Mạng chuyển tiếp thu thập năng lượng không dây trong điều kiện ước lượng kênh không hoàn hảo: Phân tích thông lượng

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

76

WIRELESS ENERGY HARVESTING RELAYING NETWORKS

UNDER IMPERFECT CSI: THROUGHPUT ANALYSIS

MẠNG CHUYỂN TIẾP THU THẬP NĂNG LƯỢNG KHÔNG DÂY

TRONG ĐIỀU KIỆN ƯỚC LƯỢNG KÊNH KHÔNG HOÀN HẢO:

PHÂN TÍCH THÔNG LƯỢNG

Dinh Viet Hoa, Nguyen Thai Anh, Do Dinh Thuan

Ho Chi Minh City university of Technology and Education

Received 16/5/2016, Peer reviewed 19/6/2016, Accepted for publication 5/12/2016

ABSTRACT

The purpose of this research aims to investigate an amplify-and-forward-based (AF)

energy harvesting (EH) system with imperfect channel state information (CSI), where two-

end-nodes and one relay are operated in half-duplex mode. Power splitting-based relaying

(PSR) protocol is used to transmit information from source to destination by the energy

harvesting enabled relay. The authors propose that the initial power contained in the battery

is used to run the relay. After that, to transmit signal the relay has to harvest energy from the

attained RF signals. The exact integral and approximate closed-form expressions for the

outage probability and throughput of this system have been derived. The validity of analytical

results is verified by Monte Carlo simulations.

Keywords: Energy harvesting; imperfect channel state information (CSI); PSR protocol; half-

duplex; amplify-and-forward-based.

TÓM TẮT

Trong bài báo này, tác giả nghiên cứu một hệ thống thu thập năng lượng (EH) dựa trên

khuếch đại và chuyển tiếp (AF) trong điều kiện ước lượng kênh không hoàn hảo, nơi mà 2 nút

đầu cuối và một nút chuyển tiếp được hoạt động ở chế độ bán song công. Giao thức PSR

được sử dụng để truyền thông tin và năng lượng từ nguồn đến đích bằng nút chuyển tiếp. Cụ

thể, để truyền tín hiệu đến đích, nút chuyển tiếp phải thu thập năng lượng từ tín hiệu RF thu

được và dùng chính năng lượng đó để xử lý thông tin chuyển tiếp. Bài báo đưa ra công thức

tích phân chính xác và biểu thức gần đúng của xác suất dừng, thông lượng của hệ thống này.

Giá trị của kết quả phân tích được kiểm chứng bởi mô phỏng Monte Carlo.

Từ khóa: Thu thập năng lượng; ước lượng kênh không hoàn hảo; giao thức PSR; bán song

công; khuếch đại và chuyển tiếp.

1. INTRODUCTION

In conventional sensor networks and disadvantages such as inconveniences in the

cellular networks, wireless devices are operation of a sensor network with thousands

normally powered by replaceable or of distributed sensor nodes, danger to the

rechargeable batteries, which have the technicians when the devices are located in

limited life-time. Replacing or recharging the toxic environments, and even impossibility in

batteries periodically leads to several the case of the medical sensors implanted

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

77

inside human bodies. In such situations, system using PSR protocol [7] with

energy harvesting (EH) is a potential solution

to provide a perpetual power supply and also

is an attractive approach to prolong the

wireless networks’ lifetime [1,2]. Typical

sources for energy harvesting are solar,

constraint of imperfect CSI [8,9] is proposed.

The main contributions of this paper are

summarized as follows:



We use a protocol termed ‘‘power

switching based relaying’’ for the EH-

based system as depicted in Fig. 1,

where the relay node receives wireless

energy from source node.

vibration

and

wind.

Recently,

electromagnetic (EM) power in the radio

signals has been proposed as a new viable

source for EH, supported by the advantage

that the wireless signals can carry both

energy as well as information [3]. This is an

attractive direction for many researchers.

The

closed-form

of

system’s

performance, in terms of outage

probability, throughput is derived.

On the other hand, there are a number of

applications of relay stations (RS) to improve

the performances of wireless networks. The

application of relays was first standardized in

IEEE 802.16j [4]. For example, the RS have

also been considered in the LTE-advanced

systems to reach target throughput and

coverage requirements. Moreover, relaying

strategy is a promising technique to deal with

fading channel and path-loss in wireless

networks. The extensive studies in the

In the remainder of this study, the paper

is arranged as follows. Section 2 presents the

depiction of suggested EH relaying system.

Then Section 3 will analysis outage

probability and throughput of proposed

system. Next, in Section 4 some numerical

examples are picked and analyzed. We will

also give conclusions in this section.

