Energy Efficiency Optimization and Comparison for One- Way ...powered by batteries, such as wireless body area networks [5], [6] and wireless multimedia networks [7]. A widely used

Energy Efficiency Optimization and Comparison for One-

Way and Two-Way Decode-and-Forward Relay Systems

Jie Yang, Xuehong Cao, Rui Chen, and Dawei Zhu Department of Communication Engineering, Nanjing Institute of Technology, Nanjing, 211167, China

Email: {yangjie, caoxh, chenrui, luitt, zhudw}@njit.edu.cn

Abstract—Energy-efficient communication techniques play

great roles in applications where devices are powered by

batteries. Relaying is viewed as an energy saving technique

because it can reduce the transmit power by breaking one long

range transmission into several short range transmissions. Two-

Way Relaying Transmission (TWRT) is expected to consume

less transmit power than One-Way Relaying Transmission

(OWRT). In this paper, we study the Energy Efficiencies (EEs)

of One-Way Decode-and-Forward (OWDF) and Two-Way

Decode-and-Forward (TWDF) systems with delay constraint.

The maximum EEs of both systems are derived by jointly

optimizing the transmission duration and the transmit power

allocation. Analytical and simulation results show the impacts

of packet size, time deadline and the channel gain to EE. Index Terms—Two-Way relay transmission, one-way relay

transmission, decode-and-forward, energy efficiency

I. INTRODUCTION

Relaying has been extensively studied because it can

extend the coverage and enhance the capacity of wireless

system [1]. Two-Way Relay Transmission (TWRT) has

been viewed as a promising technique in recent years

of the One-Way Relay Transmission (OWRT) [2].

Moreover, relaying is viewed as an energy saving

technique because it can reduce the transmit power by

breaking one long range transmission into several short

range transmissions [3], [4].

Energy-efficient communication techniques play

important roles in applications where devices are

powered by batteries, such as wireless body area

networks [5], [6] and wireless multimedia networks [7].

A widely used metric for Energy Efficiency (EE) is the

number of transmitted bits per unit of energy [8].

Recently, the EE study of different relay systems has

become a hot research topic in both industry and

academia. In [9], a three-node Amplify-and-Forward (AF)

TWRT system was optimized to find the minimum total

transmit power under the constraint of Signal-to-Noise

Ratio (SNR). In [10], a relay selection strategy based on

minimizing total power consumption was proposed

Manuscript received June 23, 2015; revised January 29, 2016.

This work was supported by the NSF of Jiangsu Province Project No.BK20141389 and the Innovation Project of Nanjing Institute of

Technology No. ZKJ201510, QKJB201407, ZKJ201305. Corresponding author email: [email protected]

doi:10.12720/jcm.11.2.171-178

subject to the SNR requirements on the two transceivers.

On the other hand, in [11], joint relay selection and power

allocation scheme was proposed to minimize total

transmit power under the constraint of target rate. In [12],

the EEs of TWRT, OWRT and Direct Transmission (DT)

systems were compared, and the results show that TWRT

consumes less energy compared to OWRT and DT. It

should to noted that only the transmit power was taken

into account in Energy Consumption (EC) in [9]-[12].

However, when the power consumed by various signal

processing and RF circuits in practical systems is also

considered, the optimization problem which can

minimize the total transmit power may not necessarily

lead to high EE [13].

The EE of DT, One-Way AF (OWAF) and two-way

AF (TWAF) systems were studied in [3], [14], where

both actual output transmit powers and circuit powers of

the nodes were considered. Based on this modified power

consumption model, it was shown that TWRT is not

always the most energy efficient solution. Compared to

AF, DF protocol can achieve higher ergodic capacity

when relaying node is close to the source node [15].

