A QoS-Based Channel Allocation and Power Control Algorithm

A QoS-Based Channel Allocation and Power Control

Algorithm for Device-to-Device Communication

Underlaying Cellular Networks

Yu Baozhou1 and Zhu Qi

2

1 The Key Wireless Laboratory of Jiangsu Province, School of Telecommunication and Information Engineering,

Nanjing University of Posts and Telecommunications, Nanjing 210003, China 2 Key Laboratory on Wideband Wireless Communications and Sensor Network Technology of Ministry of Education,

Jiangsu Nanjing 210003, China

Email: [email protected]; [email protected]

Abstract—In device-to-device (D2D) communication system,

rational resource allocation can effectively reduce the

interference between cellular users and D2D users. In this paper,

based on the QoS requirement of cellular users and D2D users,

we propose a channel allocation and power control optimization

algorithm, which takes limit transmission power of each cellular

user and total D2D users into consideration when maximizing

the system capacity of total D2D users. We can achieve the

candidate cellular users set of D2D users according to the

minimum SINR requirement of D2D users. And then, the

transmission power of cellular users and D2D users are

optimized with Lagrange multiplier method, meanwhile we

calculate the capacity of each D2D user by optimal power and

allocate channel to the D2D pair, which has the maximum value

of capacity. However, the optimal algorithm has a high

complexity. We further propose a low complexity suboptimal

algorithm, which allocates channel and controls power in

different stages. Simulation results show that the proposed

algorithms effectively improve the capacity of D2D users under

the condition of guaranteeing the QoS of cellular users and the

suboptimal algorithm greatly reduces the complexity compared

with the optimal algorithm. Index Terms—D2D communication, Interference management,

Optimization theory, Resource allocation, Power control

I. INTRODUCTION

Device-to-Device (D2D) Communication [1] is a

promising communication technology, which can satisfy

the increasing data rate demand and provide better

services of users. The definition of D2D communication

underlaying cellular networks is that proximity users can

reuse radio resource to communicate directly without

going through the Base Station (BS) or core network [2].

D2D communication can improve resource reuse rate and

allow more users to access the network for its reuse of

cellular network resource.

Since D2D communication reusing resource will cause

interference to the cellular network, resource allocation of

D2D communication underlaying cellular network has

Manuscript received March 16, 2016; revised July 19, 2016. This work is supported by National Natural Science Foundation of

China (NO. 61571234.) Corresponding author email: [email protected].

doi:10.12720/jcm.11.7.624-631

been deeply studied. In [3], authors consider a system

model including one cellular user and one D2D pair, the

analysis focuses on the optimization total throughput by

resource allocation subject to QoS (Quality of Service) of

the cellular user and maximum transmission power

constraint. In [4], authors propose a criterion based on

distance constraint resource sharing, which can reduce

the interference between users and improve the system

capacity through obtaining the optimal distance between

cellular user and D2D pair that sharing the same resource.

A greedy heuristic algorithm has been proposed in [5] to

solve a Mixed Integer Nonlinear Programming (MINLP)

problem, which converts from the problem of D2D users’

radio resources allocation. And the proposed greedy

heuristic algorithm improves system performance in

terms of cell capacity without causing significance harm

between cellular users and D2D users. In [6] and [7],

combined game theory has been used to allocate

resources. A distributed merge-and-split coalition

algorithm has been proposed in [6], which achieves an

approaching preference in terms of network sum-rate

with the exhaustive search optimal resource allocation

scheme. In [7], authors formulate the resource allocation

problem as a reverse iterative combinatorial auction game.

