk K

K

I IF h

(22)

Consider the optimization problem whose optimization

goal is to minimize the total transmit power of the CR

system subject to the transmission rate of the SUs

constraints. According to (2), it can be formulated as

2

21

2 13 : min

TRk

TRk

RK k

R kk

OPh

(23)

subject to

0, 1,2,...,TR

kR k K (24)

, 1,2,...,m

TR m

k thk K

R R m M

(25)

Applying the Lagrange multiplier method, the optimal

solution can be written as

2

2ln lnTR TR k

k m

k

Rh

(26)

where , 1,2,...,TR

m m M is the Lagrange multiplier for

(25) and can be calculated by substituting (26) into

m

TR m

k thk KR R

to get

22ln

exp m

m

th k kk KTR

m

m

R h

K

(27)

Therefore, TR

kP can be obtained by substituting (26) into

(2).

In order to solve the optimization problem OP2, the

Power Interference Rate (PIR) constrained algorithm,

referred to as PIR algorithm, is proposed. We can start by

assuming that the maximum power which can be

allocated to a given subcarrier Max

kP is determined

according to the interference constraints only by using

(21) and (22) for every subcarrier , 1,2,...,lk K l L .

By such an assumption, we can guarantee that the

interference introduced to the PU bands will not exceed

the prespecified thresholds. Moreover, assume that the

initial minimum power which can be allocated to a given

subcarrier Min

kP is determined according to the

transmission rate constraints only by using (2), (26) and

(27) for every subcarrier , 1,2,...,mk K m M . The

results that violate the maximum power Max

kP are

determined with the upper bound Max

kP and the minimum

transmission rate threshold of each SU is reduced by

subtracting the transmission rate that SU have obtained so

far. Then use (2), (26) and (27) to update the minimum

power Min

kP of the subcarriers that did not violate the

maximum power Max

kP . This procedure is repeated until

the minimum power Min

kP does not violate the maximum

power Max

kP on any of the subcarriers in the new iteration.

By such an assumption, we can guarantee that the

transmission rate of the SUs will not lower than the

prespecified thresholds.

Once the maximum power Max

kP and the minimum

power Min

kP are determined, the total power constraint TP

is tested. If 1

K Min

T kkP P

, it is obvious that there does

not exist any solution to OP2, the problem is studied

except for the minimum power constraints [14].

Moreover, if 1

K Max

k TkP P

, then the solution is equal to

the tolerated maximum power allocated to each subcarrier,

i.e. * Max

k kP P . In most of the cases,

1 1

K KMin Max

k T kk kP P P

, the following problem

should be solved:

2

2 21

4 : max log 1WFk

WFKk k

P k k

P hOP

(28)

subject to

1

KWF

k Tk

P P

(29)

, 1,2,...,Min WF Max

k k kP P P k K (30)

The problem can be solved efficiently using the

modified “cap-limited” water-filling. To begin with, the

total power budget PT is reduced by subtracting the



summation of the minimum power Min

kP , the maximum

power Max

kP is reduced by subtracting the minimum

power Min

kP and the height of the container’s bottom

22

k k kd h is increased by adding the minimum

power Min

kP . Then we execute the “cap-limited” water-

filling [14] and obtain the result CWF

kP . The final solution

WF

kP of the problem OP4 is the result of the “cap-

limited” water-filling CWF

kP plus the minimum power

Min

kP . The implementation of the PIR algorithm is

described in Table II.

TABLE II: PIR ALGORITHM

1. Initialize l lO K ,

m m m mU V W K , m

m thQ R , TS P

2. Find the Max

kP as follows:

1) 1,2,...,l L , sort 22 ,l

k k k k lT IF h k O in

decreasing order with i being the sorted index

2) l

sum kk OT T

, IF l

l l th sumO I T , 1n

3) while 1

( )

IF

l i nT do

( )sum sum i nT T T , \ ( )l lO O i n ,

IF l

l l th sumO I T , 1n n

end while

4) Set 221Max IF l

k l k k kP IF h

, Max

k kP P

3. Find the Min

kP as follows:

