Content uploaded by Sami Muhaidat
Author content
All content in this area was uploaded by Sami Muhaidat on Feb 06, 2019
Content may be subject to copyright.
arXiv:1902.00332v1 [cs.IT] 1 Feb 2019
1
Opportunistic Ambient Backscatter Communication
in RF-Powered Cognitive Radio Networks
Rajalekshmi Kishore, Student Member, IEEE, Sanjeev Gurugopinath, Member, IEEE,
Paschalis C. Sofotasios, Senior Member, IEEE, Sami Muhaidat, Senior Member, IEEE,
and Naofal Al-Dhahir, Fellow, IEEE
Abstract—In the present contribution, we propose a novel
opportunistic ambient backscatter communication (ABC) frame-
work for radio frequency (RF)-powered cognitive radio (CR)
networks. This framework considers opportunistic spectrum
sensing integrated with ABC and harvest-then-transmit (HTT)
operation strategies. Novel analytic expressions are derived for
the average throughput, the average energy consumption and
the energy efficiency in the considered set up. These expressions
are represented in closed-form and have a tractable algebraic
representation which renders them convenient to handle both
analytically and numerically. In addition, we formulate an
optimization problem to maximize the energy efficiency of the
CR system operating in mixed ABC −and HTT −modes,
for a given set of constraints including primary interference
and imperfect spectrum sensing constraints. Capitalizing on this,
we determine the optimal set of parameters which in turn
comprise the optimal detection threshold, the optimal degree
of trade-off between the CR system operating in the ABC −
and HTT −modes and the optimal data transmission time.
Extensive results from respective computer simulations are also
presented for corroborating the corresponding analytic results
and to demonstrate the performance gain of the proposed model
in terms of energy efficiency.
Index Terms—Ambient backscatter communication, cognitive
radio networks, energy detection, energy efficiency, wireless
power transfer.
I. INTRO DUC TI ON
The need for efficient utilization of spectrum resources
has become a fundamental requirement in modern wireless
networks due to the witnessed spectrum scarcity and the
ever-increasing demand for higher data rate applications and
internet services. In this context, an interesting proposal has
been the development of cognitive radio (CR) networks [2],
which can adapt their transmission parameters according to the
This work will appear in part in [1].
R. Kishore is with the Department of Electrical and Electronics Engi-
neering, BITS Pilani, K. K. Birla Goa Campus, Goa 403726, India, (email:
lekshminair2k@yahoo.com).
S. Gurugopinath is with the Department of Electronics and Communi-
cation Engineering, PES University, Bengaluru 560085, India, (email: san-
jeevg@pes.edu).
P. C. Sofotasios is with the Department of Electrical and Computer Engi-
neering, Khalifa University of Science and Technology, PO Box 127788, Abu
Dhabi, UAE, and with the Department of Electronics and Communications
Engineering, Tampere University of Technology, 33101 Tampere, Finland
(email: p.sofotasios@ieee.org).
S. Muhaidat is with the Department of Electrical and Computer Engineer-
ing, Khalifa University of Science and Technology, PO Box 127788, Abu
Dhabi, UAE and with the Institute for Communication Systems, University
of Surrey, GU2 7XH, Guildford, UK, (email: muhaidat@ieee.org).
N. Al-Dhahir is with the Department of Electrical Engineering, University
of Texas at Dallas, TX 75080 Dallas, USA (e-mail: aldhahir@utdallas.edu).
characteristics of the communication environment. Cognitive
radios have been shown to be efficient in increasing spec-
trum utilization due to their inherent spectrum sensing (SS)
capability [3]. In this regard, dynamic spectrum access (DSA),
where the secondary users (SU) can opportunistically access
the underutilized frequency bands, is the standard solution
for the realization of DSA [4], which is envisioned to be
an integral part of future communication systems [5]. In
order to realize DSA, three strategies have been proposed,
namely the underlay, the overlay and the interweave. In the
underlay technique, the SUs coexist with a PU provided that
the interference level at the PU remains below a certain
threshold [6]. In the overlay paradigm, the SUs would be
allowed to share the band with PU by exploiting the knowledge
of its message and codebook in order to reduce interference.
Finally, in the interweave technique, the SU can only access
the licensed spectrum of the PU when it is idle [7].