In [8], authors propose a novel resource allocation

algorithm that D2D users can reuse more than one

resource of cellular users. After that, they discuss the

selection of resource allocation scheme through the

proposed algorithm, and the proposed algorithm can

increase the total system throughput to a large extent. The

above relevant references focus on researching the

resources allocation of users under the conditions of

determined power, while the literatures that optimizing

the transmission power and resource allocation of users

simultaneously are not much. Authors investigate the

joint resource block assignment and transmit power

allocation problem to optimize the network performance

in [9], which establishes the interference graph composed

of D2D communication links and cellular communication

links and proposes resource allocation scheme under the

interference graph. Meanwhile, they optimize the

transmission power of D2D pair, but the transmission

power of the cellular user is a certain value.

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Journal of Communications Vol. 11, No. 7, July 2016

©2016 Journal of Communications

In this paper, we assume that the radio resource

allocation [10] of cellular users has been completed.

Based on QoS of cellular users and D2D users, a

channel allocation and power control algorithm in D2D

communication underlaying cellular networks is proposed.

Firstly, obtaining candidate cellular users set of D2D user

according to the minimum SINR demand of D2D user.

And then, taking communication quality of cellular users

and D2D users, limited transmit power of cellular user

and D2D user into consideration. We build an optimal

subjective function to maximize the capacity of total D2D

users. The transmit power of D2D users and cellular users

is optimized with Lagrange multiplier method and the

capacity of D2D users is calculated by optimal power.

Meanwhile, we allocate the channel to one D2D pair,

which has the maximum value of capacity. However, the

optimal algorithm has a high complexity. We further

propose a low complexity suboptimal algorithm, which

allocates channel and controls power in different stages.

Simulation results show that the capacity of D2D users is

improved with the proposed algorithms in a certain extent.

And the performance of suboptimal algorithm with low

complexity is close to the optimal algorithm.

The rest of the paper is organized as follows. We

describe the system model of D2D communications

underlaying the cellular networks in Section 2. Then, in

Section 3, the proposed resource allocation algorithm is

investigated. Simulation results are provided and

analyzed in Section 4 to show the performance of

proposed algorithms. Finally, conclusions are drawn in

Section 5.

CUEi

CUEm

CUE2

CUE1

DUE1 Rx

DUE1 Tx

BS

DUEi Tx

DUEi Rx

Fig. 1. System model of D2D communications sharing uplink resources

of cellular users

II. SYSTEM MODEL

We investigate resource allocation for D2D

communication sharing uplink (UL) resource of cellular

networks as in Fig. 1, where M cellular users coexist

with N D2D pairs. We use 1,2, ,C M and

1,2,...,D N to indicate the sets of cellular users and

D2D users. We assume that M cellular users occupy

the K independent orthogonal channels in the cell [11].

D2D pair reuse the channel that assigned to the cellular

users, but D2D pairs can’t reuse the same channel. Each

resource can be occupied by at most one cellular user and

one D2D pair simultaneously. That is to say, there is no

interference between cellular users and no interference

between D2D pairs, the interference only exists in the

cellular user and the D2D pair that sharing the same radio

resource.

On the channel k , we suppose that cellular user i sends

the signal,c ix to the BS, and

,d jx is the transmission

signal between D2D pair j .

So, we can achieve the received signal of BS and D2D

pair j as follows

, , , . , , , 1

c d

c i i k i B c i j k j B d jy p g x p h x n (1)

, , , , , . 2

d c

d j j k j d j i k i j c iy p g x p h x n (2)

where ,

c

i kp and ,

d

j kp are the transmission power of cellular

user i and the D2D pair j that sharing the channel k .

Channel gain consists of the slow fading [12] of

distanced based PathLoss (PL) and the fast fading of

selective Rayleigh Fading. Therefore, the channel gain

between BS and the cellular user i can be written as 2

, , 0i B i Bg d g , where ,i Bd is the distance between

the cellular user i and BS, and are the channel

fading constant and channel fading exponent, respectively.

0g indicates exponential distribution of fast fading gain.

Similarly, the channel gain between the transmitter and

receiver of D2D pair j is jg ,

,j Bh is the channel gain

between the BS and D2D pair j and the channel gain

from cellular user i to the receiver of D2D pair j is ,i jh .