T

EH at R (β)

IT: R to D

IT: S to R (1-β)

literature

showed

that

the

T/2

transmission/reception cooperation between

nodes of a network provides significant

Fig.1 Power switching based relaying protocol.

benefits including bandwidth and energy 2. SYSTEM MODEL

efficiencies and reliability. In the studies

presented in [4–6], RS operate in a half-

2.1. Channel model

We consider system performance under

duplex (HD) mode due to the non-trivial

implementation problems related to

impacts of Imperfect Channel State

Information (CSI) estimation model. In

particular, all the channels are assumed to be

block fading, i.e., the channel remains

transmitting and receiving in the same

frequency band and during the same time

slot. Since a half-duplex relay can forward a

message from source to destination over two

time slots, it makes an inefficient use of the

radio channel resource.

constant over

a

block but changes

independently from one block to another. It

is assumed that the channel from S to R and

h t

R to D has the channel coefficient

and

 

However, most of previous works

assume that CSI is well known at receiver.

This assumption is not true in real practice

g t

 

, respectively. They are zero-mean and

variance.We model the channel h, g as the

and hence in this work, an AF-based EH sum of the channel estimate h, g and the

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

78

We propose that the initial power contained

in the battery is used to run to initial the

relay. After that, to transmit signal the relay

has to harvest energy from attained RF

signals. The transferring channel from the

source to relay and then to destination are

respectively assigned as h and g. The factors

of complicated channel of A and B points are

channel estimation error

and  _g

_h

respectively, as in [8].

h t  h t   t ,

 

_h 

(1)

g t  g t   t .

    _g 

2.2 Relay model

denoted by h_ABCN 0,d^with α is path

We make the following assumptions

regarding relay node:





AB

loss exponent. Information is transmitted



The relay node has no other embedded

energy supply and thus needs to first

harvestenergy from source node for

information processing. In practice,

harvested power canbe stored in batteries

and then are supplied asa source of

transmitting power in order toforward the

source information to the destination node.

mutually from

in the TWR protocol. Due to implementing

request-to-send/clear-to-send (RTS/CTS)

s

₁point to s₂point by the relay

based channel guess program, relaying

system can be supported by estimating CSI.

2.4 Signal model

The signal received at the input of the

energy harvesting receiver is expressed as:



The receiver structure at relay node

isdesigned for energy havesting.

p_s

y t 

_r 

h  h s t  n^r



  

(2)

s

a

d₁^m

2.3 Energy harvesting model

Fig.2 shows that we examine an AF-

based energy harvesting system that contains

two-end-nodes and one relay respectively

designated by S, D, and R. In usual relaying

network, with half-duplex transmission,

source-nodes S transfers their signal to relay

nodes in the first-time slot, then the signal will

be amplified and forwarded to destination

node in the second time slot by the relay.

In the PSR protocol, received signal is

divided into two paths:  y_r(t) is sent to

the energy harvesting receiver and the

information receiver got the remaining signal

1  y (t)

strength,

. At the input of the

r

energy harvesting receiver, the signal is:

1

d₁^m

 y_r(t) 

 p_shs(t)   n_a^[r](t) [9].

g

h

S

R

D

Hence, the energy harvested in PSR

protocol is given by:

d₁

d₂

p h ² ²

Fig.2 System model.

_s

_h

T

2

E_h^PSR



(3)

Furthermore, we examine a one-way

linear relaying network which the normalized

d₁^m

r  d

d₂ d₁

d

distances are denoted by

,

.

where 0  1 denotes the energy

1

r

harvesting efficiency at the energy receiver

and it depends on the rectifier and the energy

harvesting circuitry.

We implement single antenna for the source

and destination while the AF relay has single

receive antenna and single transmit antenna.

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

79

Next, the energy of end-to-end signal is

Subtituting (5), (6) and (7) into (8), the

deployed in case of implementing non- end-to-end signal can be restored as (9).

oscillating relay. In that condition, all coming

 p

 p_s

signal and noise samples are separated

individually, and the power of transmitting

relay is illustrated by:

y t 

_d 

^shgs t 

_s 

d₁^md₂^m

(9)

 g s t  h s t    s t

_s 

 





h

g

h

g

s

 p h ² ²



1  d^m

E_h^PSR



n^[R]  g n^[D]

t

 

_s

_h





g

(4)

p_r







T 2

d₁^m

2

The SNR is show in (10) at the top of

next page.

