Energy harvesting assisted cognitive radio: random location-based transceivers scheme and performance analysis

Abstract

We consider spectrum-sharing scenario where coexist two communication networks including primary network and secondary network using the same spectrum. While the primary network includes directional multi-transceivers, the secondary network consists of relaying-based transceiver forwarding signals by energy harvesting assisted relay node. In cognitive radio, signals transmitted from secondary network are sufficiently small so that all of primary network receivers have signal to noise ratio (SNR) greater than a given threshold. In contrast, the transmitted signals from primary network cause increasing noise which is difficult to demodulate at secondary network nodes and hence it leads to the peak power constraint. In this paper, we focus on the influence of random location of transceivers at primary network using decode-and-forward protocol. Specifically, we derive closed-form outage probability expression of the secondary network under random location of transceivers and peak power constraint of primary network. This investigation shows the relationship between the fraction of energy harvesting time (Formula presented.) of time switching-based relaying protocol on outage probability of secondary network and throughput. In addition, we analyse the influence of the number of primary network transceivers as well as primary network’s SNR threshold on secondary network. Furthermore, the trade-off between increasing energy harvesting and rate was investigated under the effect of energy conversion efficiency. The accuracy of the expressions is validated via Monte-Carlo simulations. Numerical results highlight the trade-offs associated with the various energy harvesting time allocations as a function of outage performance.

Full text

Energy Harvesting Assisted Cognitive Radio: Random Location-based
Transceivers Scheme and Performance Analysis
Nam Pham Minh1, Dinh-Thuan Do2,*, Tung Nguyen Tien and Tin Phu Tran1
1Telecommunication Division, Faculty of Electronics Technology, Industrial University of Ho Chi
Minh City, Ho Chi Minh City, Viet Nam
2Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Ho Chi Minh City, Vietnam
*Corresponding author: dodinhthuan@tdt.edu.vn
Abstract: We consider spectrum-sharing scenario, where coexist two communication networks:
primary and secondary networks using the same spectrum. While the primary network includes
directional multi-transceivers, the secondary network consists of one direction-less transceiver for-
warded by energy harvesting assisted relay node. Radio signals transmitted from secondary net-
work are sufficiently small so that all of primary network receivers have signal to noise ratio (SNR)
greater than a given threshold. In contrast, the transmitted signals from primary network cause in-
creasing noise which is difficult to demodulate at secondary network nodes. In this paper, we focus
on the influence of random location of transceivers at primary network using decode-and-forward
protocol. Specifically, we derive closed-form outage probability expression of the secondary net-
work under random location of transceivers and peak power constraint of primary network. This
investigation shows the relationship between the fraction of block time αon outage probability of
secondary network and throughput. In addition, we analyse the influence of the number of primary
network transceivers as well as primary network’s SNR threshold on secondary network. Further-
more, the trade-off between increasing energy harvesting and rate was investigated under the effect
of energy conversion efficiency.
1. Introduction
Recently, energy harvesting (EH) attracted the attention of researchers, starting from the simple
physical model, in which one source directly transmits to one destination without noise, until
source transmits via an relay node using amplify-and-forward (AF) as well as decode-and-forward
(DF) protocols [1]-[5]. In particular, the authors in [2] analyzed a EH assisted cognitive radio net-
work. In the literature, some models were developed into complicated systems, where a receiver
in system has interfering signals from other transmitters using time-switching scheme (TS) and
power-switching scheme (PS) [3][5]. The authors in [7][8] also built a AF two-way relaying net-
work (TWRN) and extended to other complex cooperative protocols as in [8]. In [9], the authors
investigated the power constraints in cognitive network under EH. The authors in [2] assumed
that the communication distance from secondary receiver to all unexpected primary transmitters
have the same value in order to apply the mathematical approximation characteristic, in which
1