1n and2n are the additive white Gaussian noise for BS

and the receiver of D2D pair, respectively. Without loss

of generality, we assume that all communication links

have the same noise power0N .

The SINR of cellular user i on channel k can be

expressed as

, ,

,

0 , ,

c

i k i Bc

i k d

j k j B

p g

N p h

(3)

The SINR of the receiver of D2D pair j on channel k

can be indicated as

,

,

0 , ,

d

j k jd

j k c

i k i j

p g

N p h

(4)

III. PROBLEM FORMULATION

A. Jonit Optimization Algorithm

In this section, we analyze transmission power of

cellular users, transmission power of D2D users and

channel allocation of D2D users. Taking the minimum

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QoS demands of cellular users and D2D users, limit

transmission power of each cellular user and total D2D

users into consideration, we establish the following

optimization problems

, , ,

2 , ,, ,

max log 1c di k j k j k

d

j k j kp p k j D

(5)

Subject to:

, max0 ,c c

i kp P i C (6)

, ,c c

i k th i C (7)

, ,d d

j k th j D (8)

, , , 1,2,...,d

j k j k tot

k j D

p P k K

(9)

, ,1, 0,1 , 1,2,...,j k j k

j D

k K

(10)

where ,j k represents the channel occupancy situation of

D2D users, , 1j k represents channel k is occupied by

D2D user j and , 0j k means channel k is not occupied.

max

cP andtotP indicate the maximum transmit power

constraint of each cellular user and total D2D users. c

th and d

th represent the minimum Signal-to-Interference-

plus-Noise-Ratio (SINR) threshold of cellular users and

D2D users, respectively. Formula (5) means maximizing

the capacity of the objective function of D2D users.

Formula (6) indicates limited transmission power of

cellular user. Constraints (7) and (8) represent the QoS

requirements of cellular users and D2D users,

respectively. Constraint (9) represents the limit

transmission power of total D2D users. Formula (10)

ensures that the resource of cellular user can be shared by

at most one D2D pair.

Analyzes (5), the objective function has three unknown

parameters, transmit power of cellular user ,

c

i kp , transmit

power of D2D user ,

d

j kp and channel selection factor,j k .

The optimal problem is a mixed integer programming NP

hard problem [13], which is difficult to solve directly.

Therefore, we obtain the solutions of the power control

and channel assignment problem through the joint

iteration optimization.

B. Solving Joint Optimization Problem

According to the following inequality:

,

2

0 , , 0

d

j k j d

thc

i k i j

p g

N p L h

(11)

the expression (11) is converted from (4) and (8). We can

receive the following inequality

1

2

0

,

max 0

d totth

i j d d

j th

Ph

NLP g N

(12)

where ,i jL indicates the distance between cellular user

and the receiving terminal of D2D pair, D2D pair j reuse

the resource of cellular user, which falls outside the circle

that putting receiving terminal of D2D pair as the center

and putting ,i jL as the radius. Therefore, according to (12),

we can receive the set of reusable channel for D2D user

j and the set can be indicated as

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

1,2,...

j i j i j

j

k d L k i i M j D

j N

(13)

where k represents channel k occupied by cellular user i ,

,i jd means the distance between cellular user i and D2D

pair j , and the constraint (7) can be further translated into

the following expression

, ,

, , 0 0

c

i k i Bd

j k j B c

th

p gp h N

(14)

The Lagrange function of (5) with respect to (9)

,

, , , 2 ,

0 , ,

, ,

, , , log 1

d

j k jc d

i k j k j k j kck j D i k i j

d

j k j k tot

k j D

p gL p p

N p h

p P

(15)

where is the Lagrange multiplier, and Lagrange dual

function can be expressed as

, , ,

, , ,, ,

max , , ,c di k j k j k

c d

i k j k j kp p

k tot

k

G L p p

G P

(16)

where is defined as

, , ,, , : 6 , 10 , 14c d

i k j k j kp p

kG can be expressed as follows

, , ,

,

2 , ,, ,

0 , ,

max log 1c di k j k j k

d

j k j d

k j k j kcp p j D i k i j

p gG p

N p h

(17)

We observe that expression (16) can be decomposed

into M separate problems for a given , and each

problem corresponds to a given channel k , which is (17).

