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Proceedings of the Estonian Academy of Sciences,

2020, 69, 4, 368–381

https://doi.org/10.3176/proc.2020.4.06

Available online at www.eap.ee/proceedings

Nonlinear energy harvesting based power splitting relaying in fullduplex

AF and DF relaying networks: system performance analysis

Tran Tin Phua, DucVan Phanb, DuyHung Hac, Tan N. Nguyend*, Minh Trane,

and Miroslav Voznakc

a Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

b Faculty of Automobile Technology, Van Lang University, Ho Chi Minh City, Vietnam

c Faculty of Electrical Engineering and Computer Science, VSB Technical University of Ostrava, 17. listopadu 2172/15, Ostrava,

Czech Republic

d Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi

Minh City, Vietnam

e Optoelectronics Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City,

Vietnam

Received 3 July 2020, accepted 20 september 2020, available online 30 October 2020

© 2020 Authors. This is an Open Access article distributed under the terms and conditions of the Creative Commons Attribution

NonCommercial 4.0 International License (http://creativecommons.org/licenses/bync/4.0/).

Abstract. Wireless power transfer is considered as a novel solution for energy harvesting in wireless communication networks. In

this paper, the system performance of the nonlinear energy harvesting based power splitting relaying in the fullduplex relaying

sensor network is investigated. We considered the system model network with one source, one destination, and one relay node in

both the amplifyandforward and decodeandforward modes. The closedform expressions of the system outage (OP) are analysed

and derived for verifying system performance. Then, the correctness of the OP closedform expression is verified by using the Monte

Carlo simulation. Furthermore, the influence of the primary system parameters on the system OP is suggested and investigated. The

research results indicated that the simulation curves and the analytical curves overlapped, verifying the correctness of the analytical

expressions.

Key words: amplifyandforward, decodeandforward, outage probability, nonlinear energy harvesting, sensors network. 1bbreviations

and symbols

Abbreviations and symbols

AF Amplifyandforward

AWGN Additive white Gaussian noise

DF Decodeandforward

EH Energy harvesting

FD Fullduplex

IT Information transformation

NEH Nonlinear energy harvesting

OP Outage probability

PS Power splitting

RF Radiofrequency

RV Random variable

SINR Signal to interference noise ratio

SP Success probability

* Corresponding author, nguyennhattan@tdtu.edu.vn

COMMUNICATIONS

TECHNOLOGY

SWIPT Simultaneous wireless information and power transfer

ρ Power splitting factor, 0 < ρ < 1

η Energy conversion efficiency, 0 < η ≤ 1

𝑃𝑡ℎ Saturation threshold of the rechargeable power

𝛾𝑡ℎ Threshold of the system

𝛤• Incomplete gamma function

𝜆𝑆𝑅 Mean of |ℎ𝑆𝑅|2

𝜆𝑅𝐷 Mean of |ℎ𝑅𝐷|2

𝛺𝑅𝑅 Variance of |ℎ𝑅𝑅|2

𝛽 Amplification factor

𝑃𝑆 Transmit power of the source

𝑇 Total time of processing

ψ Ratio of energy Ps to variance N0

1. INTRODUCTION

In comparison with other energy harvesting (EH) methods, such as from the sun, heat, wind, motion, etc.,

radiofrequency (RF) EH can be considered as a novel solution because energy can transfer through the air

without a cable and both energy and information can be carried using the RF signal [1–4]. In wireless

communications this technique is a comfortable solution for batterylimited applications or under conditions

that are dangerous for operating devices. For this purpose, a novel technique called simultaneous wireless

information and power transfer (SWIPT) is proposed based on the fact that the RF signals can transfer

information and energy simultaneously. The SWIPT technique can help the energyconstrained nodes harvest

energy from other nodes or the surrounding environment and use this energy to transfer information to other

nodes [1–10]. Recently SWIPT has attracted significant attention in academia.

In [6] the fundamental tradeoff between the transporting and the information rate is presented and

investigated. Improving the efficiency of simultaneous information transmission and energy transferring by

using some fundamental tradeoffs in designing wireless multipleinput multipleoutput (MIMO) systems is

studied in [11]. In [12] the authors investigate a joint beamforming algorithm for a multiuser wireless

communication network system and compare these systems with conventional systems. In [13] a multiuser

multipleinput singleoutput broadcast SWIPT system is proposed and analysed.

