Wireless Information and Power Transfer for Full Duplex Relaying Networks: Performance Analysis

Abstract

Energy harvesting (EH) based on ambient radio frequency (RF) has recently become advanced method to prolong the lifetime of the wireless networks. This paper deals with energy harvesting architecture of the full duplex relaying networks. By applying time switching based relaying (TSR) protocol and Amplify-and-Forward (AF) scheme, we derive the closed-form expression of the outage probability and hence compute the optimal throughput. An important result can be seen clearly that the time fraction in TSR impacts on the optimal throughput. Finally, numerical results show an efficient relaying strategy in full duplex cooperative networks.

Full text

Wireless Information and Power Transfer for Full
Duplex Relaying Networks: Performance Analysis
Tam Nguyen Kieu 1, Dinh-Thuan Do2, Xinh Nguyen Xuan2, Tan Nguyen Nhat 1 ,
Hung Ha Duy 1
1Department of Electronics and Telecommunications Engineering, Falcuty of Electric and
Electronic, Ton Duc Thang University, 19 Nguyen Huu Tho St., 7th Dist., Ho Chi Minh City,
Viet Nam.
2Department of Electronics and Communications Engineering, Ho Chi Minh City of Technolo-
gy and Education, 1 Vo Van Ngan St., Thu Duc Dist., Ho Chi Minh City, Vietnam
nguyenkieutam@tdt.edu.vn, dodinhthuan@gmail.com,
xuanxinhspkt@gmail.com,nguyennhattan@tdt.edu.vn
and haduyhung@tdt.edu.vn
Abstract. Energy harvesting (EH) based on ambient radio frequency (RF) has
recently become advanced method to prolong the lifetime of the wireless net-
works. This paper deals with energy harvesting architecture of the full duplex
relaying networks. By applying time switching based relaying (TSR) protocol
and Amplify-and-Forward (AF) scheme, we derive the closed-form expression
of the outage probability and hence compute the optimal throughput. An impor-
tant result can be seen clearly that the time fraction in TSR impacts on the op-
timal throughput. Finally, numerical results show an efficient relaying strategy
in full duplex cooperative networks.
Keywords: Energy harvesting, full duplex, two way relaying network, time
switching-based protocol, throughput.
1 Introduction
Applications of renewable energy in the next generation wireless networks will be
bring huge benefits for continuing operation in mobile equipments. Among other
energy sources such as solar and wind power, power extracted from radio-frequency
(RF) signals in ambient transmitters can be considered as replacements for traditional
wired power grids. Such energy harvest from the natural environment is a promising
approach to prolong the lifetime of energy constrained wireless networks such as
cellular networks or wireless sensor networks. Simultaneous wireless information and
power transfer technology (SWIPT) becomes appealing candidate since it realizes
both useful information and energy from RF signals at the same time, and thus poten-

tially offers great convenience to mobile equipments. Varshney first proposed the idea
of transmitting information and energy simultaneously in [1]. Using relay to facilitate
RF energy harvest and information transfer has also drawn significant attention,
which is able to extend the transmission range and increased capacity for system. In
[2], the authors studied the throughput performance of an amplify and-forward (AF)
relaying system for both time-switching and power-splitting protocols.
More importantly, relaying network is an effective way to combat the performance
degradation caused by fading, shadowing, and path loss. Full duplex (FD) relay net-
work has the potential to realize the successful information exchange of two sources
and more spectral efficiency than conventional half-duplex (HD) technique. When
comparing to the HD mode, the FD mode has higher capacity in practical channel
conditions. Alternatively, the FD mode can tolerate high loop interference power
while achieving the same capacity as the half-duplex mode. The main disadvantage of
FD communication is the self-interference from own node transmission, which is
much larger than signal of interest from the distant node. To help the communication
node that can transmit and receive signals over the same frequency band, many tech-
niques of suppressing self-interference have been proposed in [3-5]. Unfortunately,
the self-interference is residual due to limit technique. The residual interference still
decreases the system performance. In fact, [6] indicates that the full-duplex mode is
an attractive choice for fixed relays provided that the loop interference power is main-
tained at a tolerable level. The authors in [7] presented power allocation strategy to
maximize the sum-rate of FD-two-way relaying system under realistic residual self-
interference.
Recently, a few research trends have been conducted in FD relay system in context
of the SWIPT scheme. In [12], the throughputs are analyzed for three relay control
schemes, including the maximum relay, optimal relay, and target relay. Analytical
expressions for outage probability and ergodic capacity are also presented for these
considered relay control schemes. Later in [9], the authors consider two cases depend-
ing on the number of antennas used for harvesting and demonstrated that employing
both relay antennas for energy harvesting is always beneficial, compared to the HD
relaying architecture, results indicate that FD relaying can substantially boost the
system throughput. The author in [10] analyzed performance of two-way relaying
networks under non-ideal hardware where is linear affected by impairment levels.
However, no work related optimal throughput has considered the application of one-
way FD relaying in RF energy harvesting systems.
Therefore, in this paper, we analyze the outage probability of full-duplex relaying
with novel ability of energy harvesting and information transfer. Based on the analyti-
cal expressions, the optimal throughput and energy harvesting time are studied.
The remainder of this paper is organized as follows. Section II describes the system
model of the EH enabled FD two-way relaying network. Section III, the outage prob-
ability and throughput analysis. Simulation results are presented in section IV. Final-
ly, conclusion of section V is drawn in this paper.