According to (10), for each channel, there is at most one

,j k nonzero for all 1,2,...,k K . Therefore, we

calculate the value of kG through traversal of N

D2D users, and then assign the channel k to the D2D

pair with maximum value of kG .

j

kG is defined as the value of kG with

allocating the channel k to D2D pair j , as this time

, 1j k . Therefore, j

kG can be obtained through the

following problem for a given

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, ,

,

2 ,,

0 . ,

max log 1c di k j k

d

j k jj d

k j kcp p

i k i j

p gG p

N p h

(18)

Subject to:

, max0 c c

i kp P (19)

, ,

, , 0 0

c

i k i Bd

j k j B c

th

p gp h N

(20)

The variables ,

c

i kp and ,

d

j kp in above problem are

coupled, which can be divided into two aspects of

problem by the decomposition method [14]. In the low

layer problem, for a fixed ,

d

j kp , we can find the objective

function of the problem (18) is a monotone decreasing

function with regard to ,

c

i kp . This shows that the

objective function of the problem (18) can be acquired

maximum value with the minimum value of ,

c

i kp .

Constraints (19) and (20) can be rewritten as a more

compact form

, , 0 , max

,

c

d c cth

j k j B i k

i B

p h N p Pg

(21)

Therefore, the optimal value of ,

c

i kp can be written as

, , , 0

,

c

c dth

i k j k j B

i B

p p h Ng

(22)

In the upper layer problem, putting (22) into the

objective function of problem (18) to simplify the

problem (18)

,

,

2

, , ,

0 ,

, ,

,

max log 1

1

dj k

d

j k jj

k c cpth i j th j B i j d

j k

i B i B

d

j k

p gG

h h hN p

g g

p

(23)

Subject to:

,

d

j kp (24)

where

,

max 0

,

1 i B c

c

j B th

gP N

h

and max ,0 , the constraint (24) can be obtained

from (20). To prove the above problem as a convex

problem [15], we can get the following formula through

seeking the second derivative of (23) j

kG with ,

d

j kp

2,

2 2 2

, , , ,

2 2 djj j j j kk

d d d d

j k j k j j k j k

Ag A B g B B g pd G

d p A Bp g p A Bp

(25)

where we denote A and B as follows

,

0

,

1

c

th i j

i B

hA N

g

(26)

, ,

,

c

th j B i j

i B

h hB

g

(27)

The formula (25) is always less than zero, so j

kG is

a convex function of ,

d

j kp , the optimal solution can be

obtained by convex optimization method.

According to KKT (Karush-Kuhn-Tucker) conditions

[16], we can calculate the first derivative of j

kG with

,

d

j kp and make it to zero

2

,

, , ,, , ,

1 10

ln 2

j i B

ddi B i B j ki B i B j j k

g g A

g A g Bpg A g g B p

(28)

Obtaining the optimal value of ,

d

j kp according to (28)

, 2

,0

22 2

d

j k

i B j j

A Ap

Bg B g B g B

(29)

where [ ] min max( , ),y

x x y and can be written as

the following formula

2 2 2

, , ,

4

ln 2j i B j i B i B jg g A g g A g B g B

(30)

Putting (29) into (22) can obtain the optimal value of

,

c

i kp . j

kG can be translated into the following formula

after acquiring the optimal value of ,

c

i kp and ,

d

j kp

,

2 ,

, , ,

0 ,

, ,

log 1

1

d

j k jj d

k j kc c

th i j th j B i j d

j k

i B i B

p gG p

h h hN p

g g

(31)

We allocate channel k to D2D user with the maximum

value of j

kG through obtaining all of the value

j

kG of D2D users corresponding to channel k

arg max j

kj

j G and , 1j k (32)

It should be noted that on the channel k , for all D2D

users j j ，their values are , 0j k , , 0d

j kp .