1) 1,2,...,m M , sort 22ln ,k k k mH h k W

in decreasing order with j being the sorted index

2) m

sum kk WH H

, expTR

m m sum mQ H W ,

1n

3) while (n)ln TR

m jH do

( )sum sum j nH H H , \ ( )m mW W j n ,

expTR

m m sum mQ H W , 1n n

end while

4) Set lnMin TR

k m kR H

, 222 1kRMin

k k kP h ,

mk V

5) Repeat

if Min

k kP P

let Min

k kP P , 2 2

2log 1 Min

m m k k kQ Q P h ,

\m mV V k , m mW V , and go to step 1)

end if

until ,Min

k k mP P k U

4. if 1

K

kkP S

let *

k kP P and stop the algorithm

end if

5. Let 1

K Min

kkS S P

, Min

k k kP P P ,

2 22 2 Min

k k k k kh h P , execute the “cap-limited” water-

filling and set WF CWF Min

k k kP P P , * WF

k kP P

The computational complexity of step 2 in the proposed

PIR algorithm is 1

( log ) ( log )L

l llO K K O K K

. Step

3 has a complexity of 1

( log )M

m m m mmO K K K

( log max( ) )mO K K K , where m mK is the

number of the iterations. Step 5 of the algorithm executes

the modified “cap-limited” water-filling which has a

complexity of ( log )O K K K , where K is the

number of the iterations. Thus, the overall complexity of

the algorithm is lower than ( log )O K K K , where

0,5 is estimated via simulation. Comparing to the

computational complexity of the optimal solution, 3( )O K , the proposed PIR algorithm has much lower

computational complexity, especially for large number of

subcarriers.

IV. PERFORMANCE EVALUATION

A. Simulation Configuration

Simulations are performed with MATLAB 7.8.0 to

evaluate the performance of the proposed algorithm.

Consider a CR system of 2L PUs that each has six

subcarriers, 3M SUs and 32N subcarriers. The

bandwidth of subcarriers f is selected as 0.3125 MHz

and the AWGN variance 2

k is 610 . The channel gains h

and g are outcomes of independent, identically distributed

Rayleigh distributed random variables with mean of 1. The

OFDM and FBMC-based CR systems are evaluated. The

OFDM system is assumed to have a 6.67% of its symbol

time as the CP. For FBMC system, the prototype filter

coefficients are assumed to be equal to PHYDYAS

coefficients with overlapping factor 4N [15].

Furthermore, 1 2

th th thI I I and 1 2 3

th th th thR R R R are

assumed.

The efficiency of the proposed algorithm, which

consists of RS algorithm and PIR algorithm, is compared

with the PI algorithm proposed in [10] without the step that

make the allocated power satisfy approximately the

interference constraints. The PI algorithm maximizes the

downlink capacity of the CR system under only two

constraints, the total power and interference induced to

the PUs constraints. In the subcarrier assignment step, it

always assigns the subcarriers based on the best channel

gain criterion in order to obtain the highest

transmission rate. In the power allocation step, it turns the

interference constraints into the maximum power

constraint on each subcarrier and uses the concept of the

conventional water-filling to solve the optimization

problem.

B. Simulation Results

The capacity of the CR system using proposed and PI

algorithms for different interference thresholds with

0.5TP W and 120thR bit/s/Hz is plotted in Fig. 1. It



can be observed that the capacity increases as the

interference threshold increases. The proposed algorithm is

slightly inferior to the PI algorithm. This is because in the

subcarrier assignment step, the subcarriers are allocated

based on the requirement using the proposed algorithm, in

which the subcarriers are not always assigned to the SU

with the best channel gain, unlike the PI algorithm,

which only takes the best channel gain into account to

obtain the maximum capacity. The appearance of steep

drop is due to the guarantee that each SU can reach to the

required transmission rate in the power allocation step using

the proposed algorithm which is not the case in the PI

algorithm. The proposed algorithm transforms the

minimum transmission rate constraints into the minimum

power constraint on each subcarrier and then solves the

optimization problem with the modified “cap-limited”

water-filling, so that it may allocate the power to the

subcarriers with poor channel gain, which leads to the

drop in capacity.

In Fig. 1, the capacity achieved using the proposed

algorithm is not as ideal as that achieved using the PI

algorithm. The reason is that in the proposed algorithm,

the subcarriers may be assigned to the SUs with poor

channel gain owing to the subcarrier requirement of each

SU within the subcarrier assignment step and the power is

probably allocated to the subcarriers with poor channel

gain on account of the minimum power constraint on

each subcarrier within the power allocation step. Fig. 1

also shows that the capacity of FBMC-based CR system

is higher than that of OFDM-based CR system because

the side lobes of the subcarrier’s PSD in FBMC system

are smaller than that in OFDM one which introduces less

interference to the PU bands. Another reason is the

inserted CP in OFDM-based CR system which can

reduce the system capacity. The significant advantage in

the capacity of FBMC-based CR system over the OFDM-

based one recommends the FBMC as a candidate for the

physical layer in the future CR systems.