Therefore, the received signal at the

input of the information receiver in the PSR

protocol is expressed as:

3. OUTAGE

PROBABILITY AND

THROUGHPUT

1  p





s

y t 

_r 

h  h s t  1 n^r

_a(5)



  

3.1 Outage probability

s

d₁^m

Hence, the outage probability of system

is defined as:

By utilizing attained energy, the relay

uses a relay gain S to magnify the obtained

signal. So the received signal at the relay is

computed by:

P  Pr SNR  



₀

(11)

out

Subtituting (10) into (11) and putting:

s t  y t S

_r  _r 

(6)

a _²_g

where S is amplifying parameter, and given

by (7).

d₁^m





b   ²

 ²

n^{[ R]}





h



1  P





S





p_rd₁^m

S 

d₁^m

1  p h ² ² d^m ²

c _²_g_²_h

_²_g_n²_{[ R]}





n^{[ R]}

_s

_h

1

1  P

(7)





S



1 



1  d^md^m ²

n^{[ D]}







1

2







2P

S

In (7), the approximation value can be

derived for high transmission power case.

The sampled attained signal at the end-node

Y  g ²

X  h ²

y t

_d 

can be calculated as:

The outage probability is determined as:

1

y t 

_d 

g   s t  n^[D]

t

 

_r 



_g

(8)

XY

d₂^m











P  Pr

 

^th

out

Xa Yb  c

n^[D](k)  n^d(k)n^d(k)

th





(12)

_thc ab





g

y



_thb

where

, where the range



a

c









1

_h

y a 





th

g



1

e^

e

^dy

d



from relay to end-node is denoted by

n^[D] n_a^d n_c^d

;

2

_h



_tha

is AWGN which the average is

 ² ² ²

Finally, apply (eq. 8.407.1) given in [10]

we obtained proposition 1 as (13).

zero and the variance is

.

n^[D]

n^[_a^D]

n_c^[D]

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

80

3.2 Throughput

The delay-limited transmission of

throughput is shown as:

1

  R(1 P )

(14)

out

2

4. NUMERICAL

DISCUSSION

RESULTS

AND

This section includes the comparison of

trial test results and analytical outcomes of

outage probability and throughput. To be

simple, it is proposed that the connection

channels of base station and practical energy

station are independent with each other

andsimilarly Rayleigh fading. It is supposed

that energy transmission at S, R, D are the

same. The unit of SNR is dB. The length

between S and R, R and D are equal to each

other. The authors set the source transmission

rate as R = 3 bps/Hz, energy harvesting

efficiency η = 1, source transmission P_s= 1

Joules/sec, path loss exponent m = 2.7 and

the outage SINR threshold is given by γ₀=

2^R-1; then make use of the notation δ_hand δ_g

in figure to denote the variances of the

channel estimation errors from S to R and R

to D, respectively.

Fig.4 Outage probability of proposed system in

different β.

Fig.5 Outage probability of proposed system in

different SNR.

Fig.6 Through put of proposed system in

different SNR

g ²h ²

SNR 





1  d^md^m ²

d₁^m

(10)





n^[D]

g ² ²

_n²_{[ R]} h ² ²_²_g_²_h

_n²_{[ R]}_²_g

1

2





h

g

1  p

 p_s









s





b

_g



_h

_tha

^th





1

4_th_h(c _thab)

4_th(c _thab)

P 1

e

K



¹







(13)

out

_h

_g

_g_h

Fig.5 shows the outage probability at increased at source node. In this experiment,

noise = 0.01; β = 0.03; δ_h= δ_g= 0, 0.01, 0.02, the impact of imperfect CSI noise on outage

0.03, 0.04, 0.05; 0 ≤ SNR ≤ 30. The system probability and throughput can also be seen

performance will be enhanced when SNR is in Fig.5 and Fig.6, respectively. It is noted

Journal of Technical EducationScience No.40 (1/2017)

Ho Chi Minh City University of Technology and Education

81

that Fig. 6 shows the throughput at noise = SNR variation of the fading channels, the

0.01; β = 0.03; δ_h= δ_g= 0.05, 0.04, 0.03, authors formulate the outage probability and

0.02, 0.01, 0; 0 ≤ SNR ≤ 30.

the throughput is evaluated for the best

performance at high SNR scenario in terms

of imperfect channel state information (CSI).

With such a practical CSI modeling, exact

approximation expression for the overall

outage probability with proper power

splitting fraction in energy harvesting to

obtain optimal throughput have been derived.

5. CONCLUSION

In this paper, the impact of imperfect

channel estimates on the overall performance

of a two-hop relay system that employs a

two-phase AF network over Rayleigh fading

has

been

investigated.

Specifically,

considering the imperfect estimation and

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Corresponding author:

Do DinhThuan

Ho Chi Minh City University of Technology and Education

Email: [email protected]n

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