3
2 System Model
Let us consider a wireless dual-hop relay network with AF protocol system illustrated
in Fig. 1, in which the destination node can be received at long distance thanks to
relay node. The system consisting of three nodes, source node is denoted by
S
and
destination node is denoted by
D
and one relay node
R
. Each node has two antennas,
one of them is responsible for signal transmission and other is responsible for signal
reception. The cooperative relay is assumed to be an energy constrained device so that
it must harvest energy from the source, and use that energy to amplify and forward
the source information to the destination node. We assume that the link between two
sources doesn’t exist due to the deep shadowing effect.
Fig.1. System model of one way full duplex relaying.
The interference cancellation mechanism is adopted to mitigate the self-interference.
As the self-interference can not be eliminated completely, certain amount of self-
interference remains. The residual self-interference channel at
R
is denoted by

R
h
. Let
, 1, 2
j
d j  denote the distance between
S R
link and
R D
link respectively and
, 1, 2
j
h j denote the channel coefficients between
S R
link and
R D
link respec-
tively.
The scheme used in this investigation is the Time Switching-based Relaying (TSR)
protocol as derived in [2]. The main parameters of protocol are expressed in Fig. 2.
Fig.2. Illustration of the parameters of TSR protocol.

Based on the TSR protocol proposed in [2], the communication process is divided
into two phases. In the first phase, the energy transfer from the source to the relay
with a duration of
, (0 1)
T
 
 
and the second phase, the remaining time,
 
1
T

is used to transmit information, in which

is time switching coefficient and
T
is time for the considered signal frame.
Fig.3. One way relaying network for simultaneous wireless information and power transfer
During the energy harvesting phase, the received signal at the relay as
1
1
S
R S R
m
P
y h x n
d
 
(1)
where
S
P
is the source transmission power, which is the same in the two sources,
R
n
is
the additive white Gaussian noise at
R
with zero-mean and variance of
2
n

.
Regarding wireless received power, the harvested energy at the relay is given by
[2]
2
1
1
s
hm
P h
E T d

 (2)
where
m
is the path loss exponent,

is the energy conversion efficiency,
1 2
,h h
are
the channel coefficients between source-relay link and relay-destination link respec-
tively.
In the information transfer phase, assume that the source node transmits respective
signal
S
x
to
R
and
R
re-transmits signal
r
x
to the destination node.
, ,
j
x j S R
.
They have unit energy and zero–mean, i.e, 2
1
j
E x
 

 
  and
0
j
E x
 

  . Therefore,
the received signal at the relay under self-interference source is rewritten as

1
1
SR
R S R R
m
P
y x h h x n
d
  
(3)

5
where

R
h
is the residual self-interference factor at
R
.
We suppose
R
receives
R
y
and in the next timeslot,
R
uses the harvested energy
to amplify
R
y
. Hence the magnification of the prior received signal,
R
x
, is
R R R
x G P y
 (4)
where
G
is the amplification factor of
R
.
Based on AF relaying scheme at
R
, according to [8] the amplification factor is giv-
en by

