PerformanceAnalysisinDFEnergyHarvestingFull-Duplex

Research ArticlePerformance Analysis in DF Energy Harvesting Full-DuplexRelaying Network with MRC and SC at the Receiver underImpact of Eavesdropper

Phu Tran Tin 1 Van-Duc Phan 2 Dong Si Thien Chau 3 Tan N Nguyen 4

and Phu X Nguyen 5

1Faculty of Electronics Technology Industrial University of Ho Chi Minh City Ho Chi Minh City Vietnam2Faculty of Automobile Technology Van Lang University Ho Chi Minh City Vietnam3Modeling Evolutionary Algorithms Simulation and Artificial Intelligence Faculty of Electrical amp Electronics EngineeringTon Duc (ang University Ho Chi Minh City Vietnam4Wireless Communications Research Group Faculty of Electrical and Electronics Engineering Ton Duc (ang UniversityHo Chi Minh City Vietnam5Department of Computer Fundamentals FPT University Ho Chi Minh City Vietnam

Correspondence should be addressed to Dong Si ien Chau dongsithienchautdtueduvn

Received 12 January 2021 Revised 2 April 2021 Accepted 19 June 2021 Published 28 June 2021

Academic Editor Jit S Mandeep

Copyright copy 2021 Phu Tran Tin et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

is paper investigates the decode-and-forward (DF) full-duplex (FD) relaying system under the presence of an eavesdropperMoreover the relay node is able to harvest energy from a transmitter and then it uses the harvested energy for conveyinginformation to the receiver Besides both two-hop and direct relaying links are taking into consideration In the mathematicalanalysis we derived the exact expressions for intercept probability and outage probability (OP) by applying maximal ratiocombining (MRC) and selection combining (SC) techniques at the receiver Next the Monte Carlo simulation is performed tovalidate themathematical analysise results show that the simulation curves match themathematic expressions which confirmsthe analysis section

1 Introduction

Radio frequency- (RF-) enabled wireless power transfer (WPT)has recently become a promising technique to overcome theenergy limitation for wireless communication networks [1ndash10]Moreover because RF signal is able to carry both energy andinformation one attractive direction is to transmit informationand energy simultaneously (SWIPT) jointly e SWIPT re-laying networks have been intensively studied in [11ndash16]Besides energy harvesting physical layer security for relaynetworks received great attention from researchers [17ndash22]Recent advances in self-interference cancellation (SIC)

techniques achieve high SI reduction erefore FD relayingcommunications become a promising solution to overcomethe spectrum scarcity of wireless systems [23ndash25]

In this paper we consider a new system model to in-vestigate the trade-off between physical layer security (PLS)and reliability for an energy-constrained FD relaying networkFurther the direct link between transmitter and receiver istaken into account to improve the total network performanceMoreover the maximal ratio combining (MRC) and selectioncombining (SC) protocols are exploited at the eavesdropperand destination to enhance their received rate e researchcontributions are summarized as follows

HindawiJournal of Electrical and Computer EngineeringVolume 2021 Article ID 5547658 9 pageshttpsdoiorg10115520215547658

(i) We present an FD- and SWIPT-assisted relayingnetwork in decode-and-forward (DF) under thepresence of a direct link Particularly an eavesdropperis able to overhear the information transmission fromsource to destination via a relay Moreover an FD-enabled relay node is able to get energy from atransmitter and use it to transfer signals to the areceiver Notably the relay node can simultaneouslyreceive information from the source and transmit it tothe destination using the FD technique

(ii) We derive closed-form expressions of interceptprobability (IP) at the eavesdropper E and outageprobability (OP) at the destination D in maximalratio combining (MRC) and selection combining(SC) techniques

(iii) e correctness of the developed analysis is vali-dated through the Monte Carlo simulation On onehand we investigate the security perspective interms of intercept probability On the other handsystem reliability is also studied through outageprobability Consequently a trade-off between IPand OP can provide many insightful and usefulperspectives for system designers

2 System Model

In Figure 1 we consider a relaying network where a relay Raids in conveying data from a transmitter S to a receiver D inthe presence of one eavesdropper E In particular aneavesdropper is trying to get the information from S and Rby applying maximal ratio combining (MRC) and selectioncombining (SC) techniques In Figure 2 the relay R canharvest energy from the source during αT In the remainingtime (1 minus α)T the information process is executed

We assume that the channel between two users followsblock Rayleigh fading where channel coefficients are un-changed during a time frame and change independentlyacross time frames Moreover let us denote hXY forXY isin SRRDRR SDRE SE as the channel coefficient ofthe link between nodes X and Y Because the channels areRayleigh distribution the channel gains such as |hRD|2 and|hSD|2 are exponential random variables (RVs) whose cu-mulative distribution function (CDF) and probabilitydensity function (PDF) are respectively represented as

FX(x) 1 minus exp(minusλx)

fX(x) zFX(x)

zx λ exp(minusλx)

(1)

where λ is rate parameter of exponential distributione received signal at the relay can be expressed as

yR hSRxS + hRRxR + nR (2)

where xS is the energy symbol and E |xS|21113966 1113967 PS xR is theloopback interference due to full-duplex relaying and sat-isfies E |xR|21113966 1113967 PR where Ε middot denotes the expectationoperation nR denotes the zero mean additive white Gaussiannoise (AWGN) with variance N0