distribution of the sum of exponential random variables becomes a gamma distribution.
Considering cognitive radio (CR) networks, the previous works assumed that the system with
one primary receiver, one cognitive transmitter-receiver pair, and one energy harvesting relay as
in [10]-[13]. In order to cope with the stringent demand and scarcity of the radio spectrum in
the next generation of wireless communication, it is believed that CR is promising to do so. The
authors derived analytical expressions for the outage probability, as well as their high signal-to-
noise ratio (SNR) approximations in closed form as [10][12]. Furthermore, the authors in [11]
proposed a dynamic power splitting (DPS) scheme in which the received signal is divided into two
streams with adjustable power levels for energy harvesting and information processing separately
with the consideration of the instantaneous channel condition. If the interference temperature is
under a controllable level [14], or the use of the spectrum is unavailable, access to the spectrum
licensed to primary users (PUs) from a secondary user (SU) is permitted. A new CR paradigm has
just been suggested from the concept of cooperative communication for cognitive radio networks
(CRN), where parts of spectral sources are leased to SUs by the primary network so as to cooperate
[15]-[18].
According to the aforementioned studies, harvesting technology’s development is in the begin-
ning. For that reason, numerous deployments and system models are found in order to introduce
applications in various circumstances. It is believed that wireless communication also enjoys one
of a state-of-the-art method, including the mixture of relay transmission and cognitive radio, be-
cause cognitive radio enhances spectrum use by sharing between primary users (PUs) and sec-
ondary users (SUs) while relay transmission helps improve throughput and extends cover age over
conventional point-to-point transmissions. Additionally, the difficulty of throughput optimization
in terms of energy harvesting in relay systems is only affected by only one time slot, including
relay-destination link and the data transmission time of the source-relay link. In addition, there
are some other investigations into the area of cognitive networks in [19]-[21]. Scavenging energy
from ambient sources or cognitive radio transfer systems is available, the derived throughput of the
secondary transmitter was studied in [19]. Meanwhile, [20] examined random access for a cogni-
tive radio, where energy harvesting secondary terminal can be cooperated in signal transmission.
Furthermore, so as to derive the upper bound of the total throughput, an ideal spectrum access
policy energy harvesting CR was outlined in [21]. The optimization of the spatial SU throughput
subject to SU transmit power and SU density in a given geography utilizing stochastic geometry
is noticed by the authors in [22]. It is assumed that if a SUs is close enough to a PU node, the
former can scavenge power from the latter. Any SU in harvesting zone is capable of scavenging
the PU transmitted energy because each PU transmitter contains a harvesting zone with a small
radius satisfying the threshold energy harvesting circuit’s requirements.
It is noting that transmitters and receivers are conventional located at anywhere, received signal
in arbitrary node are suffered simultaneously by the influence of unexpected transmitters which
becomes the main focus of this paper. In particular, this paper employs RF signal to transmit infor-
mation and harvest energy from radio wave in cognitive network with assume that all the channels
are subject to slowly varying Rayleigh fading. In principle, there are two independent communi-
cation networks operating on the same spectrum: primary and secondary. Primary network (called
P Net) has many independent information links. Secondary network (called S Net) has only one
information source, which transmits through a relay node to the destination receiver. All of trans-
mitters are supplied by independent energy source (i.e. grid power) except relay node. Radio wave
supplies energy to the relay node in S Net. Continuously, relay node still uses this energy to trans-
mit information to the destination. It is noting that the more signals to relay node, the more energy
2

to support transmission. It means that communication distance is prolonged. However, when the
power transmitted from source or relay node becomes too strong, it causes noise at the destinations
of P Net. Consequently, the performance of wireless communication on P Net becomes worse.
Therefore, both the transmitted power of relay node and source node in S Net are also limited by
a given threshold that P Net can transmit information successfully. Consequently, received signals
have exponential distribution form with different scales.
The main contributions of this paper can be summarized as in the follow:
•This paper derives the secondary network’s closed-form outage probability expression under
random location of transceivers and the peak power constraint of primary network. In gen-
eral, the location of P Net’s transceivers is arbitrary. Therefore, signal at a receiver is not
simply a sum of many identically received signals despite the fact that all of primary network
transmitters have the same power.
•By simulation, it can be found the off-line optimal fraction of block time on secondary net-
work to achieve better outage performance employing TSR protocol.
•This paper investigates the effect of random location of transceivers on S Net’s outage prob-
ability. Obviously, re-arrangement cause reliable communication to be changeable.
•We analyse the influence of primary network’s threshold and the number of transceivers on
secondary network outage probability. Increasing the number of transceivers leads to slightly
less outage performance.
•We consider the trade-off between rate and energy harvesting. Clearly, more harvested energy
not only increase rate in the first phase due to satisfying transmitting power but also decrease
rate in second phase, when fraction of block time is larger than optimal value.
The remainder of the paper is organized as follows. Section II describes the considered system
model and Section III presents some fundamental preliminaries regarding the secondary network
performance analysis. Specifically, Sections III examine the trade-off between ergodic capacity
and energy transfer and the outage probability and throughput performance in scenario of energy
harvesting. Numerical results and useful insights are provided in Section IV, followed by our
conclusions in Section V.
2. System Model and Power Constraint Condition
2.1. System Model
As shown in Figure 1, two networks coexist simultaneously in a space and operate on the same
spectrum. The first network known as P Net consists of L transmitter nodes and L receiver nodes,
respectively. The other known as S Net has one transmitter node (ST) which transfers information
to destination node (SD) through a relay node (RL).
In spectrum-sharing scenario, a network needs to constrain its transmitting power that not to
completely disrupt communication from another one. In particular, RF signals from ST and RL
are sufficiently small so that receiver nodes PRe[i] have SNR[i] that are better than given threshold
γP. Otherwise, signals from P Net cause noise to demodulate at RL and SD. Thus, SNR decreases
substantially at these nodes. However, harvested energy significantly increases at RL node that
support higher rate on second hop.
3