The interference channel in SWIPT is carefully studied in [14–16]. In [14] a geodesic energy beamforming

scheme with channel state information (CSI) is proposed to reduce the feedback overhead in the

communication system. A novel approach for realizing SWIPT in a broadband system with orthogonal

frequency division multiplexing and transmit beamforming is proposed and investigated in [15]. In [16] the

optimal design for SWIPT in downlink multiuser orthogonal frequency division multiplexing systems where

the users harvest energy and decode information using the same signals received from a fixed access point

is studied.

A cooperative relaying communication network in both amplifyandforward (AF) and decodeand

forward (DF) modes is considered in [17–19]. In that network an energyconstrained relay node receives the

energy from the source node, and the information is transferred from the source node to the destination with

the help of a relay. Wireless powered communication and its potential applications and promising research

directions are studied in [20–24]. Moreover, in [25] the theoretical symbol error probability (SEP) of a

cooperative relaying system network is derived. In [26] a novel distributed spacetime block code (DSTBC)

scheme in multihop power line communication (PLC) networks is proposed. In [27] a simple adaptive

relaying protocol (ARP) for general relaying system networks is studied. From this review of literature, we

can state that the research direction in SWIPT is extremely hot and needs to be developed more and more.

In SWIPT the rectenna is considered as a critical component of the farfield RF harvesting circuits because

of the conversion of the input RF signal to DC voltage by the antenna and the rectifier. The nonlinearity of

harvested power as a function of input power is also corroborated by the fact that the conversion efficiency

in the literature on microwave circuits is always referenced to a specific level of input power [28–30].

To the best of our knowledge, there are very few recent SWIPT researches that study nonlinear RF

harvesting models. In this paper the system performance analysis of nonlinear energy harvesting (NEH)

based power splitting (PS) relaying in fullduplex (FD) relaying networks is proposed and investigated. In

this research we considered the system network with one source (S) and one destination (D) node, which

communicate by helping the intermediate relay (R) node in both AF and DF modes. The closedform

expressions of the system outage probability (OP) are analysed and derived for both AF and DF modes. Then,

the correctness of the analytical OP is verified by using the Monte Carlo simulation. Furthermore, the

influence of the primary system parameters on the system OP is investigated. The research results indicated

that the simulation curves and the analytical curves overlapped, verifying the correctness of the analytical

expressions. Here are the main contributions of this research:

●NEH based PS relaying in the FD relaying sensor network is presented.

●The closed form of the system OP in both the AF and the DF mode is derived.

●The Monte Carlo simulation is conducted to verify the correctness of the results, and the effect of the

main system parameters on the system OP is analysed.

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 369

The structure of the rest of this paper is as follows. Section 2 presents the system model, the energy

harvesting, and information transmission phases. Section 3 presents the OP analysis for deriving the closed

form of the system OP. Section 4 proposes some numerical results and discussions. Finally, some conclusions

are drawn in Section 5.

2. SYSTEM MODEL

The NEH based PS relaying in the FD relaying sensor network is proposed in Fig. 1. In addition, the loopback

interference is considered at R. In this system model, all links are Rayleigh block fading channels.

The EH and information transformation (IT) for the proposed model system are illustrated in Fig. 2. The

time of information transmission and energy transferring is denoted as T. In the interval T, the relay R harvests

energy ρPs from the source node S, and the source uses the energy (1 – ρ)Ps for information transmission to

the relay R and the destination D (here ρ is the power splitting factor) [31–34].

2.1. Nonlinear energy harvesting phase

In the EH phase, the received signal at the relay can be given as

In most literature, the total harvested energy at the relay is formulated as a linear model [31–34]. In this

paper, the nonlinear transformation model proposed in reference [35–37] is used. The average transmit power

at the relay can be obtained as

where Ptℎ is the saturation threshold of the rechargeable power of the hardware circuit.

2.2. Information transmission phase

The received signal at the relay R in the information transmission phase is

Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

370

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Fig. 1. System model. S denotes source, D is the destination and

R stands for relay; hSR and hRD are channel coefficients, and hRR is

the loopback interference coefficient.

6

6

rsSRsr

yPhxn

6 6

Fig. 2. Energy harvesting and information processing.