At the first phase the harvested energy at the relay can becomputed by

ER ηαTPS hSR1113868111386811138681113868

11138681113868111386811138682 (3)

where 0lt ηle 1 denotes the energy conversion efficiencyFrom (3) the average transmit power of the relay node

can be obtained as

PR ER

(1 minus α)TηαPS hSR

111386811138681113868111386811138681113868111386811138682

(1 minus α) κPS hSR

111386811138681113868111386811138681113868111386811138682 (4)

where κ ηα1 minus α

Next in the second phase the eavesdropper E mayintercept signals from both relay R and sourceS Nevertheless source S also generates artificial noise 1113957xS toprevent E from overhearing the source informationMoreover since the relay R and destination D are legitimateusers they are assumed to know the artificial noise createdby S Consequently they can cancel the artificial noise at thereceiver circuiterefore the received signal at E from relayR and source S can be respectively expressed as

yIE hRExR + n

IE y

IIE hSExS + hSE1113957xS + n

IIE (5)

where nE EIn nII

E is the AWGN with variance N0Since we adopt the decode-and-forward (DF) protocol the

signal to interference noise ratios (SINR) at the eavesdropper inthe second phase from (5) are respectively given by

cIE

hRE1113868111386811138681113868

11138681113868111386811138682PR

N0 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682 c

IIE Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1 (6)

where Ψ PsN0

hRD

hRD

E

D

R

S

Residual self-interference

hSR

hRR

hREhSE

Wiretap links Information flowEnergy flow

Figure 1 System model

T

αT (1 ndash α) T

Energy harverting at RInformation transmission

S R DS D

Figure 2 IT and EH processes

2 Journal of Electrical and Computer Engineering

As mentioned in the above discussion the destination Dcan cancel the artificial noise from source S Consequentlythe received signal at the destination from relay R and sourceS during the second phase can be expressed as

yID hRDxR + n

ID y

IID hSDxS + n

IID (7)

where nD nID nII

D is the AWGN with variance N0

3 Intercept Probability (IP) Analysis

Destination D will be intercepted if E can successfullywiretap signal that is cE ge cth where cth 2R minus 1 and R isthe target rate

erefore the IP of the system can be expressed as

IP Pr cE ge cth( 1113857 (8)

31 Instantaneous End-to-End SNR at E Using the MRCTechnique In this case the end-to-end SNR at E from (6)can be given by

cMRCE c

IE + c

IIE κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1 (9)

en the IP in (7) can be rewritten as

IPMRC Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1ge cth

⎛⎝ ⎞⎠

Pr X + Yge cth( 1113857 1 minus 1113946

cth

0

FX cth minus y( 1113857 times fY(y)dy

(10)

where X κΨ|hSR|2|hRE|2 Y Ψ|hSE|2Ψ|hSE|2 + 1

In order to find the probability in (10) we have to findthe CDF of X and PDF of Y So the CDF of X can becalculated by

FX(x) Pr(Xltx) Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682 ltx1113872 1113873

Pr hSR1113868111386811138681113868

11138681113868111386811138682 lt

x

κΨ hRE1113868111386811138681113868

11138681113868111386811138682

⎛⎝ ⎞⎠ 1113946

infin

0

FhSR| |

2x

κΨy| hRE

111386811138681113868111386811138681113868111386811138682

y1113888 1113889 times fhRE| |

2(y)dy

1 minus 1113946

infin

0

λRE exp minusλSRx

κΨyminus λREy1113888 1113889dy

(11)

By applying (Eq 33241 [26]) (11) can be obtained by

FX(x) 1 minus 2

λSRλREx

κΨ

1113971

times K1 2

λSRλREx

κΨ

1113971

⎛⎝ ⎞⎠ (12)

Next the CDF of Y can be formulated as

FY(y) Pr(Ylty) PrΨ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1lty⎛⎝ ⎞⎠

Pr hSE1113868111386811138681113868

11138681113868111386811138682 lt

y

Ψ(1 minus y)1113888 1113889 1 minus exp minus

λSEy

Ψ(1 minus y)1113888 1113889with 0ltylt 1

(13)

e PDF of Y is given by

fY(y) zFy(y)

zyλSEΨ

timesexp minusλSEyΨ(1 minus y)( 1113857

(1 minus y)2 (14)

Applying (12) and (14) the IP in this case can beclaimed by

IPMRC 1 minus 1113946

1

0

1 minus 2λSRλRE cth minus y( 1113857

κΨ

1113970

times K1 2

λSRλRE cth minus y( 1113857

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

timesλSEΨ


(1 minus y)2 dy

(15)

Journal of Electrical and Computer Engineering 3

32 Instantaneous End-to-End SNR at E Using the SCTechnique In this case the end-to-end SNR at E can begiven by

cSCE max c

IE c

IIE1113872 1113873 max κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1⎛⎝ ⎞⎠

max(X Y)

(16)

en the IP can be expressed as

IPSC Pr cSCE ge cth1113872 1113873 Pr max(X Y)ge cth( 1113857

1 minus Pr Xlt cth( 1113857Pr Ylt cth( 1113857(17)

By applying (12) and (13) the expression of IPSC can beexpressed as

IPSC 1 minus 1 minus exp minusλSEcth

Ψ 1 minus cth( 11138571113888 11138891113896 1113897 times 1 minus 2

λSRλREcth

κΨ

1113971

times K1 2

λSRλREcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (18)