ST
RL
SD
`
h
sr
h
rd
Secondary Network
Desired link
Primary Network
Interference link
PReL
PTrL
h
pp[i]
PRe1
PRe2
PTr1
PTr2
h
sp[i]
h
pr[i]
h
rp[i]
h
pd[i]
Fig. 1.S Net and P Net under spectrum-sharing scenario.
Energy Harvesting at
RL ( T) Information Transmission from
ST to RL (1- )T/2 Information Transmission from
RL to SD (1- )T/2
Fig. 2.TSR Protocol structure.
2.2. Power Constraint Condition
We consider the effect of transmitting power from ST on a receiver nodes PRe[i] with assuming
that all of PRe[i] have the same SNR threshold γP. This power must be small enough that all of
outage probability on ithith link is smaller primary outage threshold Ψin the P Net.
Pout−PRe = Pr Max
i=1:LPout,PRe[i]≤Ψ(1)
To ensure that completely successful communication in P Net, outage probability on node sat-
isfies as
Pout,PRe[i]= Pr Bwlog21 + γPRe[i]≤RP≤Ψ(2)
where γP Re[i]is the SNR on PRe[i], RPis primary rate (assumed equal value of each primary
link), Bw is bandwidth of a channel. It can be seen that (2) shows the relationship between γP Re[i]
and RPin accordance with known probability Ψ. It means that all of γP Re[i]must be greater than
γp= 2RP/Bw −1. Conventionally, PRe[i] suffers from noise from nearby transmitters and ST, RL.
In this paper, S Net employs TSR protocol as Fig. 2, which consists of three phases: (a) energy
harvesting, in which ST transmits, (b) information transmission from ST to RL, (c) information
transmission from RL to SD. In another words, ST and RL must not transmit concurrently. Thus,
arbitrary PRe[i] is not affected from both ST and RL simultaneously.
It is assumed that ith link in P Net is only influenced from ST, SNR of PRe[i] is given by
4

γPRe[i]=PP T [i]hpp[i]2
L
P
j=1,j6=i
PP T [j]hpp[j]2+PST hsp[i]2+σ2Pri
(3)
where hpp[i],hsp[i]is channel gains of ith directional link and interference link from ST, respectively.
PST is power from ST. PPT [i], which is transmitting power from PTr[i], is assumed equal value of
each transceivers, called PT. Obviously, the contribution of noise is much less than signal power.
Thus, denominator in (3) can re-write with noise term eliminated. Because of concentrating on
S Net, we assume that the influence of signals inside P Net is ignored. Formula (3) is reduced as
follow
γPRe[i] =PThpp[i]2
PST hsp[i]2(4)
Without loss of generality, we only consider one receiver node known as PRe, and hpp symbol-
izes the channel gain hpp[i]. According to [2], the power constraint at ST is shown as
Pr (γPRe ≤γp) = 1 −PTλpp
PST λspγp+PTλpp L
≤Ψ(5)
PST ≤PTλpp 1−L
√1−Ψ
λspγpL
√1−Ψ(6)
Similarly, the power constraint at RL is given by
PR≤PTλpp 1−L
√1−Ψ
λspγpL
√1−Ψ(7)
3. Performance analysis of secondary network
3.1. Outage probability performance
We first consider the outage probability at relay node. Based on system model shown in the previ-
ous section, SNR at RL is given by
γRL =PSmin|hsr |2
L
P
i=1
PP T [i]hpr[i]2+σ2
RL
(8)
where PSmin =Min hPST , PTiis real transmitting power from ST, hpr[i]is the channel gain
of ith interference link from ith transmitter to RL, hsr is the channel gain between ST and RL,
σ2
RL is typically internal noise characterized as Gaussian distribution with zero-mean and variance
σ2
RL =σ2. For simplicity in computations, we assume that PP T [i]=PT.
γRL =
PSmin
σ2|hsr|2
L
P
i=1
PT
σ2hpr[i]2+ 1
(9)
5