Circuit Power Consumption (PC) considered SE and EE

of DF system have been studied in some previous works

[16]-[18]. Circuit PC considered SE and EE of One-Way

Decode-and-Forward (OWDF) is analyzed in [16], it was

shown that the SE-EE trade off in OWDF has better

performance compared to DT. EE for Two-Way Decode-

and-Forward (TWDF) with relay power constraint is

studied in [17], but the idle status and the power

consumption in idle status are not considered. EE

comparisons for TWAF and TWDF were given in [18]

without considering the idle status. Considering the

quality of service requirements of actual application

systems, where the data delivery must be finished within

a hard time deadline, e.g., wireless multimedia

communication and wireless sensor networks [5], [19], it

is essential for delay constraint to be taken into account in

EE analysis. Unfortunately, delay constraint is not

considered in [16]-[18]. Furthermore, the EE

performances of OWDF and TWDF systems were not

compared in the previous work.

In this paper, we analyze the EE performances of both

OWDF system and TWDF system, considering both the

transmit power and the circuit power consumed by

transmit-and-receive processing in each node. We

consider a delay-constrained three-node relay system,

171

Journal of Communications Vol. 11, No. 2, February 2016

©2016 Journal of Communications

than that because of its Spectrum Efficiency (SE) is higher

where the messages at two source nodes are periodically

generated and must be transmitted within a hard time

deadline. From an energy saving perspective, during the

relay transmission process, it is more preferable for a

node to switch to idle status if it does not need to transmit

or receive in some time slot. Thus, during the relay

process, each node can operate in three possible states:

transmission, reception and idle. For the whole relay

transmission system, it is also more preferable for the

system to transmit a block of data in a short duration and

then switch to idle status until the next block [20]. In this

paper, we maximize the EEs of OWDF and TWDF by

optimizing transmission duration and transmit powers. To

solve this joint optimization problem, we first express the

transmit powers as functions of the two independent

transmission durations, and then optimize transmission

durations to minimize the EC. In the simulations, we

compare the optimized EEs and optimum transmit

duration of TWDF with that of OWDF, and show the

impacts of packet size, time deadline and the channel

gain to EE.

The remainder of this paper is organized as follows.

System model and the EC model of the two transmit

strategies are described in Sections II and III, respectively.

Then the EEs of both strategies are optimized in Section

IV. Simulation results are given in Section V. Section VI

concludes the paper.

h1r

h1r

h2r

h2r

User

Equipment (S1)

Base Station

(S2)

Relay

(R)

h1r

h1r

h2r

h2r

Relay

(R)

(a) OWRT (b) TWRT

User

Equipment (S1)

Base Station

(S2)

Fig. 1. One- way relay system and two-way relay system model

II. SYSTEM MODEL

The general layouts of OWRT and TWRT are illustrated in Fig. 1. Both system consists of a User

Equipment (1

S ), a Relay ( R ) and a Base Station (2

S ),

where 1

S and 2

S intend to exchange information with the

assistance of relay. Assume that all terminals are single-

antenna devices and there is no direct path between 1

S

and 2

S . Within a hard deadline T , 1

S and 2

S intend to

transmit 12

B and 21

B bits to each other. The channels

among three nodes are assumed as frequency flat fading

channels, which are denoted as 1r

h and 2rh respectively.

Channel gains between every pair of nodes are assumed

symmetric (i.e. 1 1r rh h ), and noise power 0

N is

assumed to be identical at each node. The PCs in transmission, reception, and idle mode are denoted as

c

tP P , r

cP and i

cP , respectively, where P is the

transmit power, (0,1] denotes the power amplifier

efficiency, t

cP , r

cP , and i

cP are the circuit PCs in

transmission, reception and idle modes, respectively.

S1:transmit

R:receive

S2:idle

S1:idle

R:transmit

S2:receive

S1:idle

R:receive

S2:transmit

S1:receive

R:transmit

S2: idle

S1:idle

R: idle

S2:idle

(a) OWDF

(b) TWDF

transmission

mode

tt12/2 t12 t12+t21/2 t12+t21 T0

T

S1:transmit

R:receive

S2:transmit

0 t1 t1+t2

S1:receive

R:transmit

S2:receive

S1:idle

R: idle

S2:idle

t

transmission

mode

Fig. 2. Transmission duration and operation mode during each block of

OWRT and TWRT

III. ENERGY CONSUMPTION MODEL

A. Energy Consumption of OWDF

During each block, OWDF system transmits with a

duration 12t in 1S → 2S direction and another duration 21t

in 2S → 1S direction. Then, all the three nodes switch to

idle mode with duration 12 21T t t , as shown in Fig. 2(a).

