Outage analysis of cognitive two-way relaying networks with SWIPT over Nakagami-m fading channels

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Outage analysis of cognitive two-way relaying networks with SWIPT over Nakagami-
$\boldsymbol m$ fading channels
YANG Jing, GAO Xiqi, HAN Shanyang, Kostas P. PEPPAS and P. Takis MATHIOPOULOS
Citation: SCIENCE CHINA Information Sciences 61, 029303 (2018 ); doi: 10.1007/s11432-017-9159-y
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SCIENCE CHINA
Information Sciences
February 2018, Vol. 61 029303:1–029303:3
doi: 10.1007/s11432-017-9159-y
c
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.LETTER .
Outage analysis of cognitive two-way relaying
networks with SWIPT over Nakagami-m
fading channels
Jing YANG1,2*, Xiqi GAO1, Shanyang HAN2,
Kostas P. PEPPAS3& P. Takis MATHIOPOULOS4
1National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China;
2School of Information Engineering, Yangzhou University, Yangzhou 225009, China;
3Department of Telecommunication Science and Technology, University of Peloponnese, Tripoli 22100, Greece;
4Department of Informatics and Telecommunications, National and Kapodistrian University of Athens,
Athens 15784, Greece
Received 28 March 2017/Revised 20 April 2017/Accepted 3 July 2017/Published online 22 September 2017
Citation Yang J, Gao X Q, Han S Y, et al. Outage analysis of cognitive two-way relaying networks with SWIPT
over Nakagami-mfading channels. Sci China Inf Sci, 2018, 61(2): 029303, doi: 10.1007/s11432-017-9159-y
Dear editor,
Green wireless communication has attracted the
attention of the research community in recent
years [1,2]. Simultaneous wireless information and
power transfer (SWIPT) technique is an attractive
research area, since it enables the wireless nodes to
continually acquire energy from external sources
in energy-limited environments [3–5]. In [6], the
SWIPT was utilized in a cognitive two-way relay-
ing network as an efficient means to improve en-
ergy and spectral efficiency. Assuming Rayleigh
fading, the authors in [6] investigated the outage
probability (OP) performance. It is well known
that Nakagami-mfading can well characterize the
wireless propagation channel in many practical
cases and span a wide range of fading scenarios via
the mparameter, including the one-sided Gaus-
sian distribution (m= 0.5) and Rayleigh fading
(m= 1) as special cases. In our contribution, we
generalize the analysis of [6] to the more general
Nakagami-mchannel model. Specifically, we de-
rive the exact expressions on OP for the two pri-
mary users and a tight approximate expression on
OP for the secondary user. Simulations are also
performed to verify the correctness of our theoret-
ical analysis.
System model. Here, we consider a two-way cog-
nitive amplify-and-forward (AF) relaying network,
with two primary users, Sand D, and two sec-
ondary users, Rand C. Node Rhas its own infor-
mation to broadcast to Cand also acts as a relay
to assist primary transmission. Assume that the
two primary users Sand Dhave fixed power sup-
ply, PS, but no energy is provided to relay R. The
whole communication takes place in two phases. In
the first phase, Sand Dtransmit their informa-
tion to Rsimultaneously. In the second phase, R
harvests energy from the part of its received signal
from Sand D, and employs the harvested energy
to deliver the resulting information with a power
gain, along with the message intended for C. It is
also assumed that Sand Dcan successfully decode
the interference from secondary transmission.
Let g1,g2and g3represent the channel coeffi-
cients in S↔R,R↔Dand R↔Clinks, respec-
tively. Since all channels undergo Nakagami-m
fading, |gj|2follows the Gamma distribution with
fading parameter mj, and mean power Ωj. As-
* Corresponding author (email: jingyang@yzu.edu.cn)
The authors declare that they have no conflict of interest.
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Yang J, et al. Sci China Inf Sci February 2018 Vol. 61 029303:2
suming the integer values of mj, the probability
density function (PDF) and cumulative distribu-
tion function (CDF) of |gj|2are given as [7]
f|gj|2(x)= ωmj
j
Γ(mj)xmj−1exp (−ωjx),(1)
and
F|gj|2(x)= 1−exp(−ωjx)
mj−1
X
k=0
(ωjx)k
k!,(2)
respectively, where ωj=mj/Ωj,j= 1,2,3.
The instantaneous signal-to-noise ratios (SNRs)
at S,D, and Ccan be expressed as [6]
γS=aγ|g1|2|g2|2
a1|g1|2+ 1 ,(3)
γD=aγ|g2|2|g1|2
a1|g2|2+1 ,(4)
and
γC= min {γS,C ,γD, C ,γC,C },(5)
respectively, where a=αηλ,a1=αηλ/(1 −λ),
γ=PS/σ2
0,σ2
0represents the additive noise power
at all users, λ∈(0,1) denotes the portion of in-
formation split for energy harvesting, η∈[0,1]
represents the energy conversion efficiency, and
α∈[0,1] indicates the fraction of the harvested
power to broadcast the remaining information.
Besides, γG,C ,G∈ {S, D, C }, denotes the in-
stantaneous signal to interference plus noise ratio
(SINR) at node Gto decode secondary information
intended for C. We have the following approxima-
tions, which are very accurate at high SNRs [6]:
γS,C ≈
bγ |g1|2|g1|2+|g2|2
aγ |g1|2|g2|2+1 ,(6)
γD,C ≈
bγ |g2|2|g1|2+|g2|2
aγ |g1|2|g2|2+1 ,(7)
and
γC,C ≈
bγ |g3|2|g1|2+|g2|2
aγ |g3|2|g1|2+|g2|2+ 1
,(8)
where b= (1 −α)ηλ.