Thus, the outage probability can be expressed as
FRL (γs) = P r 



PSmin
σ2|hsr|2
L
P
i=1
PT
σ2hpr[i]2+ 1 ≤γs


(10)
Lemma 1: Let (Xi)i=1÷L, L≥2be independent exponential distributed random variables (ERVs)
that have
pdf (Xi) = 1
λie−x
λix≥0
0x < 0(11)
where λiis the scale of Xi. Then probability density function (PDF) of their sum is
fL
P
i=1
Xi
(x) = YL
i=1
1
λi×
L
X
j=1
e−x
λj
L
Q
k=1,k6=j1
λk−1
λj(12)
And cumulative distribution function (CDF) of their sum is
Pr L
X
i=1
Xi≤x!=YL
i=1
1
λi×
L
X
j=1
Pr (Xj< x)
1
λj
L
Q
k=1,k6=j1
λk−1
λj(13)
Proof:
The PDF was found in [25]. The CDF is given by:
Pr L
X
i=1
Xi≤x!=Zx
0
fL
P
i=1
Xi
(u)du =YL
i=1
1
λi×
L
X
j=1
x
R
0
1
λje−u
λjdu
1
λj
L
Q
k=1,k6=j1
λk−1
λj(14)
Proposition 1: The cumulative distribution function FRL (γs)is computed as
FRL (γs)=1−YL
i=1
1
λpr[i]×
L
X
j=1
e−γs
λsr λsr
λsr+γs.λpr [j]×λpr[j]
L
Q
k=1,k6=j1
λpr[k]−1
λpr[j](15)
where λsr =PSmin
σ2,λpr[i]=PT
σ2,γs= 2
2RS
Bw.(1−α).L −1.
Proof: The proof is proven in Appendix A.
Similarly, the expression of outage probability at destination node is derived. In decode-and-
forward mode, signal from source to relay node is received and decoded to extract information.
Then the information is re-encoded and transmitted to the final destination and hence SNR at
destination node is given by
6

γSD =PRmin.|hrd|2
L
P
i=1
PP T [i]hpd[i]2+σ2SD
(16)
where PRmin =Min hPREH , PRiis the real power that RL transmits to SD, σ2
SD symbolizes as
the noise at SD. Since RL has no external power supply, its output power totally depends on the
received energy EREH , which contributes to produce PREH . However, when PREH large enough,
it can cause transmitting signal to influence to P Net as mentioned above. Thus, real output power
at RL is constrained by minimum PREH and PR, which was referred to (7). For simplicity, we
assume that noise at RL and SD have Gaussian distribution with zero mean and variance σ2.
In principle, harvested energy is described as
EREH =δαT PSmin|hsr |2+
L
X
i=1
PP T [i]hpr[i]2+σ2!(17)
Therefore, the harvested power at RL is given by
PREH =2αδ
1−α PSmin|hsr |2+
L
X
i=1
PP T [i]hpr[i]2+σ2!(18)
It is noting that real output power at RL is known as
PRmin =Min hPREH , PRi(19)
And then expression of outage probability at SD is derived by
FSD (γs) = P r (γSD ≤γs) = Pr 



Min hPREH , PRi |hrd|2
L
P
i=1
PP T [i]hpd[i]2+σ2≤γs


(20)
Proposition 2: The cumulative distribution function FSD(γs)is given by
FSD (γs) = (1 −K)×M+K×N(21)
where
K=YL+1
i=1
1
λpr[i]×
L+1
X
j=1
1−e−ˆw
λpr[j]
1
λpr[j]
L+1
Q
k=1,k6=j1
λpr[k]−1
λpr[j](22)
M= 1 −YL
i=1
1
λpd[i]×
L
X
j=1
e−γs
λnomi hλnomi
λpd[j].γs+λnomi i
1
λpd[j]
L
Q
k=1,k6=j1
λpd[k]−1
λpd[j](23)
7

N=hQL+1
i=1
1
λpr[i]ihQL
i=1
1
λpd[i]i1
λrdn
×
L+1
P
m=1
e
+1
λpr[m]
L+1
Q
k=1,k6=m1
λpr[k]−1
λpr[m]×
L
P
n=1
I(m,n)
L
Q
k=1,k6=n1
λpd[k]−1
λpd[n]
(24)
with ˆw=PR(1−α)
2αδσ2−1,λrd =PR
σ2,λpd[i]=PP T [i]
σ2,λnomi =PR
σ2P Lrd, in which P Lrd is path-loss
factor from RL to SD. I(m, n) = Γ (2) e+1
λpd[n]λrdnλpr[m]λpd[n]e
γsλpd[n]
2λrdnλpr [m]W−1,−1
2γsλpd[n]
λrdnλpr [m]
Proof: The proof is given in Appendix B.
Next, outage probability of overall system can be calculated based on the previous results. To
transmit from source to destination, information must go through two hops. Then
Pout (γs) = Pr (Min hγRL, γSD i)≤γs(25)
where γs= 2
2.RS
(1−α).Bw.L −1under TSR protocol. In fact, probability to transmit successfully
information from ST to SD depends on the ability of successful transmission on each hop: ST →
RL, RL →SD.
Applying complementary probability theory, probability to transmit successfully information
from source to relay is 1−FRL (γs). Similar argument is applied for second hop. The successful
probability is [1 −FRL (γs)]×[1 −FSD (γs)] . Otherwise, outage probability is shown in following
expression. The outage probability of the considered model is found as
Pout =FRL (γs) + FSD (γs)−FRL (γs)×FSD (γs)(26)
where FRL,FSD calculated as in (15) and (21), respectively.
3.2. Throughput performance in delay-limited transmission mode
As assumed above, all of channels in model are slowly varying fading channels. This means that
parameters of a channel are virtually changeless during a block time. Outage capacity is defined as
the maximum rate of transferred information, which is possible to maintain when being transmitted
through channels under slow fading and given outage probability threshold. The outage capacity
unit were standardized according to bandwidth is bit/s/Hz. It is affected by the harvested energy
process at RL and followed TSR protocol in [4]. The throughput in delay-limited transmission
mode can be written as
TS=(1 −α)
2RS[1 −Pout (γs)] (27)
In this context, throughput in (27) shows the relationship between throughput S Net and Pout.
Figure 5 shows that, each Ψthreshold in P Net corresponds to one characteristic line of S Net’s
throughput, of which the maximum throughput can be found.
3.3. Rate and energy trade-off
In this section, we investigate the relationship between energy harvesting at RL and ergodic capac-
ity of S Net. Based on [13], the average harvested energy at RL is shown as
ERL =E{αδERE H }(28)
8