During the first half of 12t , node 1

S transmits to R with

transmit power 1P , 1S is in transmit mode, R is in

receive mode, and 2S is idle. Using DF strategy, R

decodes the messages and create the transmit signal for

the second half of 12t . During the second half of 12t , R

forwards the recoded information to node 2S with

transmit power rP , and thus R is in transmit mode, 2S is

in receive mode, and 1S is idle. In the duration for

2S → 1S direction, the relay process is similarly. The EC

of OWDF during each block is given by

12

21 2

12 21

1 2

12 21

1( )2

( )2

( )( )

( ) ( )2 2

t r i t r i

o c c c c c c

t r i t r ir

c c c c c c

i i i

c c c

r r

c i c i i

rtE P P P P P P

t P PP P P P P P

T t t P P P

P P P Pt P P t P P TP

P P

(1)

where t r i

c c c cP P P P , 3 i

i cP P .

The achievable bidirectional data rates can be obtained from the capacity formulas for OWDF [21], which are

122 1 1 2 2

12

min log 1 , log 1r r r

BW G P G P

t (2)

212 2 2 2 1

21

min log 1 , log 1r r r

BW G P G P

t (3)

where

2 2

1 2

1 2

0 0

,r r

r r

h hG G

N N .

To guarantee successful decoding at the relay and the

two terminals, according to (2) and (3), transmit powers

should satisfy

11

1r

PG

, 1

2

r

r

PG

, 2

2

2

r

PG

, 2

1

r

r

PG

(4)

172



where 121

12

( )B

Wt , 21

2

21

( )B

Wt , and ( ) 2 1x

x .

B. Energy Consumption of TWDF

During each block, the TWDF system completes the

bidirectional transmission with duration 1 2twt t t , then,

all the three nodes switch into the idle mode with

duration 1 2- -T t t , as shown in Fig. 2(b). In the first time

slot 1t (multiple-access phase, MA phase),

1S (

2S )

transmits the message 1x (

2x ) simultaneously to the relay

node. In the second phase 2t (broadcasting phase, BC

phase), R broadcasts the recoded message to 1

S (2

S ) with

transmit power ,1rP (, 2r

P ), where the node R is in transmit

mode, 1

S and 2

S are in receive mode.

The overall EC of TWDF system is given by

1 2

1

1 2

2 1 2

1 21 2 1 2

1 2

( )

( ) ( )(3 )

( ) ( )

t t r

tw c c c

t r r ir r

c c c c

r r

c i c i i

P PE t P P P

P Pt P P P T t t P


(5)

where 12

t r

c ccP P P , 2

2t r

c ccP P P , 3 i

i cP P .

In the first time slot, the received signal at relay node

is

1 1 1 2 2 2r r r ry P h x P h x n (6)

Using successive interference cancellation (SIC)

strategy [22], the relay node first compare the received

SNRs of the two messages, and then decodes the message

with the higher SNR treating the power of the other

message as unknown interference. After that, the message

with the higher SNR can be subtracted from (6), and then

the other message can be decoded with no interference.

Based on the above reasons, two cases may exit:

Case 1: 2 2

1 1 2 2r rP h P h . In order to guarantee

successful decoding at the relay, channel capacity should

satisfy:

2

1 1 122 2

10 2 2

212 2 2

1

log 1

log 1

r

r

r

P h BW

tN P h

BW G P

t

(7)

From (7), we can get

3 3 4 3 3 44 42 1 1 2

2 1 1 1 2 1

, ,r r r r r r

P P P PG G G G G G

(8)

where 3 12 1 4 21 1

( ( )), ( ( ))/ /B W t B W t .