Dual function G can be obtained by (16) after

acquiring sum of j

k kG G through traverse all

channels. Finally, we need to get the optimum

according to maximum G , and we use the second

gradient method to obtain the optimal .

Proposition 1: The second gradient of G is

,

d

tot j k

k j

P p .

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Proposition 1 shows that can be updated according

to the following formula

,1 d

tot j k

k j

t t t P p

(33)

where 0t is a series of step sequence. Reference

[17] shows that as long as t is small enough, the

above iterative update of second gradient can converge to

the optimal value. Some popular selection rules of t

are tt

, t and t

t

, where is a

constant.

Detailed steps of optimal resource allocation algorithm

are summarized as Table I.

TABLE I: OPTIMAL RESOURCE ALLOCATION ALGORITHM

Algorithm Optimal Resource Allocation Algorithm

Input: The set of cellular users C

The set of D2D pairs D

The SINR of cellular user and D2D user c

th and d

th

Output: The optimal transmission power of cellular user and D2D

user ,

c

i kp and,

d

j kp

The resource k reuse indicator for cellular user and D2D

user j ,j k

1. Initialization

2. for all j D and channel resources

from 1k to k K do

3. calculate ,

d

j k

4. if ,

d d

j k th then

5. j j k and j j D

6. end if

7. end for

8. If 0 then

9. for the D2D user has no available channel resource

and the algorithm ends

10. end if

11. Initializes and set 1t

12. while 1t t do

13. for i C and j D

14. for all channels k do

15. calculate,

c

i kp and ,

d

j kp by (222) and (29).

16. calculate j

kG by formula (31) then

17. ,

arg max j

kk j D

j G

and then , 1j k

18. for all j j do

19. set , 0j k , , 0d

j kp

20. end for 21. end for

22. end for

23. update ,( 1) ( ) ( )( )d

tot j k

k j

t t t P p

24. 1t t

25. end while

C. Suboptimal Algorithm

We propose a two-stage suboptimal algorithm to

further reduce the computational complexity of the

proposed optimization algorithm, which has a high

computational complexity for joint optimizing the power

control and channel allocation. The two-stage method of

channel allocation and power control is performed

separately. In the first phase, each channel resource is

allocated to the D2D user, which has the maximum value

of 0 max ,( )c

j i jg N P h . In the second phase, power is

assigned to the above D2D users and cellular users with

the method that is similar to the power control of optimal

algorithm.

Detailed steps of the two-stage algorithm are presented

as Table II.

TABLE II: SUBOPTIMAL ALGORITHM

Algorithm Suboptimal Algorithm

Input: The set of cellular users C

The set of D2D pairs D

The SINR of cellular user and D2D user c

th and d

th

Output: The optimal transmission power of cellular user and

D2D user ,

c

i kp and,

d

j kp

The set of resources sharing between cellular user and

D2D pair S

1. Initialization S and

2. for all j D and channel resources from 1k to k K

do

3. calculate ,

d

j k

4. if ,

d d

j k th then

5. j j k and j j D

6. end if

7. end for

8. for all i C and j D do

9. calculate 0 max ,

j

c

i j

g

N P h

10. ,

0 max ,

arg maxj

ci C j D

i j

gj

N P h

then

11. &j j j jS S k k i k and S S j D

12. end for

13. if 0 then

14. for the D2D user has no available channel resource and

the algorithm ends

15. end if

16. Initializes and set 1t

17. while 1t t do

18. for k S and j D

19. calculate,

c

i kp and ,

d

j kp by (22) and (29).