The ergodic capacity is given by
R=E1
2(1 −α) log2(1 + γSD ) + 1
2log2(1 + γRL)(29)
The characteristic of rate energy (R-E) trade-off shows the relationship between ergodic capac-
ity and the average harvested energy, is presented as below
CR−E=(R, ERL) : ERE H >EOpt, R 6E1
2(1 −α) log2(1 + γSD ) + 1
2log2(1 + γRL)
(30)
4. Numerical results and discussion
For numerical results, the allocation of transceivers in P Net is provided as below: the first trans-
mitter is placed at (1, 1), the next ones are located at points with progressive difference from the
previous one 0.25, according to both vertical and horizontal coordinates. Similarity, first receiver
is located at (1, 2) and progressive difference is used as above. ST transmitter in S Net at the
origin (0, 0), relay at (0, 0.5) and destination receiver at (0, 1). This arrangement ensures that all of
transmitters in P Net have completely differential communication distance when they influence to
receivers in S Net. In addition, RP= 1.5bits/s/Hz, transmitting power PT= 20dB, bandwidth
Bw = 1H z for both networks. Energy conversion factor δ= 0.5,RS= 0.2bits/s/Hz. Employed
path loss model P LAB =d−ρ
AB in condition of suburban area with ρ= 4,dAB is the distance from
A to B.
4.1. Interference-Assisted Energy Harvesting to encourage successful communication
Fig 3 shows a plot of the outage probability versus time switching fraction in EH protocol. It
can be observed that as considering fraction of block time αin the range of zero to 1, Pout is
decreased rapidly when αbegins increasing from zero value. At the beginning of throughput line
in Fig 5, its value is also approximately zero. However, harvested energy increases rapidly after
changing α. When αis larger αopt, throughput starts decreasing due to reducing communication
time. Especially, αapproximately equal 1, TSapproaches to zero. It is noted that αis too small, the
energy obtained from the radio waves is insignificant and insufficient to supply energy to transmit
on second hop within the reach of low outage probability. αis increased means that more energy
is supplied to RL. Energy harvesting occurs speedily because there are so many signals coming to
RL that leads to the outage probability on second hop decreased very rapidly. Furthermore, energy
harvesting happens quickly. There is less time to reach the limited-energy, which produce power
constrained in (7). When harvested energy is as valuable as limited-energy, the fraction of block
time has optimal value, called αopt. After that, although αcontinues increasing, Pout decreases.
Practically, larger αresults in shorten time for communication in TSR protocol. Moreover, RL
is being subjected to power constraint that could not support to increase rate. This is reason why
Pout decreases. When αcomes towards 1, there is no longer time to transfer information and the
result is Pout almost equal 1, meaning that it’s impossible to communicate in S Net. In addition,
Fig 3 also shows that in case of the number of transceivers L = 3, outage probability is lower than
the case that L = 7. Clearly, more transceivers would reduce SNR in S Net and contribute to raise
outage probability. However, this difference is very small.
9

0 0.2 0.4 0.6 0.8 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
α
Pout in Secondary Net
Sim: L = 3
Analytical: L = 3
Sim: L = 5
Analytical: L = 5
Sim: L = 7
Analytical: L = 7
Fig. 3.Effect of αon Pout
0 0.2 0.4 0.6 0.8 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
α
Pout in Secondary Net
Sim: ψ=0.01
Analytical: ψ=0.01
Sim: ψ=0.02
Analytical: ψ=0.02
Sim: ψ=0.03
Analytical: ψ=0.03
Fig. 4.Effect of threshold Ψ
10