Case 2: 2 2

2 2 1 1r rP h P h . In order to guarantee

successful decoding at the relay, channel capacity should

satisfy:

2

2 2R 212 2

10 1 1R

122 1 1

1

log 1

log 1 r

P h BW

tN P h

BW G P

t

(9)


3 3 4 3 3 44 41 2 1 2

1 2 2 21 2 2

, ,r r r r r

P P P PG G G G G G

(10)

In the second time slot 2t , the received signal at 1

S (2

S )

is

,1 2 ,2 1( ) 1, 2

i ir r r iy h P x P x n i (11)

After self-interference cancellation, the end-to-end

SNRs at 1

S (2

S ) is

1 ,1r rG P (

2 ,2r rG P ). In order to guarantee

successful decoding at the terminals, ,1r

P and ,2r

P should

satisfy

21 12

2 1 ,1 2 2 ,2

2 2

log 1 , log 1r r r r

B BG P G P

t tW W (12)


6 5 5 6,1 ,2 ,1 ,2

1 2 2 1

, ,r r r r

r r r r

P P P PG G G G

(13)

where 5 12 2 6 21 2

( ( )), ( ( ))/ /B W t B W t .

IV. ENERGY EFFICIENCY OPTIMIZATION

In this section, we optimize the EEs for OWDF and

TWDF. The EE is defined as the number of bits

transmitted in two directions per unit of energy, i.e.,

12 21EE

B B

E

(14)

where E is the EC per block of each strategy.

EE maximization is equivalent to EC minimization for

a given pair of 12

B and

21B . Consequently, we will

minimize the EC per block.

A. EE Optimization of OWDF

As shown in (3), the EC of OWDF is a function of the

transmit powers as well as the transmission duration. The

EC can be minimized by jointly optimizing the transmit

powers and transmission time. Combining (3) and (4), EC

can be minimized as

1 2 12 21

1 2

12 21

max max max

12 21 1 2

1 1 2 2

1 2

1 2 2 1

, , , ,

min ( ) ( )2 2

. . , , ,

. . , , ,

t t t

r

r r

c i c i i

r

r r

r r r r

P P P t t


s t t t T P P P P P P

s t P P P PG G G G

(15)

To solve this joint optimization problem, we first

express the transmit power as functions of the

173



transmission duration 12t and 21t , then optimize the

transmission duration to minimize the EC. We denote the

minimum value of 1 rP P as min 12

P t , and the

minimum value of 2 rP P as

min 21P t according to (4),

the minimum power value can be derived as

min 12 1 min 21 2

1 2 1 2

1 1 1 1( ) ( )

r r r r

P t P tG G G G

(16)

To ensure that all the constraints in (12) can be

satisfied, the data rates 12 12

/B T and 21 21

/B T should be

less than the maximum data rate supported by the

maximum transmit power. Those turn into the constraints

on the transmit time in two directions, which are

12

max max

2 2

12 min

1 2min log 1 , log 1

r r

B

W G P G Pt

(17)

21

max max

2 2

21 min

2 1min log 1 , log 1

r r

B

W G P Pt

G

(18)

Then the optimization problem of (12) can be

simplified to an optimization problem with only two

independent decision variables, which can be written as

12 21

min 1212 21 12

,

min 2121

12 21 12 2112 min 21 min

min ( , ) ( )2

( )2

. . , ,

c it t

c i i

P tf t t t P P

P tt P P TP

s t t t T t t t t

(19)

Optimization problem (16) contains two decision

variables, and the constraints compose a closed region R.

As the objective function is continuous in R, according to

the theory of extreme values of multivariate functions,

optimization problem (16) can be solved in three steps:

1) Find the stationary points and the corresponding

extremum in region R.