4 Outage Probability (OP) Analysis

e OP can be defined by

OP Pr cD lt cth( 1113857 (19)

41 Instantaneous End-to-End SNR at D Using the MRCTechnique From (2) and (7) outage probability of relay linkcan be computed at

OP1 Pr(source minus relay or relay minus destination is in outage)

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎛⎝ ⎞⎠

(20)

From (20) we can see that to successfully receive data atthe destination D the system needs to decode in the first andsecond hop

Equivalently we can represent the end-to-end SINR ofthe relay path by

T min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ (21)

By using MRC technique the received SINR at desti-nation can be given as

cMRCD min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ + Ψ hSD

111386811138681113868111386811138681113868111386811138682

T + Z

(22)

where Z Ψ|hSD|2e OP in this case can be expressed by

OPMRC Pr T + Zlt cth( 1113857 1113946

infin

0

FT cth minus z( 1113857 times fZ(z)dz

(23)

From (21) FT(t) can be calculated as

FT(t) Pr(Tlt t) Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt t⎛⎝ ⎞⎠

1 minus Pr 1κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873

1113980radicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradic1113981P1

Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873

1113980radicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradic1113981P2

(24)

where

P1 Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t⎛⎝ ⎞⎠ Pr hRR

111386811138681113868111386811138681113868111386811138682 le

1κt

1113874 1113875 1 minus exp minusλRRκt

1113888 1113889

(25)

P2 1 minus Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 lt t1113872 1113873 2

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(26)

Substituting (23) and (24) into (22) FT(t) can bemathematically calculated as

FT(t) 1 minus 2 1 minus exp minusλRRκt

1113888 11138891113896 1113897 times

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(27)

By substituting (25) into (21) OPMRC can be given by


OPMRC 1113946

infin

0

1 minus 2 1 minus exp minusλRR

κ cth minus z( 11138571113888 11138891113896 1113897

times

λSRλRD cth minus z( 1113857

κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎭

timesλSDΨ

exp minusλSDz

Ψ1113888 1113889dz (28)

42 Instantaneous End-to-End SNR at D Using the SCTechnique Similar to MRC technique as mentioned abovethe overall SNR at D can be given by

cSCD max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭

(29)

Hence the OP can be calculated as

OPSC Pr cSCD lt cth1113872 1113873 Pr max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭ lt cth⎡⎢⎢⎣ ⎤⎥⎥⎦

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1113980radicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradicradic1113981P3

Pr Ψ hSD1113868111386811138681113868

11138681113868111386811138682 lt cth1113872 1113873


(30)

where

P3 Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1 minus Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge cth

⎛⎝ ⎞⎠Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge cth1113872 1113873

1 minus 2 1 minus exp minusλRRκcth

1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠

P4 1 minus exp minusλSDcth

Ψ1113888 1113889

(31)

Finally substituting (28) and (29) into (27) the OP inthis scenario can be expressed as

OPSC 1 minus exp minusλSDcth

Ψ1113888 11138891113896 1113897

times 1 minus 2 1 minus exp minusλRRκcth

1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(32)


5 Simulation Results

e simulation results are given to validate the performancethat is IP and OP of our proposed schemes under maximalratio combining (MRC) and selection combining (SC)techniques e results are obtained by averaging 105Rayleigh channels [27ndash29]

In Figures 3 and 4 we investigate the IP and OP asfunctions of Ψ(dB) where cth 1 α 05 η 1 One canobserve from Figure 3 that as Ψ increases from minus5 to 20 dBthe IP performance improves accordingly e sourcersquostransmit power is proportional toΨ value since Ψ is definedas a ratio between source transmit power and additive whiteGaussian noiseus the higher theΨ value is the better theSNR at eavesdropper can be obtained Furthermore the IP ofthe MRC technique outperforms that of the SC technique Itis because the eavesdropper can overhear information fromboth source S and relay R using MRC while only receivingsignals from the source with the SC technique In Figure 4the outage performance of MRC is superior to that of the SCmethod It is because the destination can combine signalsfrom relay and source in MRC which only receives thisinformation from relay user in the SC method As shownfrom Figures 3 and 4 the performances of both destinationD and eavesdropper E can be continuously improved byincreasing the transmit power us the designer shouldselect a suitable value of Ψ when designing in practice fortrade-off between security and reliability of the system

Figures 5 and 6 show the IP and OP as a function of α forthe time-switching relaying (TSR) protocol wherecth 1Ψ 3 dB η 1 e value of α is crucial since itinfluences both the harvested energy at the relay and theinformation transmission from the relay to the destinationAs a result the higher the value of α is the more energy therelay can harvest However there is less time for informationtransmission to the destination erefore the OP canobtain the best value at the optimal point of α then theperformance worsens Notably when the value of α is smallthe eavesdropper has a low probability of intercepting theinformation For instance the IPs of MRC and SC are 0073and 00068 respectively when α equals 005 When α ishigher than the optimal value the outage performance andsystem security are worse It provides useful information fordesigning a practical system

In Figures 7 and 8 we investigate the IP and OP as afunction of rate threshold requirement to decode the signalsuccessfully where α 085Ψ 5 dB η 1 As observedfrom Figures 7 and 8 as the rate threshold increases from025 to 4 bpsHz the IP and OP performance degradesaccordingly It is expected since when the rate requirement ishigher the eavesdropper and destination need to obtain ahigher transmission rate to decode the signal However thetransmission rate is limited by many factors such as channelgain and allocated time for data transmission One moreinteresting point is that the IP and OP performances ofMRCand SC are converged to a saturation value when the ratethreshold increases