0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α
Throughput on Secondary Net (bits/sec/Hz)
Sim: ψ=0.01
Analytical: ψ=0.01
Sim: ψ=0.02
Analytical: ψ=0.02
Sim: ψ=0.03
Analytical: ψ=0.03
Fig. 5.Effect of αand Ψon throughput
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
20
40
60
80
100
120
140
160
180
200
Rate (bits/sec/Hz)
Energy Unit
δ=1
δ=0.5
Fig. 6.Rate energy trade-off, PT= 20 dB and δ= 0.5and 1
11

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d1
Pout in Secondary Net
Sim: ψ=0.01
Analytical: ψ=0.01
Sim: ψ=0.02
Analytical: ψ=0.02
Sim: ψ=0.03
Analytical: ψ=0.03
Fig. 7.Effect of relocation in S Net
As observed from Fig 4 and Fig 5, energy harvesting occurs at relay node has an important role.
The more transmitters PTr[i], the more energy obtained. The transmitting power from RL depends
entirely on harvested energy. More energy means that the transmission from RL to SD is better.
This is not exact when transmitted power was fully satisfied. In this situation, the transmitted
power increase from RL without constraint by (7) leads to the reduction of reliable communication
from PTr[i] to PRe[i]. This is explained by outage probability exceeds a given threshold that is
considered as failure transmission. Obviously, larger Ψvalue leads to better transmission quality
from RL to SD. Thus, outage probability occurring in two hops of S Net decreases. In particular,
the simulation result with L = 3 shows that when Ψ = 0.01, the minimum probability achieves
0.35; when Ψ = 0.02 and Ψ = 0.03, the outage probability fells down from 0.2 to 0.15 at optimal
condition.
Fig 6 illustrates rate and energy trade-off. While αslides up from zero to optimum value αopt,
received energy in RL increases rapidly and outage capacity also goes along with it. However,
when αpasses over αOpt, the received energy at RL continues to rise while real transmitting power
is being constrained by (7). Thus, some part of received energy is not used for transmission. Fur-
thermore, because communication time reduces while αincreases, outage capacity becomes lower.
Although the harvested energy at relay increases, outage capacity still decreases. We consider in-
consistency between them inside the range of αopt to one.
4.2. Effect of transceiver allocation
According to mathematical results as above, transceivers are not constrained by place inside both
networks. We investigate the effect of transceiver arrangement on both.
Fig 7 shows the relationship between d1distance and outage probability in S Net, in which d1
is space between ST and RL. In the range of coverage distance from 0.1 to 0.9, the optimal outage
12

0 0.2 0.4 0.6 0.8 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
α
Pout in Secondary Net
Sim: Line topology
Analytical
Sim: Rhomboid topology
Analytical
Fig. 8.Effect of relocation in P Net
capacity is reached at d1 = 0.55. In addition, this figure also shows that the higher Ψ, the smaller
outage probability in S Net.
We observe trend of the outage probability in terms of relocation primary transceivers in Fig
8. To make clear study, we compare two topologies, in which secondary network is unchanged:
(a) line arrangement as mentioned above with L = 4, (b) rhumboid arrangement: first transceiver
at (0, 1.5) and (1.5, 1.5), second at (0.25, 1.5) and (1.75, 1.5), third at (0.25, 1.75) and (1.75,
1.75), forth at (0.5, 1.75) and (2, 1.75). Fig 8 show the outage probability change in terms of
relocation primary transceivers. Result also indicates that if channel was approximated by gamma
distribution, we would not have achieved success.
5. Conclusion
In this paper, we investigate energy harvesting in cognitive network, which consists of two net-
works sharing frequency spectrum together: P Net includes multiple independent communication
links, which all of transmitters arranged with any location, while S Net consists of one transmit-
ter node, one receiver node and one relay node, which employs energy harvesting and forwards
information concurrently. Our research derives closed-form of secondary network outage proba-
bility expression. By using TSR protocol, the paper shows the optimal fraction of block time to
achieve better outage performance. In addition, we investigate the effect of random location pri-
mary transceivers and relay node on S Net’s outage probability as well as analyse the influence
of P Net’s threshold and the number of transceivers on secondary network outage probability. We
conclude that outage performance is slightly influenced by the number of transceivers in P Net. It
is also confirmed that harvested energy and rate must not go along together at all.
13

6. Appendices
6.1. APPENDIX A
PROOF OF PROPOSITION 1
Obviously, we can rewrite (9) as:
γSR =X
Y+ 1 (31)
where X=PSmin
σ2|hsr|2,Y=
L
P
i=1
PT
σ2|hsr|2. X is the exponential distributed random variable
(ERV) with mean λsr =PSmin
σ2P Lsr, Y is the sum of ERVs, in which each part has mean λpr[i]=
PT
σ2P Lpr[i],respectively. By applying Lemma 1, the pdf(Y) and cdf(Y) are proven. Probability of
(31) in (10) is solved by separating two cases:
Pr X
Y+1 ≤γs=