Recently, energy efficiency (EE) has emerged as a major
design and performance criterion for the current and forth-
coming wireless systems [8]–[12], mainly driven by the ever
increasing operating expenditure of communication networks.
In this context, it has been shown that combining effective en-
ergy harvesting (EH) techniques with CR can simultaneously
improve the spectrum efficiency and the energy efficiency
[13], [14]. Furthermore, powering mobile devices by harvested
energy from ambient sources and/or external transmission
activities enables wireless networks to achieve an increased
degree of self-sustainability for a longer period of time [15].
More recently, the integration of RF energy harvesting tech-
niques with CR networks has lead to the development of
a new communication paradigm, known as RF-powered CR
networks [16]. In such networks, a CR transmitter harvests
RF energy when a primary user is present and utilizes it for
data transmission when the spectrum is vacant. This protocol
is referred to as harvest-then-transmit (HTT) [16], [17].
However, a major challenge associated with this method
is the reduction of the throughput of the secondary network
when the harvested energy is low and/or when the data
transmission time is shorter. To overcome this shortcoming,
the concept of simultaneous wireless information and power
transfer (SWIPT) was introduced [18], which has attracted
significant research attention [19], [20]. In addition, in 5G
communication systems and beyond, as well is in the context
of the Internet of Things (IoT) applications, the SWIPT
technology can be fundamentally important for energy and
information transmission across different wireless systems and
2
network architectures, including CR-based networks [21]–
[23].
A. Ambient Backscatter Communication (ABC)
Ambient backscatter communication (ABC) has recently
emerged as a new communication paradigm that is character-
ized by low power and low cost requirements, which renders it
a strong candidate for several IoT based applications [24], [25].
In an ABC system, there are typically two main components,
namely, an RF source which acts as a carrier emitter and a
backscatter receiver. The ambient RF sources, e.g., TV towers,
cellular base stations, and WiFi APs act as carrier emitters.
Therefore, the deployment of dedicated RF sources is not
required as opposed to the case of conventional backscattering
communication systems. As a result, this reduces the power
consumption and overall cost. Secondly, by utilizing existing
ambient RF signals, there is no need to allocate new frequency
spectrum for ABC, and hence the spectrum utility is improved
[26]. In the context of CR, the secondary transmitter (ST) can
communicate with a secondary receiver (SR) by backscattering
the primary user (PU) signal, whenever the PU is active. In
other words, instead of initiating a CR transmission only when
the PU is inactive, the ST can backscatter the PU signal
to SR, even when the PU is active. For example, ST can
employ the ON-OFF keying strategy to indicate bit 1or bit 0
by switching its antenna between reflecting or non-reflecting
states, respectively.
Based on the above, it is evident that the performance
of ABC-based CR networks depends considerably on the
availability of PU signals, which represents a major challenge
for CR networks particularly during the long idle period.
Therefore, this requires a paradigm shift towards the de-
velopment of key enabling techniques for next generation
CR networks, such as the hybrid ABC-HTT schemes, which
were recently proposed in [17]. However, a common and
major drawback in the proposed models is the assumption
of perfect knowledge of PU activities, which is unrealistic in
practical CR based communication scenarios. To this effect,
we propose a novel opportunistic hybrid ABC-HTT model
for CR networks, coined as ABC-HTT-based CR networks.
The proposed framework exploits the potentials of both ABC
and RF-powered CRNs; hence, in the context of the proposed
framework, we further evaluate and quantify the performance
of CR networks by taking into account the incurred sensing
errors under different realistic communication scenarios.
B. Related Work and Motivation
1) RF Powered Cognitive Radio Networks: RF-based en-
ergy harvesting for CR networks is an energy efficient ap-
proach to harvest energy from PU activity in order to max-
imize the network capacity [27], [28]. In [29], the authors
investigated SWIPT for spectrum sharing in CR networks,
where a CR receiver harvests energy from primary and sec-
ondary transmissions using antenna switching. In this work,
antennas were selected based on two schemes, namely, the
prioritizing data selection (PDS) scheme and the prioritizing
energy selection (PES) scheme. Then, a solution was proposed
for the optimal energy-data trade-off study for both PDS
and PES schemes under different fading conditions. In [30],
Wang et al. introduced a channel access strategy to maximize
the sum throughput of secondary users by jointly optimizing
the energy harvesting time, resource allocation, and transmit
power. Closed-form expressions for the optimal transmit power
and channel allocation were also derived, whilst it was shown
that there exists a tradeoff between the sum throughput of CR
network and harvested energy.