In Figures 9 and 10 we study the influences of energyconversion efficiency on the network performance that is IP

100

10ndash1

ndash5 0

IP versus ψ with γth = 1 α = 05 and η = 1

5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)

SC-exact analysisMRC-exact analysis

Monte Carlo simulation

Figure 3 IP versus Ψ(dB)

100

10ndash3

10ndash2

10ndash1

ndash5 0

OP versus ψ with γth = 1 α = 05 and η = 1

5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)



Figure 4 OP versus Ψ(dB)

100

10ndash2

10ndash1

0 02

IP versus α with γth = 1 ψ = 3 dB and η = 1

04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)



Figure 5 IP versus α


100

10ndash1

10ndash20 1

OP versus R with α = 085 ψ = 5 dB and η = 1

2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)



Figure 8 OP versus R (bpsHz)

035

03

025

02

0 02

OP versus α with γth = 1 ψ = 3 dB and η = 1

04 06α

08 1

Out

age p

roba

bilit

y (O

P)



Figure 6 OP versus α

1

09

08

07

06

05

04

030 1

IP versus R with α = 085 ψ = 5 dB and η = 1

2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)



Figure 7 IP versus R (bpsHz)


and OP It can be seen that both IP and OP are improvedwith higher values of IP andOPis can be explained by thefact that the higher the conversion rate is the more transmitpower at the relay R can be obtained which improves thechannel gain to eavesdropper and destination Moreoversimilar to Figures 3ndash8 the IP and OP performance of theMRC is better than that of the SC which shows the supe-riority of the MRC technique However the MRC techniquerequires more complicated hardware which is not alwayssuitable in practice us the evaluations in our work givedifferent scenarios for the designer to build a system inreality

6 Conclusion

is paper investigated the decode-and-forward (DF) full-duplex (FD) relaying networks under the presence of a direct

link Specifically the relay node can harvest energy from thesource and use it to transmit information to the destinationBy considering the above discussions we derive the closed-form expressions of the intercept probability (IP) and theoutage probability (OP) in both maximal ratio combining(MRC) and selection combining (SC) techniques at thereceiver Besides the simulation results show the exactnessof the mathematical results compared to simulation onesBesides the IP and OP of the MRC technique obtain betterperformance in comparison to those of the SC technique Inparticular the system security is improved significantlywhen the time splitting factor value is small We can extendthis work to the case where the source and eavesdropper areequipped with multiple antennas

Data Availability

No data were used in this paper e authors just proposedthe system and simulated it by MATLAB

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Phu Tran Tin (phutrantiniuheduvn) was the main per-former while Dong Si ien Chau (dongsithienchautdtueduvn) Van-Duc Phan (ducpvvlueduvn) TanN Nguyen (nguyennhattantdtueduvn) and PhuX Nguyen (phunx4fpteduvn phunx4feeduvn)worked as the advisors of Phu Tran Tin

Acknowledgments

is research was supported by the Industrial University ofHo ChiMinh City (IUH) Vietnam under Grant no 72HD-DHCN

References

[1] L R Varshney ldquoTransporting information and energy si-multaneouslyrdquo in Proceedings of the 2008 IEEE InternationalSymposium on Information (eory pp 1612ndash1616 TorontoCanada July 2008

[2] T Dinh Hieu T T Duy and S G Choi ldquoPerformanceenhancement for harvest-to-transmit cognitive multi-hopnetworks with best path selection method under presence ofeavesdropperrdquo in Proceedings of the 2018 20th InternationalConference on Advanced Communication Technology(ICACT) pp 1-2 Chuncheon Korea (South) February 2018

[3] Z Mobini M Mohammadi and C Tellambura ldquoWireless-powered full-duplex relay and friendly jamming for securecooperative communicationsrdquo IEEE Transactions on Infor-mation Forensics and Security vol 14 no 3 pp 621ndash634 2019

[4] T D Hieu G Sumit C Symeon and O Bjorn ldquoroughputmaximization for wireless communication systems withbackscatter- and cache-assisted UAV technologyrdquo httpsarxivorgabs201107955

[5] P Grover and A Sahai ldquoShannon meets tesla wireless in-formation and power transferrdquo in Proceedings of the 2010

07

06

05

04

03

02

01

00 02 04

IP versus η with γth = 1 ψ = 3 dB and α = 05

06η

08 1

Inte

rcep

t pro

babi

lity

(IP)



Figure 9 IP versus η

04

035

03

025

02

0150 02 04

OP versus η with γth = 1 ψ = 3 dB and α = 05

06η

08 1

Out

age p

roba

bilit

y (O

P)



Figure 10 OP versus η


IEEE International Symposium on Information (eorypp 2363ndash2367 Austin TX USA June 2010

[6] T N Nguyen M Tran T-L Nguyen Duy-hung Ha andMiroslav voznak ldquoPerformance analysis of a user selectionprotocol in cooperative networks with power splitting pro-tocol-based energy harvesting over nakagami-mRayleighchannelsrdquo Electronics vol 8 pp 1ndash14 2019

[7] D H Tran T D Le and B S Kim ldquoStability-aware geo-graphic routing in energy harvesting wireless sensor net-worksrdquo Sensors vol 16 pp 1ndash15 2016