As the objective function is derivable everywhere in

the closed region, the extreme value must satisfy

12

12

2 1

21

min 12

12

12 1 2 12

min 21

21

21 1 2 21

12 21 12 12 min 21 21 min

1 1 ln 2+ 2 =0

2

1 1 ln 2+ 2 =0

2

, ,

B

Wt

c i

r r

B

Wt

c i

r r

P tfP P B

t G G Wt

P tfP P B

t G G Wt

t t T t t t t

(20)

Although the optimal solution can be found through

(17), it does not have a closed form. Here, we adopt a

recursive method to find optimal solution [23]. The

algorithm steps to find optimum 12t are given as follows:

①define

12

12min1 12

12 12

1 2 12

1 1 ln 2( ) + 2

2

B

Wt

c i

r r

P tf t P P B

G G Wt

;

② _ 0t low , 12 min1_t up t , 2/10T ,

5/10T ;

③while( _ _t up t low )

_ _t low t up ;

_ _ ( _ )t up t low f t low ;

④ 12 _t t up ;

⑤ return 12t .

Taking similar steps, the optimum 21t can also be

found. Compute objective function in these points.

2) Find the extremum on the boundaries. The

substitution of the boundaries into the objective function

results in a simple function, so the optimal solution on the

boundaries can be found in a relatively easy way.

3) Smallest value from 1) and 2) is the absolute

minimum in the closed region.

If the absolute minimum is obtained from step (1), and

the optimum 12t and 21t are denoted by opt

12t and opt

21t ,

respectively, we obtain

12

12

21

21

2

min 1212

1 2 12

2

min 2121

1 2 21

1 1 ln 2( ) 2

2

1 1 ln 2( ) 2

2

opt

opt

B

Wt

c i opt

r r

B

Wt

c i opt

r r

P tP P B

G G Wt

P tP P B

G G Wt

(21)

According to (19), (20), the minimum oE can be

formulated as

12 21

12 21

2 2

min 12 21

1 2

ln 2 1 1( )( 2 2 )

opt opt

B B

Wt Wt

o i

r r

E B B TPW G G

(22)

And the optimum energy efficiency is obtained as

12 21

12 21

12 21

2 2

12 21

1 2

ln 2 1 1( )( 2 2 )

o EE

opt opt

opt

B B

Wt Wt

i

r r

B B

B B TPW G G

(23)

B. EE Optimization of TWDF

As shown in (5), the EC of TWDF is a function of the

transmit powers 1P , 2P , ,1rP and ,2rP as well as the

transmission duration. If 2 2

1 1 2 2r rP h P h is hold,

combining (5), (8) and (13), EC can be minimized as

1 2 ,1 ,1 1 2

1 21 2 1 2

1 2, , , , ,

max max max

1 2 1 2 ,1 ,2

3 3 4 6 54

2 1 ,1 ,2

2 1 1 1 2

min ( ) ( )

. . + , , ,

. . , , ,

r r

r r

c i c i iP P P P t t

r r

r r

r r r r r


s t t t T P P P P P P P

s t P P P PG G G G G

(24)

If 2 2

2 2 1 1r rP h P h is hold, combining (5), (10) and

(13), EC can be minimized as

1 2 ,1 ,1 1 2

1 21 2 1 2

1 2, , , , ,

max max max

1 2 1 2 ,1 ,2

3 3 4 6 54

1 2 ,1 ,2

1 2 2 1 2

min ( ) ( )

. . + , , ,

. . , , ,

r r

r r

c i c i iP P P P t t

r r

r r

r r r r r


s t t t T P P P P P P P

s t P P P PG G G G G

(25)

174



Since case 2 is similar to case1, here we only consider

case1. We first derive the transmit powers as functions of

the transmission duration. Denote the minimum value of

1P as 1min 1( )P t , and the minimum value of

2P as

2 min 1( )P t .