2) Ambient Backscatter Communication: Recently, Hoang
et al. [17] demonstrated that incorporating ABC with RF-
powered CR networks improves significantly the secondary
network throughput. This is because when the primary trans-
mitter is active, the CR transmitter can utilize ABC to transmit
its own data to the intended CR receiver. Also, the authors
explored a tradeoff between CR transmission in the ABC
and HTT modes, and provided insights on the optimal time
duration in these two modes. In [16], a hybrid backscatter
communication for a wireless powered heterogeneous network
was introduced, where the HTT protocol may not be optimal
due to the strict energy constraint for active RF communica-
tion. In addition to HTT, as the primary access protocol, long-
range bi-static scatter and short-range ambient backscatter
were adopted in order to increase the transmission range and
provide uniform rate distribution. Likewise, the authors in
[31], [32] focused on the tradeoff between energy harvesting,
active transmission and ambient backscatter communication
and demonstrated the superiority of the hybrid scheme in
terms of achieved throughput. Also, the effect of physical
parameters on the capacity of both legacy and backscatter
channels were analyzed in [33] by considering different re-
ceiver architectures. Assuming practical operating conditions,
it was shown that a legacy system employing an orthogonal
frequency division multiplexing (OFDM) modulation can turn
the RF interference arising from the backscatter process into a
form of multipath diversity that can be exploited for enhancing
its performance.
Nevertheless, despite the usefulness of relevant existing
contributions, the focus has been largely on the performance
enhancement in terms of achievable throughput, and not in
terms of energy efficiency and/or minimization of energy
consumption, which is a vital metric in the context of the
considered system. It is recalled here that energy efficiency
(EE) is an important performance evaluation metric for a CRN.
It is defined as the ratio of the average achievable throughput
to the average energy consumption, measured in bits/Hz/J
[34]. It can be noted that the detection accuracy in spectrum
sensing affects both the average network throughput and the
average energy consumption. However, there exists a tradeoff
in optimizing the two metrics, since an increase (or decrease)
in average achievable throughput results in an increase (or
decrease, respectively) in the average energy consumption.
The energy efficiency combines both these metrics, and hence
it is capable of accounting more effectively for the overall
performance of a CR system, as a function of the detection
accuracy.
3
C. Contributions
Motivated by the above, in the present study we analyze
the energy efficiency (EE) performance of an ABC-HTT-based
CR network in the presence of sensing errors and without
assuming knowledge of the PU activity. For simplicity, we
consider energy detection-based spectrum sensing, which has
widely known advantageous characteristics. In this context, we
derive analytic expressions for the average achievable through-
put and average energy consumption followed by a detailed
formulation of an optimization problem that maximizes the
energy efficiency subjected to several constraints, including
the interference constraint on PU. Based on this, we then
derive the expressions for the optimal detection threshold,
optimal harvesting time and optimal data transmission time,
and quantify the tradeoff between the ABC and HTT modes,
all in terms of energy efficiency.
Specifically, the main contributions of the present work are
listed below:
•We propose a novel opportunistic ABC framework for
RF-powered CR networks in the presence of sensing
errors, which operates in combination with the existing
HTT mode. We call the proposed network model as ABC-
HTT-based CR network.
•We derive novel analytic expressions for the average
achievable throughput, the average energy consumption
and the energy efficiency of the proposed ABC-HTT-
based CR network.
•We formulate an optimization problem that maximizes
the energy efficiency of the considered network, and
evaluate the optimal detection threshold, the optimal
energy harvesting time and the optimal data transmission
time, subject to PU interference and energy harvesting
constraints. Also, we quantify the requirements on the
backscattering data rate and transmit power of the CR
network as well as their impact on finding the optimal
energy harvesting time and data transmission time.
•We present detailed numerical results, which validate our
analysis and evaluate the energy efficiency performance
of the CR network in the proposed realistic platform
which includes the sensing errors. Furthermore, we quan-
tify the trade-off between ABC and HTT modes in terms
of energy efficiency. It is shown that operating the CR
network in a combination of these two modes improves
the overall energy efficiency. In addition, the impact
of sensing errors on the overall system performance is
addressed.