[8] T N Nguyen T H Quang Minh T Phuong P T Tran et alldquoPerformance enhancement for energy harvesting based two-way relay protocols in wireless ad-hoc networks with partialand full relay selection methodsrdquo Ad Hoc Networks vol 84pp 178ndash187 2019

[9] D-H Tran T X Vu S Chatzinotas S ShahbazPanahi andB Ottersten ldquoCoarse trajectory design for energy minimi-zation in UAV-enabledrdquo IEEE Transactions on VehicularTechnology vol 69 no 9 pp 9483ndash9496 2020

[10] T N Nguyen T Minh P T Tran and M Voznak ldquoAdaptiveenergy harvesting relaying protocol for two-way half duplexsystem network over rician fading channelsrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID7693016 10 pages 2018

[11] R Zhang and C K Ho ldquoMIMO broadcasting for simulta-neous wireless information and power transferrdquo IEEETransaction on Wireless Communications vol 12 no 5pp 1989ndash2001 2013

[12] L Dai B Wang M Peng and S Chen ldquoHybrid precoding-based millimeter-wave massive mimo-noma with simulta-neous wireless information and power transferrdquo IEEE Journalon Selected Areas in Communications vol 37 no 1pp 131ndash141 2019

[13] T N Nguyen P T Tran and M Voznak ldquoWireless energyharvesting meets receiver diversity a successful approach fortwo-way half-duplex relay networks over block Rayleighfading channelrdquo Computer Networks vol 172 Article ID107176 2020

[14] A Prathima D S Gurjar H H Nguyen and A BhardwajldquoPerformance analysis and optimization of bidirectionaloverlay cognitive radio networks with hybrid-SWIPTrdquo IEEETransactions on Vehicular Technology vol 69 no 11pp 13467ndash13481 2020

[15] Y Liu Y Ye H Ding F Gao and H Yang ldquoOutage per-formance analysis for SWIPT-based incremental cooperativeNOMA networks with non-linear harvesterrdquo IEEE Com-munications Letters vol 24 no 2 pp 287ndash291 2020

[16] D S Gurjar H H Nguyen and P Pattanayak ldquoPerformanceof wireless powered cognitive radio sensor networks withnonlinear energy harvesterrdquo IEEE Sensors Letters vol 3 no 8pp 1ndash4 Article ID 7500704 2019

[17] D-H Ha T N Nguyen M H Q Tran X Li P T Tran andM Voznak ldquoSecurity and reliability analysis of a two-wayhalf-duplex wireless relaying network using partial relay se-lection and hybrid TPSR energy harvesting at relay nodesrdquoIEEE Access vol 8 pp 187165ndash187181 2020

[18] Q V Do T-N-K Hoan and I Koo ldquoOptimal power al-location for energy-efficient data transmission against full-duplex active eavesdroppers in wireless sensor networksrdquoIEEE Sensors Journal vol 19 no 13 pp 5333ndash5346 2019

[19] P T Tin B H Dinh T N Nguyen D H Ha and T T TrangldquoPower beacon-assisted energy harvesting wireless physicallayer cooperative relaying networks performance analysisrdquoSymmetry vol 12 no 1 2020

[20] A Arafa W Shin M Vaezi and H V Poor ldquoSecure relayingin non-orthogonal multiple access trusted and untrustedscenariosrdquo IEEE Transactions on Information Forensics andSecurity vol 15 pp 210ndash222 2020

[21] Tin Phu Tran Dang e Hung N Tan D Tran andM Voznak ldquoSecrecy performance enhancement for underlaycognitive radio networks employing cooperative multi-hoptransmission with and without presence of hardware im-pairmentsrdquo Entropy vol 21 no 2 pp 1ndash16 2019

[22] L Xingwang Z Mengle L Yuanwei L Lihua D Zhiguo andN Arumugam ldquoSecrecy analysis of ambient backscatterNOMA systems under IQ imbalancerdquo IEEE Transactions onVehicular Technology vol 69 no 10 pp 12286ndash12290 2020

[23] H Dinh Tran D Trung Tran and S G Choi ldquoSecrecyperformance of a generalized partial relay selection protocolin underlay cognitive networksrdquo International Journal ofCommunication Systems vol 31 no 17 Article ID e38062018

[24] T N Nguyen M Tran D H Ha T T Trang andM VoznakldquoMulti-source in DF cooperative network with PRS protocolbased full-duplex energy harvesting over a Rayleigh fadingchannel performance analysisrdquo Proceedings of the EstonianAcademy of Sciences vol 68 no 3 2019

[25] D H Tran V D Nguyen G Sumit C Symeon X T Vu andO Bjorn ldquoUAV relay-assisted emergency communications inIoT networks resource allocation and trajectory optimiza-tionrdquo httpsarxivorgabs200800218

[26] D Zwillinger Table of Integrals Series and Products Aca-demic Press Springer New York NY USA 2015

[27] T Nguyen T Quang Minh P Tran and M Voznak ldquoEnergyharvesting over rician fading channel a performance analysisfor half-duplex idirectional sensor networks under hardwareimpairmentsrdquo Sensors vol 18 no 6 2018

[28] P Tran Tin T N Nguyen M Tran and L Sevcik ldquoExploitingdirect link in two-way half-duplex sensor network over blockRayleigh fading channel upper bound ergodic capacity andexact SER analysisrdquo Sensors vol 20 no 4 1165 pages 2020