Denote the minimum value of 1 2

t tP P as

min 1P t ,

according to (8), we can get

min 1

3 3 442min 1 1min 1

2 1 1

3 3 441 2 min

1 2 1

( ) , ( )

( )

r r r

r r r

P t

P t P tG G G

P PG G G

(26)

Considering that both 1min 1( )P t and

2min 1( )P t in (26) are

the monotone decreasing functions of 1t , supposing that

max

1min 1( )P t P and

max

2 min 1( )P t P , we can obtain two

transmit time lower-bounds. We keep the larger one of

the two lower-bounds and denoted it as min 1t . Denote

the minimum value of ,1 ,2r rP P as min 2

P t , according

to (13), the minimum value of ,1 ,2r rP P can be computed

as

min 2

5 6,1 ,2 min

2 1

r r

r r

P t P PG G

(27)

Since min 2

P t is the monotone decreasing functions of

2t , supposing min 2 2

maxP t P , we can obtain a transmit

time lower-bound and denote it as min 2t . Substituting

(26), (27) to (24), the optimization problem can be

simplified to an optimization problem with only two

independent decision variables, which is

1 2

11

1 2 1

22

2

min

,

min

1 2 1 min 1 2 min 2

min ( , )

. . + , ,

c i

c i i

t t

P tf t t t P P

P tt P P TP

s t t t T t t t t

(28)

Optimization problem (28) contains two optimization

variables, and the constraints compose a closed region R.

As the objective function is continuous in R, according to

the theory of extreme values of multivariate functions,

optimization problem (28) can be solved in three steps:

1) Find the stationary points and the corresponding

extremum in region R.

As the objective function is derivable everywhere in

the closed region, the extreme value must satisfy

21

1

12 21

1

21

2

12

2

min 1

21

1 1 2

21 21

1

min 2

21

2

12

1

2

1

1

2

2

ln 2 1 1+

ln 2 1=0

ln 2

ln 2 =0

2

2

12

12

( )

c i

r r

r

c i

B

Wt

B B

Wt

B

Wt

r

B

Wt

r

P tfP P B

t Wt G G

B BWt G

P tfP P B

t Wt

BWt

G

G

(29)

Here, we adopt the recursive method to find optimal

solution. The algorithm steps to find optimum 1t are

given as follows.

① define 21

1

12 21

1

min 1

21

1 2

21 21

1

1

1

1

ln 2 1 1+

ln 2 1

2

2

( )

( )

c i

r r

r

B

Wt

B B

Wt

P tP P B

Wt G G

B BWt G

f t

;

② _ 0t low , min 1_t up t , 2/10T , 5/10T ;

③while( _ _t up t low )

_ _t low t up ;

_ _ ( _ )t up t low f t low ;

④ 1 _t t up ;

⑤ return 1t .

Taking similar steps, the optimum 2t can also be

found. Compute objective function in these points.

2) Find the extremum on the boundaries of R.

3) Smallest value from 1) and 2) is the absolute

minimum in the closed region. If the absolute minimum is obtained from step (1), and

the optimum 1t and 2t are denoted by opt

1t and opt

2t ,

respectively, according to (25), (26), we can get the

minimum twE for Case1.

Case 1: 2 2

1 1 2 2r rP h P h .

12 21 21

1 1

2

1min 1

min 1

2min 2

2

( )

12 2121

1 1 2

21

1

ln 2

ln 2 ( ) 1 12 2

12

opt opt

opt

opt

tw c i

opt

opt

c i i

B B B

Wt Wt

r r r

B

rW

P tE t P P

P tt P P TP

W

B BB

G G G

BG

1 12

2 2

12

2

12

opt opt

i

B

Wt Wt

r

TPBG

(30)

Similarly, we can get the minimum twE for Case2.

Case 2: 2 2

2 2 1 1r rP h P h .

12 21 12

1 1

2

1min 1

min 1

2min 2

2

( )

12 2112

2 2 1

21

1

ln 2

ln 2 ( ) 1 12 2

12

opt opt

opt

opt

tw c i

opt

opt

c i i

B B B

Wt Wt

r r r

B

rW

P tE t P P

P tt P P TP

W

B BB

G G G

BG

1 12

2 2

12

2

12

opt opt

i

B

Wt Wt

r

TPBG

(31)

And the optimum energy efficiency is

175



12 21

min

tw EE

tw

opt B B

E

(32)

V. SIMULATION RESULTS

A. Simulation Parameter

Simulation parameters are listed in Table I.