To the best of the authors’ knowledge, no analysis on the
energy efficiency in the presence of sensing errors in the
context of ABC-HTT-based CR networks has been reported
in the open technical literature.
D. Organization
The remainder of this paper is organized as follows: Sec. II
describes the proposed network model and summarizes the
performance of energy-based spectrum sensing. The energy
efficiency expression is derived in Sec. III and the optimization
problem is formulated in Sec. III-B. The corresponding analy-
sis and related insights are provided in Sec. IV, followed by the
corresponding validation through comparisons with numerical
results in Sec. V. Finally, conclusions are drawn in Sec. VI.
II. NET WO RK MOD EL
Consider an ABC-HTT-based cognitive radio network as
shown in Fig. 1, which consists of a secondary user transceiver
pair, denoted by (ST, SR), and a primary transceiver pair,
denoted by (PT, PR). We model the CR network in the
opportunistic spectrum access (OSA) paradigm, in which the
PU channels are accessed opportunistically using SS to detect
spectrum holes. The ST is equipped with an energy-based SS
unit, an RF energy harvesting unit and an ABC unit. Also,
we consider a typical coarse sensing framework, where SS is
carried out followed by data transmission over a time frame
of Tf r seconds, which is normalized such that Tf r = 1. The
time diagram for the proposed model is shown in Fig. 1;
based on this, when the PT is declared present, the ST can
harvest energy and store it in a battery, or perform ABC for
data transmission, as shown in Fig. 1(a). In this case, the
network is in the ambient backscatter communication (ABC)
mode, where τdenotes the normalized data transmission
period, and (1 −τ)denotes the normalized sensing duration
of the secondary user transceiver pair. Furthermore, we let ατ
represent the time fraction utilized for energy harvesting and
(1−α)τrepresent the time fraction for ABC, when the PT-PR
channel is declared occupied. The harvested energy during the
time ατ will be stored in the ST battery, and is used for data
transmission over the ST-SR link, when the PT-PR channel is
idle. On the contrary, when the PT is declared absent, the ST
uses the harvested energy to transmit data to SR during the
data transmission period. In this case, the network is said to
be in the harvest-then-transmit (HTT) mode, which is shown
in Fig. 1(b). In this case, µ∈(0,1) denotes the fraction of
τwhich is used for data transmission, the choice of which
depends on the amount of harvested energy.
It is recalled that in the present set up, we consider energy
detection-based SS, given its numerous advantages such as
simple realization and moderate computational complexity
[35]. Based on this, the probabilities of false-alarm and signal
detection at the ST are given by [36]
Pf=Qh ε
σ2−1p(1 −τ)Nsi,(1)
and
Pd=Q"ε
σ2−γ−1s(1 −τ)Ns
2γ+ 1 #,(2)
respectively, where Ns=fsTtdenotes the number of obser-
vations, fsis the sampling frequency, Ttis the duration of the
entire frame, σ2is the noise variance, εis the detection thresh-
old, and γdenotes the received SNR at ST. Furthermore, Q(·)
denotes the complementary cumulative distribution function of
a standard Gaussian random variable.
When the PT is declared to be occupied, the ST employs
ABC to transmit its own data to the SR, such that a certain
quality of service is guaranteed to the primary system. On
4
Sense Backscatter
Communication
Energy
Harvesting Sense Data
Transmission
(1- a)t at m t
(1-t) tt
(a) (b)
PT
ST SR
PT
ST SR
Sense Sense
PT signal
ST backscatter signal
ST transmit signal
Sensed PT signal
PT
ST SR
Sense
(1-t)
Fig. 1. Time slot structure when: (a) the PU is declared to be present; (b) when the PU is declared to be absent.
the contrary, when the PT is declared to be inactive, the ST
operates in the HTT mode using conventional RF transmission.
It is noted here that it was recently shown that switching be-
tween these two modes improves the overall throughput of the
secondary system [17]. A similar idea is adopted in the present
work with the difference that our analysis concerns the study
of a CR network operating in ABC-HTT framework, using the
OSA paradigm in the presence of the sensing errors in terms of
Pfand Pd, as opposed to the analysis in [17] which considers
CR operation in the opportunistic communication mode. In
addition, we quantify the performance of the proposed model
in terms of energy efficiency of the CR network in the presence
of sensing errors, unlike [17] that analyzes the throughput
performance in the simplistic case of no sensing errors.