20. end for

21. update ,( 1) ( ) ( )( )d

tot j k

k j

t t t P p

22. 1t t

23. end while

IV. SIMULATION RESULTS AND ANALYSIS

In this section, we evaluate the preference of the

proposed algorithms. Consider an isolated cellular cell,

where traditional cellular users and D2D users are

distributed randomly within the cell. The cell is a circular

area with the radius R , in which the Base Station locates

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in the center and each D2D pair has a fixed distance

between the transmitter and the receiver. The list of

detailed simulation parameters is summarized in Table III.

TABLE III: SIMULATION PARAMETERS

Cell radius R (m) 500

Distance between D2D pairs Rd (m) 10,20,30,…,100

Number of CUs M 5,10,15,…,40

Number of D2D pairs N 10

Maximum CU transmit power max

cP (dBm) 24

Maximum D2D total transmit power totP (dBm) 30

Noise power 0N (dBm) -114

Cellular user SINR c

th (dBm) 0

D2D user SINR d

th (dB) 0

Pathloss exponent 4

Pathloss constant 0.01

5 10 15 20 25 30 35 400

100

200

300

400

500

600

700

The number of cellular users

Tota

l C

apacity o

f th

e D

2D

pairs(b

ps/H

z)

Proposed Optimal

Proposed Suboptimal

Algorithm in [8]

Greedy

Random

Fig. 2. D2D total capacity for different number of cellular users.

In Fig. 2, in terms of system capacity performance of

D2D users, we compare five resource allocation

algorithms for the D2D communications underlaying

cellular networks, i.e., the proposed joint optimization

scheme, the proposed suboptimal scheme, algorithm in

[8], a greedy algorithm and a random resource allocation

scheme. Algorithm in [8] calculates the ratio between the

channel gain of cellular users and BS and the channel

gain of D2D pairs, and then the resource is allocated to

D2D pair, which has the maximum value of gain ratio.

And the D2D pair can reuse more channels of different

cellular users. The greedy resource allocation algorithm

allocates some resources to the D2D pair who have

enough higher SNR on the corresponding resources and

the power of the D2D pair on the allocated resources are

fixed. It is seen that the performance of the five resource

allocation algorithms increases with the ascent number of

cellular users. The number of cellular users’ resources

that can be occupied by D2D user increases with the

increasing number of cellular users, and then the capacity

of D2D users also increases. From Fig. 2, it is clearly

shown that the proposed suboptimal resource allocation

scheme can acquire an approaching performance with the

proposed optimal algorithm. Besides, compared with the

algorithm in [8] and the Greedy algorithm, we can see

that the two proposed resource sharing schemes have a

significant performance gain in terms of capacity of D2D

users, which verifies the good performance of the

proposed algorithms.

10 20 30 40 50 60 70 80 90 10050

100

150

200

250

300

350

400

450

500

The distance between D2D pair(m)

Tota

l C

ap

acit

y o

f th

e D

2D

pa

irs(

bps/H

z)

Proposed Optimal

Proposed Suboptimal

Algorithm in [8]

Greedy

Random

Fig. 3. D2D total capacity for different distance between D2D pairs.

Fig. 3 shows D2D total capacity of five different

resource allocation schemes with different distance

between D2D pair. The channel gain of D2D link

decreases with the distance increasing between D2D pair,

which leads to the slight decrease of D2D total capacity.

Therefore, total capacities of D2D users decrease with the

increasing distance between D2D pair. From the Fig. 3,

we can see that the proposed algorithms have much

capacity gain compared with the algorithm in [8], the

Greedy algorithm and the Random resource allocation

algorithm with small distance between D2D pair. When

the distance between D2D pair is more than 90m, the

proposed algorithms have lower capacity gain of D2D

pairs according to the less number of candidates.

5 10 15 20 25 30 350

0.5

1

1.5

2

2.5

3

3.5x 10

4

The number of cellular users

Itera

tion t

imes

Proposed Optimal

Proposed Suboptimal

Fig. 4. Iteration times of proposed optimal and suboptimal for different

number of cellular users.