Pr Y≥X−γs
γs, X ≥γs
Pr Y≥X−γs
γs= 1 , X < γs
= 1 −
∞
R
γs
fX(x) Pr Y < X−γs
γsdx
(32)
and vice versa.
After reducing (32), we obtain the express as in (15).
6.2. APPENDIX B
PROOF OF PROPOSITION 2
From (20) we can write:
FSD (γSD ) = Pr (PREH > PR)
| {z }
1−K
Pr 



PR
σ2|hrd|2
L
P
i=1
PP T [i]
σ2hpd[i]2+ 1
6γs



| {z }
M
(33)
+ Pr (PREH 6PR)
| {z }
K
Pr 



PREH
σ2|hrd|2
L
P
i=1
PP T [i]
σ2hpd[i]2+ 1
6γs



| {z }
N
We need to solve three subcases: (22), (23) and (24). Firstly, substituting the value of PREH in
(18) to Kform in (33), we receive
K= Pr 2αδσ2
1−α(X1+X2+... +XL+XL+1 + 1) 6PR(34)
= Pr (X1+X2+... +XL+XL+1 6ˆw)(35)
14

where Xi:i= 1 ÷L:pdf (Xi) = 1
λpr[i]e−x
λpr[i],XL+1 :pdf (XL+1) = 1
λsr e−x
λsr ,ˆw=
PR(1−α)
2αδσ2−1. Applying Lemma 1, we get (22).
Secondarily, Mform in (33) is given by
M= Pr U
V+ 1 6γs(36)
where V=
L
P
i=1
Vi=
L
P
i=1
PP T [i]
σ2hpd[i]2(37) is the sum of ERVs, U=PR
σ2|hrd|2is ERV. (36) and (31)
have similar in form. Thus, we use the same way to get (23).
Finally, Nform in (33) is expressed as
N= Pr 



PREH
σ2|hrd|2
L
P
i=1
PT
σ2hpd[i]2+ 1
6γs


(38)
Let us denote T=2αδ
(1−α)|hrd|2,Z=PSmin
σ2|hsr|2+
L
P
i=1
PP T [i]
σ2hpr[i]2+ 1,PREH in (18), Vin
(37) can be substituted, we obtain
N= Pr T Z
V+ 1 6γs(39)
Applying Rohatgi’s well-known results in [24] and formula eq. 3.471.9 in [23], we have
pdf(U=TZ)
fU(u) = YL+1
i=1
1
λpr[i]×1
λrdn
L+1
X
j=1
2e+1
λpr[j].K02qu
λrdn.λpr [j]
L+1
Q
k=1,k6=j1
λpr[k]−1
λpr[j](40)
where λrdn =P Lrd ×2αδ
(1−α)and pdf(V) is similarly proved in Lemma 1.We can write Nas:
N=YL+1
i=1
1
λpr[i]YL
i=1
1
λpd[i]1
λrdn ×
L+1
X
m=1
e+1
λpr[m]
L+1
Q
k=1,k6=m1
λpr[k]−1
λpr[m]
×
L
X
n=1
I2
z }| {
Z∞
0
I1
z }| {
Zγsv
0
2K02ru
λrdnλpr[m]e−v−1
λpd[n].dudv
L
Q
k=1,k6=n1
λpd[k]−1
λpd[n](41)
I1is calculated when apply eq. 5.522 in [23] where p=−1and K−v=Kv.
15