[29] D Le D H Tran S Choi B Kim and B An ldquoImpact ofbeamforming on the path connectivity in cognitive radio ad-hoc networksrdquo Sensors MDPI vol 17 no 4 2016


(i) We present an FD- and SWIPT-assisted relayingnetwork in decode-and-forward (DF) under thepresence of a direct link Particularly an eavesdropperis able to overhear the information transmission fromsource to destination via a relay Moreover an FD-enabled relay node is able to get energy from atransmitter and use it to transfer signals to the areceiver Notably the relay node can simultaneouslyreceive information from the source and transmit it tothe destination using the FD technique

(ii) We derive closed-form expressions of interceptprobability (IP) at the eavesdropper E and outageprobability (OP) at the destination D in maximalratio combining (MRC) and selection combining(SC) techniques

(iii) e correctness of the developed analysis is vali-dated through the Monte Carlo simulation On onehand we investigate the security perspective interms of intercept probability On the other handsystem reliability is also studied through outageprobability Consequently a trade-off between IPand OP can provide many insightful and usefulperspectives for system designers

2 System Model

In Figure 1 we consider a relaying network where a relay Raids in conveying data from a transmitter S to a receiver D inthe presence of one eavesdropper E In particular aneavesdropper is trying to get the information from S and Rby applying maximal ratio combining (MRC) and selectioncombining (SC) techniques In Figure 2 the relay R canharvest energy from the source during αT In the remainingtime (1 minus α)T the information process is executed

We assume that the channel between two users followsblock Rayleigh fading where channel coefficients are un-changed during a time frame and change independentlyacross time frames Moreover let us denote hXY forXY isin SRRDRR SDRE SE as the channel coefficient ofthe link between nodes X and Y Because the channels areRayleigh distribution the channel gains such as |hRD|2 and|hSD|2 are exponential random variables (RVs) whose cu-mulative distribution function (CDF) and probabilitydensity function (PDF) are respectively represented as

FX(x) 1 minus exp(minusλx)

fX(x) zFX(x)

zx λ exp(minusλx)

(1)

where λ is rate parameter of exponential distributione received signal at the relay can be expressed as

yR hSRxS + hRRxR + nR (2)

where xS is the energy symbol and E |xS|21113966 1113967 PS xR is theloopback interference due to full-duplex relaying and sat-isfies E |xR|21113966 1113967 PR where Ε middot denotes the expectationoperation nR denotes the zero mean additive white Gaussiannoise (AWGN) with variance N0

At the first phase the harvested energy at the relay can becomputed by

ER ηαTPS hSR1113868111386811138681113868

11138681113868111386811138682 (3)

where 0lt ηle 1 denotes the energy conversion efficiencyFrom (3) the average transmit power of the relay node

can be obtained as

PR ER

(1 minus α)TηαPS hSR

111386811138681113868111386811138681113868111386811138682

(1 minus α) κPS hSR

111386811138681113868111386811138681113868111386811138682 (4)

where κ ηα1 minus α

Next in the second phase the eavesdropper E mayintercept signals from both relay R and sourceS Nevertheless source S also generates artificial noise 1113957xS toprevent E from overhearing the source informationMoreover since the relay R and destination D are legitimateusers they are assumed to know the artificial noise createdby S Consequently they can cancel the artificial noise at thereceiver circuiterefore the received signal at E from relayR and source S can be respectively expressed as

yIE hRExR + n

IE y

IIE hSExS + hSE1113957xS + n

IIE (5)

where nE EIn nII

E is the AWGN with variance N0Since we adopt the decode-and-forward (DF) protocol the

signal to interference noise ratios (SINR) at the eavesdropper inthe second phase from (5) are respectively given by

cIE

hRE1113868111386811138681113868

11138681113868111386811138682PR

N0 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682 c

IIE Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1 (6)

where Ψ PsN0

hRD

hRD

E

D

R

S

Residual self-interference

hSR

hRR

hREhSE

Wiretap links Information flowEnergy flow

Figure 1 System model

T

αT (1 ndash α) T

Energy harverting at RInformation transmission

S R DS D

Figure 2 IT and EH processes



yID hRDxR + n

ID y

IID hSDxS + n

IID (7)

where nD nID nII





IP Pr cE ge cth( 1113857 (8)


cMRCE c

IE + c

IIE κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1 (9)


IPMRC Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1ge cth

⎛⎝ ⎞⎠

Pr X + Yge cth( 1113857 1 minus 1113946

cth

0


(10)




11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682 ltx1113872 1113873

Pr hSR1113868111386811138681113868

11138681113868111386811138682 lt

x

κΨ hRE1113868111386811138681113868

11138681113868111386811138682

⎛⎝ ⎞⎠ 1113946

infin

0

FhSR| |

2x

κΨy| hRE

111386811138681113868111386811138681113868111386811138682

y1113888 1113889 times fhRE| |

2(y)dy

1 minus 1113946

infin

0

λRE exp minusλSRx


(11)


FX(x) 1 minus 2

λSRλREx

κΨ

1113971

times K1 2

λSRλREx

κΨ

1113971

⎛⎝ ⎞⎠ (12)



111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1lty⎛⎝ ⎞⎠

Pr hSE1113868111386811138681113868

11138681113868111386811138682 lt

y


λSEy


(13)


fY(y) zFy(y)

zyλSEΨ


(1 minus y)2 (14)