Fig. 4 demonstrates the computational complexity of

the proposed optimal algorithm and proposed two-stage

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suboptimal algorithm. It is shown that iteration times of

the proposed suboptimal algorithm is less than the

proposed optimal algorithm. The difference of iteration

times between the optimal algorithm and suboptimal

algorithm becomes greater with the increasing number of

cellular users, which indicates that the computational

complexity of the proposed suboptimal algorithm is much

lower than the optimal algorithm. In summary, compared

with the proposed optimal algorithm, the suboptimal

algorithm can acquire approaching best performance with

lower computational complexity.

V. CONCLUSIONS

In this paper, we have proposed a resource allocation

and power control algorithm, which can obtain the

optimal system capacity of D2D users under the

conditions of QoS of cellular users and D2D users. The

candidate cellular users of each D2D pair can be received

through the SINR requirement of D2D users. We can

obtain optimal transmission power of cellular user, which

is represented by the transmission power of D2D user

through the SINR demand of cellular user. And then the

optimal transmission power of D2D users can be received

by Lagrange multiplier method. The algorithm solves the

resource allocation problem of D2D user and coordinates

the interference between cellular users and D2D users.

We also propose the suboptimal algorithm for the high

computational complexity of the proposed optimal

algorithm. Simulation results show that the proposed

algorithms outperform the algorithm in [8], the greedy

algorithm and the random resource allocation algorithm

in terms of capacity of D2D users. Meanwhile, the

capacity of D2D users of the suboptimal algorithm is

approaching to the optimal algorithm, but the

computational complexity of the proposed suboptimal

algorithm has much lower than the proposed algorithm.

APPENDIX A PROOF OF PROPOSITION 1

Proof: in [16], we know that if

1 2 1 2G G s is found for all 2 0 , so s

is the second gradient of G at 1 . Therefore, we can

get the following inequality

1 1 1k tot

k

G G P

,

2 1 , 1

0 , ,

log 1

d

j k j d

j k totck j D i k i j

p gp P

N p h

,

2 1 , 1

0 , ,

log 1

d

j k j d


p gp P

N p h

,

2 1 , 1

0 , ,

log 1

d

j k j d


p gp P

N p h

2 , 2 ,

d d

tot j k tot j k

k j D k j D

P p P p

,

2 2 , 2

0 , ,

1 2 ,

log 1

( )

d

j k j d


d

tot j k

k j D

p gp P

N p h

P p

2 1 2 ,( ) ( ) d

tot j k

k j D

G P p

,

c

i kp and ,

d

j kp are the optimal solutions according to 1 ,

while ,

c

i kp and ,

d

j kp are the optimal solutions according to

2 , inequality is due to that ,

c

i kp and ,

d

j kp are the optimal

solutions with respect to1 . Thus, Proposition 1 is

proved.

ACKNOWLEDGMENT

This work is supported by National Natural Science

Foundation of China (61571234， 61401225), Jiangsu

Provincial National Science Foundation (BK20140894).

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Bao-Zhou Yu was born in Jiangsu Province, China, in 1991.

He received the B.E. degree in Communication Engineering

from Nantong University, Nantong, in 2014. He is now

pursuing master's degree in the department of Communication

and Information Engineering. He researches on the area of

resource management and power control of D2D

communication underlaying cellular networks

Zhu Qi (corresponding author) was born in Suzhou, Jiangsu,

China, in 1965. She received the M.S. degree in radio

engineering from Nanjing University of Posts and

Telecommunications in 1989. Now she is a professor in the

Department of Telecommunication and Information

Engineering, Nanjing University of Posts and

Telecommunications, Jiangsu, China. Her research interests

focus on technology of next generation communication,

broadband wireless access, OFDM, channel and source coding,

dynamic allocation of radio resources.

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A QoS-Based Channel Allocation and Power Control Algorithm