I2is solved when conducted from eq.6.643.6 in [23], where m= 1 and α=λr dnλpr[m]
γsλpd[n]. After
solving (22), (23), (24), equation (21) is clearly.
7. References
[1] Y. Gu, Sonia Assa, ”RF-Based Energy Harvesting in Decode-and-Forward Relaying Systems:
Ergodic and Outage Capacities,” IEEE Trans. on wireless communications, Vol. 14, No. 11,
Nov. 2015.
[2] Sanket S.Kalamhar, Adrish Banerjee, ”Interference-Assisted Wireless Energy Harvesting in
Cognitive Relay Network with Multiple Primary Transceivers,” in Proc. of GLOBECOM, San
Diego, CA, USA., Dec. 2015, pp. 1-6.
[3] Y. Gu, Sonia Assa, ”Interference Aided Energy Harvesting in Decode-and-Forward Relay-
ing Systems,” in Proc. of IEEE International Conference on Communications (ICC), Sydney,
Australia., June. 2014, pp. 5378 5382.
[4] A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy, ”Relaying Protocols for Wireless Energy
Harvesting and Information Processing”, IEEE Trans. on Wireless Communications., Vol. 12,
Issue 7, pp. 3622 3636, Jul. 2013.
[5] A. A.Nasir, X. Zhou, S. Durrani, R. A. Kennedy, ”Throughput and Ergodic Capacity of Wire-
less Harvesting Based DF Relaying Network,” in Proc. of IEEE ICC Sydney, Australia, June.
2014, pp. 4066 4071.
[6] Trung Q. Duong, P. L. Yeoh, V. N. Q. Bao, M. Elkashlan, N.Yang, ”Cognitive Relay Networks
with multiple primary transceivers under spectrum-sharing”, IEEE Signal Processing Letter,
Vol. 19, No. 11, Nov. 2012.
[7] Z. Wang, Z. Chen, Y. Yao, B. Xia and H. Liu, ”Wireless Energy Harvesting and Information
Transfer in Cognitive Two-Way Networks,” in Proc. of IEEE GLOBECOM, Austin,Texas, US.,
Dec. 2014, pp. 3465-3470.
[8] Y. Liu, L. Wang, M. Elkashlan, Trung Q. Duong and A.Nallanathan, ”Relaying Networks with
Wireless Power Transfer policies design and throughput analysis,” in Proc. of IEEE GLOBE-
COM, Austin,Texas, US., Dec. 2014, pp. 4030 - 4035.
[9] Y. Liu, S. Ali Mousavifar, Y. Deng, Cyril Leung, M. Eskashlan, ”Wireless Energy Harvesting
in a Cognitive Relay Networks,” IEEE Trans. on Wireless Communication, Vol. 15, No. 4, pp.
2498-2508, Dec. 2015.
[10] Z. Yang, Z. Ding, P. Fan, G. K. Karagiannidis, ”Outage Performance of Cognitive Relay Net-
works With Wireless Information and Power Transfer”, IEEE Trans. on Vehicular Technology,
Vol. 65, No. 5, pp. 3828-3833, 2016.
[11] L. Liu, R. Zang, K.C. Chua, ”Wireless Information and Power Transfer: A Dynamic Power
Splitting Approach,” IEEE Trans. on Communications, Jul. 2013, Vol 61, Issue 9, pp. 3990-
4001.
16

[12] Z. Yang , P. Fan, G. K. Karagiannidis, ”Outage Performance of Cognitive Relay Networks
with Wireless Information and Power Transfer,” IEEE Trans. on Vehicular Technology, Vol.
65, No. 5, pp. 3828 - 3833, June. 2015.
[13] X. Zhou, R. Zhang and C. K. H, ”Wireless information and power transfer: Architecture
design and rate-energy trade-off,” IEEE Trans. on Wireless Communications, Vol .61, No.11,
pp. 4754 - 4767, Oct. 2013.
[14] M. Gastpar, ”On capacity under receive and spatial spectrum-sharing constraints,” IEEE
Trans. on Information Theory, vol. 53, no. 2,pp. 471-487, 2007.
[15] K. B. Letaief and W. Zhang, ”Cooperative communications for cognitive radio networks,”
Proc. IEEE, vol. 97, no. 5, pp. 878-893, May 2009.
[16] O. Simeone, l. Stanojev, S. Savazzi, Y Bar-Ness, U. Spagnolini, and R. L. Pickholtz, ”Spec-
trum leasing to cooperating secondary ad hocnetworks,” IEEE J. Set. Areas Commun., vol. 26,
no. I, pp. 203-213, Jan. 2008.
[17] L. Stanojev, O. Simeone, U. Spagnolini, Y Bar-Ness, and R. L. Pickholtz, ”Cooperative ARQ
via auction-based spectrum leasing,” IEEE Trans. Commun, vol. 58, no. 6, pp. 1843-1856,
June 2010.
[18] K. Lee, O. Simeone, C. B. Chae, and J. Kang, ”Spectrum leasing via cooperation for enhanced
physical-layer secrecy,” in Proc. of IEEE ICC, Kyoto, Japan, June 2011.
[19] S. Park and D. Hong, Achievable throughput of energy harvesting cognitive radio networks,
IEEE Trans. Wireless Commun., vol. 13, no. 2, pp. 10101022, Feb. 2014.
[20] A. Shafie and A. Sultan, Optimal random access for a cognitive radio terminal with energy
harvesting capability, IEEE Wireless Commun. Lett., vol. 17, no. 6, pp. 11281131, June 2013.
[21] S. Park and D. Hong, Optimal spectrum access for energy harvesting cognitive radio net-
works, IEEE Trans. Wireless Commun., vol. 12, no. 12, pp. 61666179, Dec. 2013
[22] [18] S. Lee, R. Zhang, and K. Huang, Opportunistic wireless energy harvesting in cognitive
radio networks, IEEE Trans. Wireless Commun., vol. 12, no. 9, pp. 47884799, Sept. 2013.
[23] I.S. Gradshtein, I.M. Ryzhik, ”Table of Integrals,” 7th Ed.
[24] V. K. Rohatgi, ”An introduction to probability theory and mathematical statistics,” Wiley,
New York, 1976.
[25] Athanasios Papoulis, ”Probability, Random Variables, and Stochastic Processes,” McGaw-
Hill Inc, 3rd Ed.
17