TABLE I: SIMULATION PARAMETERS

Parameters Values

Distance between nodes ( 1 2,r rd d ) 1 2 100mr rd d

Packet sizes in two directions( 12 21B B ) 4 5[2 10 ,7 10 ]

Block time duration ( T ) 10ms

System bandwidth ( W ) 10MHz

Noise power at each node ( 0N ) -94dBm

Path loss attenuation 1030 40log ( ) dBd

Maximum transmit power ( maxP ) 45dBm

Circuit power ( ,t r

c cP P ) 50mw

Circuit power in idle mode ( i

cP ) 10mw

The small scale fading channels are independent and

identically distributed (i.i.d.) Rayleigh block fading,

which remain constant during one block but are

independent from one block to another. Circuit power

consumption in a practical system ranges from tens to

hundreds mW [4]. Therefore, we set the circuit PCs in

this range in the simulations, and the power amplifier

efficiency is set as 0.35 [24], which is quite justified as

the PA efficiency is generally less than 50% for wireless

applications. We consider that the three nodes are located

on a straight line, and the total distant is fixed to 100m,

but the relay node can move from one side to another side.

0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100

Total spectral efficiency in two directions (bit/s/Hz)

Optim

al energ

y e

ffic

iency (

Mbits/J

)

OWDF,B12

/B21

=1,d2r

/d1r

=1

TWDF,B12

/B21

=1,d2r

/d1r

=1

OWDF,B21

/B12

=2,d2r

/d1r

=1

TWDF,B21

/B12

=2,d2r

/d1r

=1

OWDF,B21

/B12

=3,d2r

/d1r

=1

TWDF,B21

/B12

=3,d2r

/d1r

=1

Fig. 3. EE comparison among OWDF and TWDF with different packet

sizes ( 10msT )

B. Simulation Results and Analysis

Fig. 3 illustrates the optimal EEs of OWDF and TWDF

systems with equal and unequal bidirectional packet sizes.

The x-axis is the overall number of transmitted bits in

two directions normalized by the block duration and

bandwidth, i.e., 12 21

( ) / /B B T W , which can be viewed as

the average bidirectional SE per block. Based on the

results, it is possible to see that OWDF achieves better

EE than TWDF in low-traffic region, but in the high-

traffic region, OWDF is inferior to TWDF. The impact of

asymmetric packet sizes is also showed in this figure. It

can be seen that the EE of OWDF reduces fast as the

difference between 12B and 21B is increases, but the

impact of asymmetric packet size to the EE of TWDF is

trivial. While, in AF schemes, the asymmetric packet

sizes in two directions only reduces the EE of TWRT

[14]. In this case, the impact of asymmetric packet sizes

to DF strategies is opposite to that of AF strategies.

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

9

10


Optim

um

tra

nsm

issio

n t

ime (

ms)

DF-OWRT,B12

:B21

=1,T=10ms

DF-OWRT,B21

:B12

=2,T=10ms

DF-TWRT,B12

:B21

=1,T=10ms

DF-TWRT,B21

:B12

=2,T=10ms

(t12

opt + t21

opt)

(t1

opt + t2

opt)

Fig. 4. optimum bidirectional transmission time comparison among

OWDF and TWDF with equal and unequal bidirectional packet sizes

In Fig. 4, we compare the optimum transmission time

12 21

opt optt t and

1 2

opt optt t , given different values of

bidirectional packet sizes. It is shown that, in both

schemes, the optimum transmit time of the system with

equal bidirectional packet sizes is shorter than that of the

system with unequal bidirectional packet sizes. This is

because, using DF strategy, correct decoding for high-rate

bits needs more transmit power than correct decoding for

low-rate bits. From this point of view, the transmission

time must be increased in order to decrease the data rate

in the direction with higher packet size, and then decrease

the power consumption.