1

0


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

timesλSEΨ


(1 minus y)2 dy

(15)



cSCE max c

IE c

IIE1113872 1113873 max κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1⎛⎝ ⎞⎠

max(X Y)

(16)







λSRλREcth

κΨ

1113971

times K1 2

λSRλREcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (18)



OP Pr cD lt cth( 1113857 (19)



Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎛⎝ ⎞⎠

(20)



T min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ (21)


cMRCD min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ + Ψ hSD

111386811138681113868111386811138681113868111386811138682

T + Z

(22)


OPMRC Pr T + Zlt cth( 1113857 1113946

infin

0


(23)



κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt t⎛⎝ ⎞⎠

1 minus Pr 1κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


(24)

where

P1 Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t⎛⎝ ⎞⎠ Pr hRR

111386811138681113868111386811138681113868111386811138682 le

1κt


1113888 1113889

(25)

P2 1 minus Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 lt t1113872 1113873 2

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(26)



1113888 11138891113896 1113897 times

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(27)



OPMRC 1113946

infin

0


κ cth minus z( 11138571113888 11138891113896 1113897

times


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎭

timesλSDΨ

exp minusλSDz

Ψ1113888 1113889dz (28)


cSCD max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭

(29)



1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭ lt cth⎡⎢⎢⎣ ⎤⎥⎥⎦

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦


Pr Ψ hSD1113868111386811138681113868

11138681113868111386811138682 lt cth1113872 1113873


(30)

where

P3 Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1 minus Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge cth

⎛⎝ ⎞⎠Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge cth1113872 1113873


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠


Ψ1113888 1113889

(31)



Ψ1113888 11138891113896 1113897


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(32)








100

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)




100

10ndash3

10ndash2

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)




100

10ndash2

10ndash1

0 02


04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)





100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)




035

03

025

02

0 02


04 06α

08 1

Out

age p

roba

bilit

y (O

P)




1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


06η

08 1

Inte

rcep

t pro

babi

lity

(IP)




04

035

03

025

02

0150 02 04


06η

08 1

Out

age p

roba

bilit

y (O

P)
































yID hRDxR + n

ID y

IID hSDxS + n

IID (7)

where nD nID nII





IP Pr cE ge cth( 1113857 (8)


cMRCE c

IE + c

IIE κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1 (9)


IPMRC Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682

+Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1ge cth

⎛⎝ ⎞⎠

Pr X + Yge cth( 1113857 1 minus 1113946

cth

0


(10)




11138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682 ltx1113872 1113873

Pr hSR1113868111386811138681113868

11138681113868111386811138682 lt

x

κΨ hRE1113868111386811138681113868

11138681113868111386811138682

⎛⎝ ⎞⎠ 1113946

infin

0

FhSR| |

2x

κΨy| hRE

111386811138681113868111386811138681113868111386811138682

y1113888 1113889 times fhRE| |

2(y)dy

1 minus 1113946

infin

0

λRE exp minusλSRx


(11)


FX(x) 1 minus 2

λSRλREx

κΨ

1113971

times K1 2

λSRλREx

κΨ

1113971

⎛⎝ ⎞⎠ (12)



111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1lty⎛⎝ ⎞⎠

Pr hSE1113868111386811138681113868

11138681113868111386811138682 lt

y


λSEy


(13)


fY(y) zFy(y)

zyλSEΨ


(1 minus y)2 (14)



1

0


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

timesλSEΨ


(1 minus y)2 dy

(15)



cSCE max c

IE c

IIE1113872 1113873 max κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1⎛⎝ ⎞⎠

max(X Y)

(16)







λSRλREcth

κΨ

1113971

times K1 2

λSRλREcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (18)



OP Pr cD lt cth( 1113857 (19)



Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎛⎝ ⎞⎠

(20)



T min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ (21)


cMRCD min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ + Ψ hSD

111386811138681113868111386811138681113868111386811138682

T + Z

(22)


OPMRC Pr T + Zlt cth( 1113857 1113946

infin

0


(23)



κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt t⎛⎝ ⎞⎠

1 minus Pr 1κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


(24)

where

P1 Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t⎛⎝ ⎞⎠ Pr hRR

111386811138681113868111386811138681113868111386811138682 le

1κt


1113888 1113889

(25)

P2 1 minus Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 lt t1113872 1113873 2

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(26)



1113888 11138891113896 1113897 times

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(27)



OPMRC 1113946

infin

0


κ cth minus z( 11138571113888 11138891113896 1113897

times


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎭

timesλSDΨ

exp minusλSDz

Ψ1113888 1113889dz (28)


cSCD max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭

(29)



1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭ lt cth⎡⎢⎢⎣ ⎤⎥⎥⎦

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦


Pr Ψ hSD1113868111386811138681113868

11138681113868111386811138682 lt cth1113872 1113873


(30)

where

P3 Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1 minus Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge cth

⎛⎝ ⎞⎠Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge cth1113872 1113873


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠


Ψ1113888 1113889

(31)



Ψ1113888 11138891113896 1113897


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(32)








100

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)




100

10ndash3

10ndash2

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)




100

10ndash2

10ndash1

0 02


04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)





100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)




035

03

025

02

0 02


04 06α

08 1

Out

age p

roba

bilit

y (O

P)




1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


06η

08 1

Inte

rcep

t pro

babi

lity

(IP)