Outage probability analysis. The OP is the prob-
ability that the instantaneous SNR γGat user G
falls below a predefined threshold tG, i.e., PG
out =
Pr (γG< tG), G∈ {S, D, C }.
Theorem 1. The OP at Sand Dare given in
closed-form as
PS
out = 1−2ωm1
1e−ω2a1dS
Γ(m1)
m2−1
X
k=0
k
X
p=0
a1k−p(ω2dS)k
p!(k−p)!
×dSω2
ω1
m1−p
2
Km1−p(2pdSω1ω2) (9)
and
PD
out = 1−2ωm2
2e−ω1a1dD
Γ(m2)
m1−1
X
k=0
k
X
p=0
a1k−p(ω1dD)k
p!(k−p)!
×dDω1
ω2
m2−p
2
Km2−p(2pdDω1ω2) (10)
respectively, where dχ=tχ
aγ , χ ∈ {S, D}, and
Kn(·) is the modified Bessel function of the second
kind and order n[8, Eq. (8.407)].
Proof. Define X=|g1|2,Y=|g2|2. We have
FγS(tS)= Z∞
0
Pr y<tSex +tS
aγx fX(x)dx. (11)
Substituting (1) and (2) into (11), and employ-
ing [8, Eq.(3.471.9)], Eq. (9) is obtained. Simi-
larly, Eq. (10) can be obtained.
Theorem 2. The OP at C,PC
out = 1, if τC,
1/tC6a/b. Otherwise, PC
out can be approximated
as
PC
out ≈1−f(m1, m2, m3)−f(m2, m1, m3)
−g(m1, m2, m3),(12)
where
f(mx, my, mz) = ωmx
x
Γ(mx)
ωmy
y
Γ(my)
×
mz−1
X
k=0
my−1
X
p=0
(−1)my−1−pωk
zω−(p−k+1)
y
hkk!my−1
p
×ZX0
0
xmx+my−2−pe(ωy−ωx)x
×Γp−k+ 1, ωyx+gx +1
hxdx,
g(mx, my, mz) = ωmx
x
Γ(mx)
ωmy
y
Γ(my)
mz−1
X
k=0
ωk
z
hkk!
×Z∞
X0Z∞
X0
xmx−1ymy−1e−ωxx−ωyy−ωz
h(x+y)
(x+y)kdydx,
g=bτc
a−bτc,h=γ(bτc−a) and X0=1
√γ(2bτc−a).
Proof. Refer to Appendix A.
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Yang J, et al. Sci China Inf Sci February 2018 Vol. 61 029303:3
0 5 10 15 20 25 30
10−6
10−5
10−4
10−3
10−2
10−1 (a)
(b)
100
γ
(dB)
Outage probability
10−6
10−5
10−4
10−3
10−2
10−1
100
Outage probability
Analysis, Eqs. (9) or (10)
Simulation, at S
Simulation, at D
Analysis, Eq. (12)
Simulation, at C
m1=1, m2=3
m1=2, m2=3
m1=1, m2=3
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
m1=2, m2=3
Analysis, Eqs. (9)
or (10)
Simulation, at S
Simulation, at D
Analysis, Eq. (12)
Simulation, at C
α
Figure 1 (a) OP against the γ, when Ω1= Ω2= Ω3= 8
dB, η= 1, λ= 0.25, α= 0.24, and tS=tD=tC= 3.
(b) OP versus α, when Ω1= Ω2= Ω3= 4 dB, γ= 20 dB,
η= 1, λ= 0.65, tS=tD= 3, and tC= 1.
Theorem 2 contains integrals with simple ele-
mentary function. Although it is difficult to derive
the closed-form solution for them, they can be eas-
ily calculated numerically by some math software,
such as Matlab, Mathematica or others.
Performance evaluation results. Figure 1(a)
shows the OP at S,Dand Cagainst γwhen
fading parameter m1=m3= 1, m2= 3 and
m1=m3= 2, m2= 3. From it, we observe
that the numerical results obtained from (9) and
(10) perfectly match well with simulations. Be-
sides, the analysis results of (12) we obtained are
very close to the simulation results. Figure 1(b)
depicts the OP against power split coefficient α
when fading parameter m1=m3= 1, m2= 3
and m1=m3= 2, m2= 3. It can also be found
that our analysis results of (9), (10) and (12) show
a good agreement with their corresponding simu-
lated ones. Besides, it can be seen that with the
increase of α, the OP of primary users become
smaller while the OP of secondary user increases,
which is consistent with the definition of α. In
addition, Figure 1(a) and (b) demonstrate under
the SWIPT protocol, although there is no extra
power provided for node R, the system can also
acquire a reasonable OP performance.
Conclusion. Exact expressions for the OP of
the primary users and a tight approximate ex-
pression on the OP of the secondary user for a
two-way cognitive AF relaying system operating
over Nakagami-mfading channels and employing
SWIPT have been derived. Numerical results ac-
companied with monte-carlo simulations have ver-
ified the accuracy of the proposed mathematical
analysis.
Acknowledgements This work was supported by
National Natural Science Foundation of China (Grant
No. 61301111) and China Postdoctoral Science Foun-
dation (Grant No. 2014M56074).
Supporting information Appendix A. The sup-
porting information is available online at info.scichina.
com and link.springer.com. The supporting materi-
als are published as submitted, without typesetting or
editing. The responsibility for scientific accuracy and
content remains entirely with the authors.
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