2
2
1 2
1
1
SR
R n
m
P
d
G h P h

   (5)
It is worth noting that harvested power then help operation for the next hop trans-
mission ,
R
P
is given by
 
2
1
1
1
h
R S
m
h
E
P P
T
d


 
 (6)
where

is defined as
1




.
Next, we obtain the received signal at destination as
2
2
D R D
m
h
y x n
d
 
(7)
where
d
n
is Gaussian noise at destination node.
Substituting (4), (6) into (7), we calculate the received signal as
 

1
2 2 2
2 1 2 2
SR
D R S R R R R D
m m m m
signal RSI noise
h P
h h h
y G P x G P h x G P n n
d d d d

   
  
(8)
In the above equations, the instantaneous received SINR at
j
S
through
R
is deter-
mined as
 
   
2
OW
2 2
E signal
E noise E RSI


(9)
By simple replacement, we obtain new formula as



2 2
1 2
2
1 2
2 2
2
2
1 2
2
2
1
S R
m m R
R
n S R
n
m
m
R
R
P h P h
d d P h
P h P h
d
P h d



 
(10)
We assume that the channel gains
2 2
1 2
,
h h
are independent and identically distri-
buted (i.i.d.) exponential.
3 Outage Probability and Throughput Analysis
In this section, we analyze the outage probability of full-duplex one-way relaying
with energy harvesting and information transfer. Based on that analytical expressions,
the throughput of scheme is derived and the optimal amount of time for harvesting
energy

is also achieved.
3.1 Outage probability analysis
The outage probability of FD relaying network is calculated as
 
Pr
out
P Z

  (11)
where
R
is target rate and
2 1
R
Z 
.
Proposition 1: the outage probability of the energy harvesting enabled two way full
duplex relay is derived as


   
2 2
1 2
2
1 2
2 2
2
21 2
2
2
1
2 2
2 2
1 2 1 2
1/
1
0
Pr
1
1 2 2
S R
m m r
R
out
n S R
n
m
m
R
R
m m m m
n n
y
n n
Z
r
s d S S s d S S r
P h P h
d d P h
P Z
P h P h
d
P h d
d d Z y d d Z y
K e dy
P P Zy P P Zy



 
 
 
      

 
 
 
 
 
 
 
 
 
 
 
 
   
 
 
   
 
   
    
 
 
 
 

(12)
where
, ,
s d r
  
are the mean value of the exponential random variables

1 2,
, , R
h h h
,
respectively and
 
1
K x
is Bessel function defined as (8.423.1) in [11]
Proof:

7
We denote
2 2
1 2
x h h
and

2
R
y h
then we have:
2
2
1 2
1
Pr ,
1
1,
m m n
n
S S
out
d d Z y
x y
P P Zy Z
P
y
Z


 

 
 

 
 
 
 
 
 

 
 
 












(13)
Interestingly, the cumulative distribution function of
x
is calculated by
   
 
1
Pr 1 2 / 2 /
x s d s d
F a x a a K a
   
    (14)
and
y
can be modeled with probability distribution function
   
 
/
1/ b
r
y r
f b e



then the Proposition 1 is achieved after some simple manipulations.
3.2 Optimal throughput analysis
In the Proposition 1, the outage probability at the scheme, when the relay harvests
energy from the source signal and uses that power to amplify and forward the source
signal to the destination is a function of the energy harvesting time α, and exchange
when α increase from 0 to 1. In the delay-limited transmission protocol, the transmitter
is communicating at a fix transmission rate R bits/sec/Hz is and
 
1
T

 is the effec-
tive communication time . Therefore, the throughput of system is obtain as
 
 
1
1out
T
P R
T



  (15)
Unfortunately, it is difficult to derive optimal throughput mathematically but we
can obtain the optimal value by simulation as presented in the next section.
4 NUMERICAL RESULTS
In this section, we use the derived analytical results to provide the outage probabili-
ty, optimal throughput, optimal energy harvesting time. We set the source transmis-
sion rate
 
3, 4, 5 /
R bps Hz
, and hence the outage SINR threshold is given by
2 1
R
Z 
. The energy harvesting efficiency is set to be
1


, the path loss exponent

is set to be
3
m

. For simplicity, we set the distance 1 2
1
d d
 
. Also, we set
1; 0.1
s d r
  
   .
It can be seen from Fig. 4,the outage probability of different scenarios of time allo-
cation is