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rsSRsrRRrr

yPhxPhxn

6 6

In this phase, the received signal at the destination can be formulated as

where hRD is the channel coefficient and nd is the zero mean AWGN with variance N0.

2.2.1. AF mode

In the AF protocol, the relay amplification factor 𝛽 is set as

Please note that for convenience in this analysis the residual selfinterference at the relay nodes is modelled

as AWGN with zero mean and variance ΩRR [33,38].

Hence, the amplification factor can be rewritten as

By substituting (5) into (4) and then combining with (3), we have that

The end to end signal to the interference noise ratio (SINR) from (7) can be obtained as

After doing some algebra, equation (8) can be reformulated as

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 371

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44

44

45

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32

AF

rs SR RD

rRD RR rRD

rs SR RD

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signal

SINR

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Ph Ph N N

PP h h

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2.2.2. DF mode

In the DF mode, the SINR at the relay R from (3) can be given as

From (4), the SINR at the destination D can be expressed as

3. SYSTEM PERFORMANCE

3.1. AF mode

In the AF mode the OP can be defined as

where SP

AF is the success probability (SP), which can be given as follows:

where 𝛾th is the threshold of the system.

By substituting (3) into (12), equation (12) can be rewritten as

where

Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

372

7

7

4

5

3sSR

R

rRR

Ph

SINR PN

27 135/7

7

7

4

5

2

rRD

D

Ph

SINR N

7133/7

)

AF AF

OP SP

,

*

*

)

)

sSR RD

AF AF th th

SR s

rRD RR RR

r

Ph h

SP SINR

hPN

Ph N

P

, ),

*

*

)

)

sSR RD

sSR RD RR RR

AF

th s SR th

Ph h

N

Ph h N

SP

Ph P

,

*

*)

)

)

sSR RD

SR s

th RD RR RR

th

th s SR th

Ph h

hPN

Ph N PP

P

Ph P

,)

+

(13)

*

*

)

)

)

sSR RD

sSR RD RR RR

th s SR th

Ph h

N

Ph h N

P

Ph P

, ),

We denote X = |hSR|2, Y = |hRD|2 and a1 =

ηρ

(1 –

ρ

) Ps,b1 =

η

2

ρ

2PsΩRR, c1 = (1–

ρ

) N0 + 𝜂

ρ

N0ΩRR, d =

so equation (14) can be reformulated as

Consider

(16)

where λRD is the mean value of the random variable (RV) |hRD|2.

If we choose the condition of the threshold a1 > γth b1 ↔ γth< then by substituting (16) into (15) P1

can be obtained as follows:

Substituting (18) into (17), we have

By applying equation (3.381,3) from the table of integrals [38], equation (20) can finally be obtained as

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 373

th

s

P

P

,

=>=>

++

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//

. - ,+ ,+

th th th

axY

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###

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d

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th

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a1

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We denote that a2 =

ηρ

(1–

ρ

)PsPth,b2 =

η

2

ρ

2P2

thQRR, c2 = (1–

ρ

)PsN0,e2 =

ηρ

PthN0QRR. Hence, equation (22)

can be reformulated as

Consider

By substituting (24) into (23), P2 can be obtained as

Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

374

'*'%*'!* !%$*P*

*

*

$#

$#

(

(

#

#

$

"

sSR RD

SR s

th RD RR RR

th

th s SR th

Ph h

hPN

Ph N

P

P

Ph P

* (*

=>>=

++ ++>

(22)

ƒx (x)dx. (23)

(24)

.

(25)

(26)

++

>

By substituting (21) and (28) into (13), the SP of the system can be obtained as

Finally, the OP of the system in the AF mode can be claimed as

3.2. DF mode

From equations (10) and (11), the end to end SINR of the DF mode can be given as

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 375

(27)

(28)

(29)

(30)

By substituting (27) and (2)6 and applying equation (3.381,3) from the table of integrals [38], P2 can

finally be expressed as

Then we apply the Taylor series as follows:

(31)

The SP in the DF mode can be expressed as

We consider the term of equation (32) by substituting equation (2) and by denoting as above in the AF

where

In the AF mode we selected the condition . Hence, the condition (1–

ρ

)Ps–

ηρ

PsγthΩRR > 0

is satisfied.