III. ENE RG Y EFFICI ENC Y AND PRO BL E M FOR MUL ATI ON
A. Average Achievable Throughput and Energy Consumption
It is recalled that the energy efficiency of the CR network
is a defined as the ratio of its average achievable throughput
to its average energy consumption [37], [38]. In what follows,
we calculate the energy efficiency of the proposed model
and then formulate an optimization problem that enables
the calculation of the optimal values of ε,µ,αand τ
that maximize the energy efficiency, under PU interference
and energy harvesting constraints. It is noted that due
to the presence of the sensing mechanism, the average
achievable throughput depends on the sensing accuracy and
the communication link between PT and ST. This can be
categorized into the following four scenarios, which are
summarized in Table I. Here, P(H0)and P(H1)denote
the prior probabilities of the PT being inactive and active,
respectively.
S1: In this scenario, the ST correctly declares the presence
of the PT with probability P(H1)Pd. Since the licensed
band is occupied and the primary transmission is active, the
throughput in this case is achieved due to ST using only the
ABC mode, and is given by [17]
Rb,S1= (1 −α)τ Bb,(3)
where Bbis the achievable backscatter rate in the ABC mode.
It is worth noting that in this scenario, the SR should
be able to decode the data without using power-demanding
components such as analog to digital converter (ADC) and
oscillators. An ultra low power receiver should be utilized to
decode the modulated signal [39]. The receiver strategy pro-
posed in [39], namely the averaging mechanism, requires only
an envelope average and threshold calculator. The envelope
circuit first smoothes the average of the received signals, and
then a threshold value based on two signal levels is calculated.
Finally, the smoothened signal strengths are compared with
this selected threshold to detect bits 1 and 0, followed by
decoding.
S2: In this scenario, the ST incorrectly declares the PT to
be active with probability P(H0)Pf. This results to a lack
of throughput since the CR network achieves no throughput
by operating in the ABC mode. Furthermore, ST misses a
transmission opportunity.
S3: In this scenario, the ST incorrectly declares the PT to be
absent, with probability P(H1)(1−Pd); as a consequence, the
ST misses an opportunity to use the ABC mode. Moreover, the
ST transmits to SR in the HTT mode and creates interference
to PT. In the presence of the interference from PT, the CR
network achieves a partial throughput of
Rh,S3=µτκW log21 + Ptr
ZIPT,P U +P0,(4)
with a partial throughput factor κ∈(0,1), which quantifies
the partial throughput achievable in this scenario, where Wis
the bandwidth of the primary link, P0is the ratio between the
noise power N0and gc, the channel gain coefficient between
ST and SR, that is P0=N0
gc,Ptr denotes the transmit power of
the ST in the data transmission period µτ ∈(0, τ ), as shown
in Fig. 1(b), ZIdenotes the ratio of the channel gain between
the PT and the ST to gc, and PT ,PU denotes the transmission
power of the PU.
5
TABLE I
AVER AGE A CH IE VAB LE T HR OU GH P UT A ND THE AVE RAGE E NE RG Y CON SU MP TIO N FO R D IFF ER EN T COM MU NI CATIO N SC ENA RI OS IN A BC -HT T-B AS ED
CR N ET WO RK .
Scenarios Harvested Energy Consumed Energy Throughput
P(H1)Pdα τ PRPs(1 −τ)Rb= (1 −α)τ Bb
P(H0)Pf0Ps(1 −τ)0
P(H1)(1 −Pd)0Ps(1 −τ) + Ptrµτ Rh=κµτ W log2(1 + Ptr
ZIPT,P U +P0), κ ∈(0,1)
P(H0)(1 −Pf)0Ps(1 −τ) + Ptrµτ Rh=µτ W log2(1 + Ptr
P0)
Next, Ptr can be expressed as
Ptr =Eh−Es−Ec
µτ ,(5)
where Es=Ps(1−τ)is the energy consumed during sensing,
Ec=µτPcis the energy consumption of the circuitry in
the transmission time µτ ,Eh=ατ PRis the total harvested
energy, and PRis the harvested RF power obtained from
the PT signal at the ST, which is determined from the Friis’
equation as follows [40] :
PR=δPT ,P U
GTGRλ2
(4πd)2,(6)
where δ∈[0,1] is the energy harvesting efficiency, GTis
the PT antenna gain, GRis the ST antenna gain, λis the
wavelength of the emitted wave, and dis the distance between
the PT and ST. Based on the above, it follows that
Rh,S3=µτκW log21 + ατ PR−µτPc−Ps(1 −τ)
[ZIPT,P U +P0]τµ .