By sacrificing a little system capacity, the proposed

algorithm has a good guarantee of transmission rate

requirement as shown in Fig. 2, which plots the

transmission rate of a specific SU versus the required

transmission rate of the SU with 0.5TP W and 10thI

mW for different algorithms. It can be noted that the

practical transmission rate of the SU varies with the

transmission rate requirement and always strictly satisfies

it in the proposed algorithm while it remains constant

regardless of the transmission rate requirement in the PI

algorithm. This is because in the proposed algorithm, with

the change of the required transmission rate, both the

assignment of the subcarriers to SUs in the first step and

the allocation of the power to subcarriers in the second

step will vary, which leads to a different transmission rate.

Fig. 3 illustrates the transmission rate per SU versus

SU index with 0.5TP W, 10thI mW and 120thR

bit/s/Hz using different algorithms. We can observe that all

three SUs can satisfy its transmission rate requirement in

the proposed algorithm. Nevertheless, in the PI algorithm,

only SU 2 can achieve the required transmission rate since

there are not any efficient transmission rate requirement

assurance schemes in it. More subcarriers and power are

allocated to SU 2 in virtue of its better channel gains,

which results in that the transmission rate of SU 2 is

much higher than the required transmission rate and the

other two SUs cannot reach to it.

Fig. 1. Capacity of secondary users versus interference threshold for OFDM and FBMC-based CR systems.

Fig. 2. Transmission rate versus required transmission rate of a specific secondary user for OFDM and FBMC-based CR systems.

Fig. 3. Transmission rate per secondary user versus secondary user index for OFDM and FBMC-based CR systems.



Fig. 4 shows the instantaneous transmission rate of a

specific SU over time for different algorithms with 0.5TP

W, 10thI mW and 120thR bit/s/Hz. In both

algorithms, the instantaneous channel gains are exactly the

same. It can be noted that the proposed algorithm keeps the

instantaneous transmission rate above 120thR bit/s/Hz

all the time within this observation period while the PI

algorithm cannot. This demonstrates that the proposed

algorithm can achieve a better guarantee of transmission

rate requirement than the PI algorithm.

Fig. 4. Instantaneous transmission rate of a specific secondary user for OFDM and FBMC-based CR systems.

V. CONCLUSION

In this paper, an efficient resource allocation algorithm

with rate requirement consideration for downlink in

multicarrier-based CR networks is proposed. The

proposed algorithm maximizes the total downlink capacity

of the multicarrier-based CR networks while respecting

the available power budget and guaranteeing that no

excessive interference is introduced to the PU bands and

each SU can achieve the required transmission rate. The

minimum transmission rate limit is considered in both

subcarrier assignment and power allocation steps. In the

subcarrier assignment step, the subcarriers are allocated to

the SUs based on the required number of subcarriers for

every SU using the proposed RS algorithm. In the power

allocation step, the proposed PIR algorithm is performed,

where the minimum transmission rate constraints are

converted into the minimum power constraint on each

subcarrier and the modified “cap-limited” water-filling is

executed to solve the optimization problem efficiently.

Simulation results prove that the proposed algorithm has a

significant advantage in the strict guarantee of

transmission rate requirement over the PI algorithm with a

little expense of the system capacity. They also

demonstrate that the capacity of FBMC-based CR system

is more than OFDM-based one and recommend FBMC as

a candidate for transmission in CR networks. In our future

work, we plan to extend the applications of 5G in CR

networks.

APPENDIX PROOF OF THEOREM 1

The problem OP2 can be considered as a convex

optimization problem, which can be solved using the

Lagrange multiplier method [13] and the Lagrange

function can be written as

2

2 21 1

log 1K K

k k

k Tk kk

P hL P P

1 1

2

2 21

log 1

0, 0, 0, 0,

l

m

K Ll l

k k l k k thk l k K

Mk km

m thm k K k

k l m

P P IF I

P hR

(31)

where , , 1,2,...,k k K , , 1,2,...,l l L and

, 1,2,...,m m M are the Lagrange multipliers.

According to the Karush-Kuhn-Tucker (KKT)

conditions, we have

* 0, 1,2,...,kP k K

0, 1,2,...,k k K

* 0, 1,2,...,k kP k K (32)

* 22 *

10lm

k l k

k k k k

LIF

P h P

Eliminate k from (32) and rewrite the KKT

conditions as follows:

* 0, 1,2,...,kP k K

22 *

1, 1,2,...,l m

l k

k k k

IF k Kh P

(33)

*

22 *

10, 1,2,...,l m

l k k

k k k

IF P k Kh P

.

If 2 21l

l k m k kIF h , the second condition

in (33) holds if * 0kP , which implies

2

*

2

1 m kk l

l k k

PIF h

(34)

Moreover, if 2 21l

l k m k kIF h , we assume

* 0kP , which implies 2 21l

l k m k kIF h

22 *1 m k k kh P and violates the third condition

in (33). Thus, the only possible solution in this case is * 0kP .