If

the inequality will not hold. So, in this case, P3 = 0.

Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

376

.

.

.

th

RR

a

b

(34)

",

"!

*

'

th

th

th RR

N

P

!,P+,",,%%$,,

(32)

(33)

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**

''

th th

th

s s th RR th RR

NN

dP

PP

!,

"!

*

'

th

ssthRR

NXd

PP

,

(35)

%,

"!

*

'

th

s s th RR

N

PP

,

As it is difficult to find the closedform expression for P3 due to the integral exp for

any value of v1 and, v2 0, we will employ the Gaussian–Chebyshev quadrature.

First, we have to change the variable from equation (35) by denoting . Equation (35)

can be rewritten as

where

Apply the Gaussian–Chebyshev quadrature from [39–43]. Then equation (36) can be approximated as

where N is a parameter that determines the tradeoff between complexity and accuracy for the Gaussian–

Chebyshev quadrature based approximation and and

From equation (33), P4 is defined as

where .

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 377

"

m

m

v

x

&

%

$

"

!

('

vxdx

dd

xy

dd

Gy y

2

(36)

&

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(37)

,

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n

n

N

nn

dd

2

(38)

('

('

0

th th RR

s

PN

P

,

4. NUMERICAL RESULTS AND DISCUSSION

In this section, we present numerical results to demonstrate the system performance of the system network

proposed in the previous section. The correctness of the analytical analysis in the previous section is verified

by the Monte Carlo simulation as in [31–35].

In Fig. 3 we depict the OP as a function of ψ using η = 0.8, γth = 0.25 and ρ = 0.2 and 0.5. Here we vary

ψ from –15 DB to 20 dB for validating the correctness of the proposed system. We can observe in Fig. 3 that

the system OP shows a massive decrease with the rising of the ψ from –5 dB to 10 dB. At the beginning and

at the last values of the ψ, the system OP has a slight fall. Figure 4 illustrates the system OP versus the Pth

while the Pth increases from 0 dB to 15 dB. In Fig. 4 we set the primary system parameters as η = 0.8, γth =

0.25, ρ = 0.5, and ψ = 5 and 10 dB. As shown in Fig. 4, the system OP decreases significantly with the rising

of the power Pth. It can be observed that the higher the Pth in the system, the lower the system OP may become.

From Figs 3 and 4 we can see that the analytical curves and the simulation curves duplicate each other

for validating the analytical analysis in the above section. The system OP in case ρ = 0.2 with a high SNR in

Fig. 3 for the AF and DF modes can reach the value of 0.55, and the system OP with ρ = 0.5 with the AF and

DF modes can reach the value of 0.3. In the same way, when the power Pth rises to higher values, the system

OP in the case ψ = 5 can reach the value of 0.4 with the AF mode and 0.2 with the DF mode. However, in

the ψ = 10 case, the system OP can obtain the value of 0.2 for the AF mode and 0.1 for the DF mode.

Next, in Fig. 5, we depict the influence of the power splitting factor ρ on the system OP with ψ = 5 dB,

γth = 0.15, and η = 0.5 and 0.7. In Fig. 5, ρ increases from 0 to 1, and we considered both AF and DF modes.

As shown in Fig. 5, the system OP decreases considerably when ρ rises from 0 to 0.6, and after reaching the

optimal value, the system OP shows an immense increase when ρ rises to 1. The optimal value of the system

OP can be obtained with ρ from 0.5 to 0.7.

Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

378

Fig. 3. Outage probability (OP) versus the energy Ps to variance

N0 ratio ψ.

Fig. 4. Outage probability (OP) versus the saturation threshold

of the rechargeable power Pth.

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2

2

(' ('

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00

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N

SR SR

DF n

n

SR

RD th RD th

nSR

sn th

dd

OP N

d

NN

PG P

&%

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"!

2 1/2

(39)

('

00

" "

SR

RD th RD th

nSR

sn th

d

NN

PG P

&%

$#

"!

2

.