. The outage probability is 1 when
0


,
1


and so-called the worst
performance of the system. The outage is minimum at approximate
0.75, 3
R

 
.
As we can observe, the analysis curves provide a strictly agreement with simulation
curves.
As your observation, Fig. 5 examines the impact of energy harvesting time α on the
optimal throughput of systems. The throughput is maximum at approximate
0.36, 4
R

 
, and
1.45


can be called the optimal value. The throughput in-
creases as

increases from 0 to optimal value

, however it starts decreasing as

increases over its optimal value. This is because for the values of

smaller than the
optimal

, there is less time for information transmission. Consequently, less time
for forward the signal and smaller values of throughput are observed at the destination
node due to outage probability increases. On the other hand, for the values of

greater than the optimal

, more time is wasted on energy harvesting and less time is
available for information transmission. As a result, smaller throughput results at the
destination node due to smaller value of
 
1


.
Fig.4.Outage probability of FD energy-aware relaying network
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

Outage probability
Analysis
Simulation
R=3, 4, 5

9
Fig.5. Optimal throughput of FD relaying
5 CONCLUSION
In this paper, we have proposed a full duplex relaying network with wireless energy
harvesting and information transfer protocol, where an energy constrained relay node
harvests energy from the received RF signal and uses that harvested energy to forward
the source signal to the other sources. In order to determine the achievable throughput,
analytical expressions for the outage probability and the optimal value of energy har-
vesting time in TSR protocol can be found by simulation.
REFERENCES
[1] L. r. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE Int. Symp. Inf.
Theory (ISIT), pp. 1612-1616, July 2008.
[2] A. A. Nasir, X. Zhou, S. Durrani, and R. Kennedy, “Relaying protocols for wireless energy harvesting
and information processing,” IEEE Trans. Wireless Commun., vol. 12, no. 7, pp. 3622–3636, Jul.
2013
[3] P. Popovski and H. Yomo, “Bi-directional amplification of throughput in a wireless multi-hop
network,” in Proc. of Vehicular Technology Conference, vol. 2, Melbourne, Autralia, May 7-10,
2006, pp. 588–593.
[4] R. H. Louie, Y. Li, and B. Vucetic, “Practical physical layer network coding for two-way relay
channels: performance analysis and comparison,” IEEE Transactions on Wireless Communications,
vol. 9, no. 2, pp.764–777, 2010.
[5] B. Rankov and A. Wittneben, “Achievable rate regions for the two-way relay channel” in Proc. of
IEEE International Symposium on Information Theory, Seattle, WA, USA, 2006, pp. 1668–1672.
[6] T. Riihonen, S. Werner, R. Wichman, “Comparison of Full-Duplex and Half-Duplex Modes with a
Fixed Amplify-and-Forward Relay”, IEEE 2009 IEEE Wireless Communications and Networking
Conference - Budapest, Hungary, 2009.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2

Throughput (bits/s /Hz)
Analysis
Simulation
R=5, 3, 4

[7] Jingrui Yang, Xuefang Liu, Qinghai Yang, “Power Allocation of Two-Way Full-Duplex AF Relay
under Residual Self-Interference”, IEEE 2014 14th International Symposium on Communications and
Information Technologies (ISCIT) - Incheon, South Korea.
[8] T. Kwon, S. Lim, S. Choi, and D. Hong, “Optimal duplex mode for DF relay in terms of the outage
probability,”IEEE Trans. Veh. Technol., vol. 59, no. 7, pp. 3628–3634, Sep. 2010.
[9] C. Zhong, H. A. Suraweera, G. Zheng, I. Krikidis, “Wireless Information and Power Transfer With
Full Duplex Relaying”, IEEE Transactions on Communications, Vol. 62, No. 10, 2014.
[10] Dinh-Thuan Do, “Power Switching Protocol for Two-way Relaying Network under Hardware
Impairments”, RadioEngineering Journal, Vol. 24, No. 3, 2015.
[11] H. A. David, Order Statistics. New York, NY, USA: Wiley, 1970.
[12] C. Zhong, H. A. Suraweera, G. Zheng, I. Krikidis, “Relay Control for Full-Duplex Relaying with
Wireless Information and Energy Transfer”, IEEE Transactions on Communications, Vol. 62, No. 10,
2014.