0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100


Optim

al energ

y e

ffic

iency (

Mbits/J

)

OWDF,d2r

/d1r

=1,B12

/B21

=1

TWDF,d2r

/d1r

=1,B12

/B21

=1

OWDF,d2r

/d1r

=2,B12

/B21

=1

TWDF,d2r

/d1r

=2,B12

/B21

=1

OWDF,d2r

/d1r

=3,B12

/B21

=1

TWDF,d2r

/d1r

=3,B12

/B21

=1

Fig. 5. EE comparison among OWDF and TWDF with different relay locations

176



In Fig. 5, we present the impact of relay location

difference. We compare the optimum EE of OWDF and

TWDF, given different values of the distance between

nodes, i.e., 12 21d d . We can see that, in symmetric

packet sizes condition, the EE of OWDF is always higher

than that of TWDF when the channel gain between the

relay and one source is significantly different from the

channel gain between the relay and the other source. In

this case, TWDF will consume more energy than OWDF

when the relay is close to one of two terminals.

0 1 2 3 4 5 6 710

-4

10-3

10-2

10-1

100

101

102


Min

imum

energ

y c

onsum

ption (

J)

DF-OWRT,B12

:B21

=1,d2r

=d1r

DF-OWRT,B12

:B21

=2,d2r

=d1r

DF-TWRT,B21

:B12

=1,d2r

=d1r

DF-TWRT,B21

:B12

=2,d2r

=d1r

Fig. 6. Minimum energy consumption comparison among OWDF and TWDF

In Fig. 6, we compare the minimum EC of the two

strategies with equal and unequal bidirectional packet

sizes. It is shown that, in symmetric distance condition,

OWDF system consumes less energy than TWDF

strategy in low-traffic region. While in most traffic region,

TWDF strategy is more energy efficient. Which means

that, in most traffic region, TWDF strategy can support

higher packet sizes than OWDF strategy with the same

energy consumption.

VI. CONCLUSION

In this paper, we study the EEs of OWDF and TWDF

systems considering both the transmit power and the

circuit power in each node. We obtain the maximum EEs

for both OWDF and TWDF systems by minimizing the

total EC, and the total EC is derived by jointly optimizing

bidirectional transmission times and transmit powers.

Analytical and simulation results showed that OWDF can

achieve better EE performance compared to TWDF in

low-traffic region, but in the high-traffic region, OWDF

is inferior to TWDF. Asymmetric packet sizes will

decrease the EEs of both systems, but the impact of

packet size difference to the EE of TWDF is trivial. In

high SE region, the optimum total transmission time will

be allocated a maximum value, i.e. the time deadline T .

It is also showed the EE of OWDF is always higher than

that of TWDF when the channel gain between the relay

and one terminal is significantly different with that

between the relay and the other terminal.

ACKNOWLEDGMENT

This work was sponsored by the NSF of Jiangsu

Province Project No.BK20141389 and the Innovation

Project of Nanjing Institute of Technology

No.QKJA201304, QKJB201407.

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1947-1967, Apr. 2014.

Jie Yang was born in Jiangsu Province,

China, in 1979. She was born in Jiangsu,

China, in 1979. She received the B.S.

and M.S. degrees from Lanzhou

University of Technology in 2000 and

2003, respectively. She received PhD

degree from Nanjing University of Post

and Telecommunications in 2015. Now

she is the vice professor of Nanjing Institute of Technology. Her

currently research interests include cooperative communications,

relaying network, and resource allocation.

Xuehong Cao was born in Suzhou,

China, in 1964. She received the B.S.

and M.S. degrees from the Nanjing

University of Posts and

Telecommunications in 1985 and 1988,

respectively, and the Ph.D. degree in

electronic engineering from Shanghai

Jiaotong University in 1999. From 2004

to 2005, she worked as a visiting professor at the department of

electrical engineering, Stanford University. Now she is a

Professor and the vice president of Nanjing Institute of

Technology. Her research interests include multicarrier

modulation, cooperative communication system and

information theory.

Rui Chen received the B.E degree, the

M.E. degree from Southeast University,

Nanjing, China, in 1991 and 1996,

respectively. She received PhD degree

from Nanjing University of Post and

Telecommunications in 2013. Currently

she is an associate professor in Nanjing

Institute of Technology, majoring in

video coding and multimedia communication.

178



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