Therefore, the optimal solution can be written as

follows:



22

2 2

*

2

2

11, if

10, if

m klm kl kl

l k kk

k

m kl

l k

k

hIF

IF hP

hIF

(35)

which is equal to

2

*

2

1 m kk l

l k k

PIF h

(36)

ACKNOWLEDGMENT

This work was supported by Sino-Finland Cooperation

Project (No. 1018) and Chongqing Municipal Education

Commission Project (No. KJ1400437).

REFERENCES

[1] Spectrum Policy Task Force, Federal Communication

Commission, Washington, DC, 2002.

[2] J. Mitola and G. Q. Maguire Jr, “Cognitive radio: making software

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[3] 5G Waveform Candidate Selection, 5GNOW, 2013.

[4] T. Weiss, J. Hillenbrand, A. Krohn, and F. K. Jondral, “Mutual

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1877.

[5] B. Farhang-Boroujeny, “OFDM versus filter bank multicarrier,”

IEEE Signal Processing Magazine, vol. 28, no. 3, pp. 92-112, May

2011.

[6] L. Tang, Q. Chen, G. Wang, X. Zeng, and H. Wang,

“Opportunistic power allocation strategies and fair subcarrier

allocation in OFDM-based cognitive radio networks,”

Telecommunication Systems, vol. 52, no. 4, pp. 2071-2082, Apr.

2013.

[7] G. Bansal, M. J. Hossain, V. K. Bhargava, and T. Le-Ngoc,

“Subcarrier and power allocation for OFDMA-based cognitive

radio systems with joint overlay and underlay spectrum access

mechanism,” IEEE Trans. on Veh. Technol., vol. 62, no. 3, pp.

1111-1122, Mar. 2013.

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

resource allocation in OFDMA-based cognitive radio networks,”

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2011.

[9] D. T. Ngo and T. Le-Ngoc, “Distributed resource allocation for

cognitive radio networks with spectrum-sharing constraints,”

IEEE Trans. on Veh. Technol., vol. 60, no. 7, pp. 3436-3449, Sep.

2011.

[10] M. Shaat and F. Bader, “Computationally efficient power

allocation algorithm in multicarrier-based cognitive radio

networks: OFDM and FBMC systems,” EURASIP Journal on

Advances in Signal Processing, vol. 2010, pp. 13, 2010.

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radiation in multicarrier systems: A comparison,” Multi-Carrier

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OFDM systems,” IEEE Journal on Selected Areas in Commun.,

vol. 21, no. 2, pp. 171-178, Feb. 2003.

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

U.K.: Cambridge University Press, 2009.

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[15] FBMC Physical Layer: A Primer, PHYDYAS, 2010.

Ling Zhuang is an associate professor since

2010 in the College of Communication and

Information Engineering, Chongqing

University of Posts and Telecommunications

(CUPT), China. She received her Ph.D.

degree in 2009 in Control Theory and Control

Engineering from the Chongqing University,

her M.S. in 2003 in Communication and

Information System and her 4-year B.S.

degree in 2000 in Communication Engineering from CUPT. Her main

research interests are cognitive radio communications and networking,

multicarrier modulation technique for mobile communication, multi-rate

digital signal processing, and filter bank theory.

Lu Liu was born in Hunan Province, China,

in 1990. She received the B.S. degree from

CUPT in 2011. Currently she is working on

her M.S. degree in Chongqing University of

Posts and Telecommunications. Her research

interests are cognitive radio communications

and networking, multicarrier modulation

techniques for mobile communication, and

filter bank theory.

Kai Shao is an Associate Professor since

2012 in the College of Communication and

Information Engineering, CUPT. His main

research interests are filter bank theory,

multicarrier modulation technique for mobile

communication, and related topics.

Guangyu Wang is a Professor in the College

of Communication and Information

Engineering, CUPT. He received a Ph.D.

degree in 1999 in Electrical Engineering from

the Kiel University, Germany, an MSc degree

in 1988 in Telecommunication Engineering

from Beijing University of Posts and

Telecommunications, China, and a 4-year BS

degree in 1985 from CUPT. His main research

interests include high-speed signal processing and multi-rate filter bank

theory.

Kai Wang was born in China, in 1989. He

received his B.S. degree from Hubei

University of Arts and Science, China in 2012.

Currently he is working on his M.S. degree in

CUPT. His research interests are multicarrier

modulation techniques for mobile

communication and multi-rate digital signal

processing.



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