AF mode with ρ = 0.2

DF mode with ρ = 0.2

AF mode with ρ = 0.5

DF mode with ρ = 0.5

Monte Carlo simulation

AF mode with ψ = 5 dB

DF mode with ψ = 5 dB

AF mode with ψ = 10 dB

DF mode with ψ = 10 dB

Monte Carlo simulation

OP of system versus ψ with η = 0.8 and γth = 0.25 OP of system versus Pth with η = 0.8, ρ = 0.5, and γth = 0.25

Furthermore, we investigated the system OP as the function of the ΩRR as shown in Fig. 6. In Fig. 6 the

ΩRR increases from –10 dB to 2 dB, and the main system parameters are set as ψ = 5 dB, γth = 0.25, η = 0.8,

ρ = 0.5, and N0 = 1 dB and 5 dB. The results demonstrate that with the rising of the ΩRR the system OP of the

AF mode increases significantly, but that of the DF mode shows just a slight increase. Consequently, with a

rising ΩRR the system performance of the DF mode is better than of the AF mode. Finally, as illustrated in

Figs 5 and 6, the simulation results agree well with the analytical results.

Figure 7 examines the impact of the N0 on the system OP with η = 0.8, γth = 0.25, η = 0.8, ρ = 0.25, and

ΩRR = 1 dB and 5 dB. As shown in Fig. 7, the system OP of both AF and DF modes has a considerable increase

with the continuous rising of N0 from –10 dB to 5 dB. This is due to the fact that the more energy is used for

the harvesting phase, the higher the OP in the proposed system.

The system OP as the function of the energy efficiency η is illustrated in Fig. 8. Here the energy efficiency

η varies from 0 to 1, and the main system parameters are set as ψ = Pth = 5 dB, ρ = 0.5, and γth = 0.15 and

0.25. In contrast to Fig. 7, the system OP has a colossal decrease with the rising of the energy efficiency η.

This suggests that the more efficient energy use, the lower system OP can be obtained and the better system

T. T. Phu et al.: Non-linear energy harvesting based PS relaying 379

Fig. 5. Outage probability (OP) versus the powersplitting

factor ρ.

Fig. 6. Outage probability (OP) versus the variance of |hRR|2

ΩRR.

Fig. 7. Outage probability (OP) versus the AWGN variance N0. Fig. 8. Ooutage probability (OP) versus the energy conversion

efficiency η.

AF mode with ΩRR = 1 dB

DF mode with ΩRR = 1 dB

AF mode with ΩRR = 5 dB

DF mode with ΩRR = 5 dB

Monte Carlo simulation

AF mode with γth = 0.15

DF mode with γth = 0.15

AF mode with γth = 0.25

DF mode with γth = 0.25

Monte Carlo simulation

AF mode with η = 0.5

DF mode with η = 0.5

AF mode with η = 0.7

DF mode with η = 0.7

Monte Carlo simulation

AF mode with N0 = 1 dB

DF mode with N0 = 1 dB

AF mode with N0 = 5 dB

DF mode with N0 = 5 dB

Monte Carlo simulation

OP of system versus ρ with ψ = 5dB, Pth= 10 dB and γth = 0.15 OP of system versus ΩRR with η = 0.8, ρ = 10.5 and γth = 0.25

OP of system versus η with ρ = 0.5, ρ = 10.5 and ψ = Pth= 5dBOP of system versus AWGN N0 with η = 0.8, ρ = 0.25 and γth = 0.25

performance is achieved. As shown in Figs 7 and 8, the simulation curves overlap the analytical curves and

thus verify the analytical expressions in the previous section.

5. CONCLUSIONS

In this paper, the system performance analysis of NEH based PS relaying in the FD relaying network is proposed

and investigated. The closedform expressions of the system OP are analysed and derived for both AF and DF

modes. Then, the correctness of the analytical OP is verified by using the Monte Carlo simulation. Furthermore,

the influence of the primary system parameters on the system OP is investigated. The research results showed

that the simulation curves and the analytical curves overlapped, verifying the correctness of the analytical

expressions. This paper can be considered as a novel recommendation for EH communication relaying networks.

ACKNOWLEDGEMENTS

This research was supported by the Industrial University of Ho Chi Minh City (IUH), Vietnam, under grant

No. 72/HDDHCN and VSB Technical Univesity of Ostrava, Chech Republic, grant SGS, registration No.

SP2020/65. The publication costs of this article were partially covered by the Estonian Academy of Sciences.

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Proceedings of the Estonian Academy of Sciences, 2020, 69, 4, 368–381

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