04

035

03

025

02

0150 02 04


06η

08 1

Out

age p

roba

bilit

y (O

P)
































cSCE max c

IE c

IIE1113872 1113873 max κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRE1113868111386811138681113868

11138681113868111386811138682Ψ hSE

111386811138681113868111386811138681113868111386811138682

Ψ hSE1113868111386811138681113868

11138681113868111386811138682

+ 1⎛⎝ ⎞⎠

max(X Y)

(16)







λSRλREcth

κΨ

1113971

times K1 2

λSRλREcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (18)



OP Pr cD lt cth( 1113857 (19)



Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎛⎝ ⎞⎠

(20)



T min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ (21)


cMRCD min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠ + Ψ hSD

111386811138681113868111386811138681113868111386811138682

T + Z

(22)


OPMRC Pr T + Zlt cth( 1113857 1113946

infin

0


(23)



κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt t⎛⎝ ⎞⎠

1 minus Pr 1κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge t1113872 1113873


(24)

where

P1 Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge t⎛⎝ ⎞⎠ Pr hRR

111386811138681113868111386811138681113868111386811138682 le

1κt


1113888 1113889

(25)

P2 1 minus Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 lt t1113872 1113873 2

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(26)



1113888 11138891113896 1113897 times

λSRλRDt

κΨ

1113971

times K1 2

λSRλRDt

κΨ

1113971

⎛⎝ ⎞⎠

(27)



OPMRC 1113946

infin

0


κ cth minus z( 11138571113888 11138891113896 1113897

times


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎭

timesλSDΨ

exp minusλSDz

Ψ1113888 1113889dz (28)


cSCD max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭

(29)



1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭ lt cth⎡⎢⎢⎣ ⎤⎥⎥⎦

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦


Pr Ψ hSD1113868111386811138681113868

11138681113868111386811138682 lt cth1113872 1113873


(30)

where

P3 Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1 minus Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge cth

⎛⎝ ⎞⎠Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge cth1113872 1113873


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠


Ψ1113888 1113889

(31)



Ψ1113888 11138891113896 1113897


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(32)








100

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)




100

10ndash3

10ndash2

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)




100

10ndash2

10ndash1

0 02


04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)





100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)




035

03

025

02

0 02


04 06α

08 1

Out

age p

roba

bilit

y (O

P)




1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


06η

08 1

Inte

rcep

t pro

babi

lity

(IP)




04

035

03

025

02

0150 02 04


06η

08 1

Out

age p

roba

bilit

y (O

P)































OPMRC 1113946

infin

0


κ cth minus z( 11138571113888 11138891113896 1113897

times


κΨ

1113970

times K1 2


κΨ

1113971

⎛⎝ ⎞⎠

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎭

timesλSDΨ

exp minusλSDz

Ψ1113888 1113889dz (28)


cSCD max min

1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭

(29)



1κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠Ψ hSD

111386811138681113868111386811138681113868111386811138682⎧⎨

⎩

⎫⎬

⎭ lt cth⎡⎢⎢⎣ ⎤⎥⎥⎦

Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦


Pr Ψ hSD1113868111386811138681113868

11138681113868111386811138682 lt cth1113872 1113873


(30)

where

P3 Pr min1

κ hRR1113868111386811138681113868

11138681113868111386811138682 κΨ hSR

111386811138681113868111386811138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682⎛⎝ ⎞⎠lt cth

⎡⎢⎢⎣ ⎤⎥⎥⎦

1 minus Pr1

κ hRR1113868111386811138681113868

11138681113868111386811138682 ge cth

⎛⎝ ⎞⎠Pr κΨ hSR1113868111386811138681113868

11138681113868111386811138682

hRD1113868111386811138681113868

11138681113868111386811138682 ge cth1113872 1113873


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠


Ψ1113888 1113889

(31)



Ψ1113888 11138891113896 1113897


1113888 11138891113896 1113897 times

λSRλRDcth

κΨ

1113971

times K1 2

λSRλRDcth

κΨ

1113971

⎛⎝ ⎞⎠⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(32)








100

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)




100

10ndash3

10ndash2

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)




100

10ndash2

10ndash1

0 02


04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)





100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)




035

03

025

02

0 02


04 06α

08 1

Out

age p

roba

bilit

y (O

P)




1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


06η

08 1

Inte

rcep

t pro

babi

lity

(IP)




04

035

03

025

02

0150 02 04


06η

08 1

Out

age p

roba

bilit

y (O

P)





































100

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Inte

rcep

t pro

babi

lity

(IP)




100

10ndash3

10ndash2

10ndash1

ndash5 0


5 10ψ (dB)

15 20

Out

age p

roba

bilit

y (O

P)




100

10ndash2

10ndash1

0 02


04 06α

08 1

Inte

rcep

t pro

babi

lity

(IP)





100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

roba

bilit

y (O

P)




035

03

025

02

0 02


04 06α

08 1

Out

age p

roba

bilit

y (O

P)




1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

t pro

babi

lity

(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

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08 1

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04

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100

10ndash1

10ndash20 1


2R (bpsHz)

3 4

Out

age p

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035

03

025

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0 02


04 06α

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Out

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1

09

08

07

06

05

04

030 1


2R (bpsHz)

3 4

Inte

rcep

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(IP)






6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


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08 1

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6 Conclusion



Data Availability






Acknowledgments


References






07

06

05

04

03

02

01

00 02 04


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08 1

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