(7)
S4: In this scenario, the ST correctly declares the PT to be
inactive with probability P(H0)(1 −Pf), and hence the CR
network achieves the maximum achievable throughput in the
HTT mode, namely
Rh,S4=µτW log21 + Ptr
P0.(8)
Hence, substituting (5) into (8) yields
Rh,S4=µτW log21 + ατ PR−µτPc−Ps(1 −τ)
P0.
(9)
Considering the above four scenarios, the average through-
put of the ABC-HTT-based CR network is given by
R(τ, α, µ, ε) = P(H1)Pd(1−α)τBb+κP (H1)(1 −Pd)
µτ W log21+ Ptr
ZIPT,P U +P0
+P(H0)(1 −Pf)µτ W log21+Ptr
P0,(10)
which can be equivalently expressed as
R(τ, α, µ, ε) = Rb(τ , α, µ, ε) + Rh(τ, α, µ, ε),(11)
where Rb(τ, α, µ, ε)denotes the average achievable through-
put of the CR network in the ABC mode, given by
Rb(τ, α, µ, ε),P(H1)Pd(1 −α)τ Bb,(12)
and Rh(τ, α, µ, ε)denotes the average achievable throughput
of the CR network in the HTT mode, given by
Rh(τ, α, µ, ε),κP (H1)(1 −Pd)
µτ W log21+ Ptr
ZIPT,P U +P0
+P(H0)(1 −Pf)µτ W log21+Ptr
P0.(13)
It is noted that in order for the throughput to be non-
negative, the harvested energy should be greater than the con-
sumed energy. Thus, this requirement imposes the following
constraint
Eh=ατPR≥Ec+Es,(14)
which implies that
α≥Ec+Es
τ PR
.(15)
Denoting α†,(Ec+Es)/(τ PR)as the minimum energy
harvesting time to obtain enough energy for the ST to operate
in the HTT mode, we have the constraint that α∈[α†,1].
In other words, Rh(τ, α, µ, ε)>0, only when α∈[α†,1];
otherwise, Rh(τ, α, µ, ε) = 0, that is
Rh(τ, α, µ, ε)
=
κP (H1)(1 −Pd)µτ W log21+ Ptr
ZIPT,P U +P0
+P(H0)(1 −Pf)µτ W log21+Ptr
P0,if α†≤α≤1,
0,otherwise.
(16)
By recalling that Psdenotes the power required by ST to
perform sensing, the average energy consumption in the CR
network, from Table I, is given by
E(τ, α, µ, ε) = Eb(τ , α, µ, ε) + Eh(τ, α, µ, ε)(17)
=Ps(1 −τ) + µτPtr {P(H1)(1 −Pd)
+P(H0)(1 −Pf)},(18)
where Eb(τ, α, µ, ε)and Eh(τ , α, µ, ε)denote the energy
consumed by the CR network, while operating in the ABC
mode and HTT mode, respectively.
In the same context, the energy efficiency of the CR
network, in bits/Hz/J, is defined as
EE(τ, α, µ, ε),R(τ, α, µ, ε)
E(τ, α, µ, ε),
=EEb(τ , α, µ, ε) + EEh(τ, α, µ, ε),(19)
6
where
EEb(τ , α, µ, ε),Rb(τ, α, µ, ε)
E(τ, α, µ, ε)(20)
and
EEh(τ , α, µ, ε),Rh(τ, α, µ, ε)
E(τ, α, µ, ε),(21)
denote the energy efficiency values due to the ST operating
in ABC and HTT modes, respectively. Furthermore, the con-
straint α∈[α†,1] yields the following condition on the overall
energy efficiency.
EE(τ, α, µ, ε)
=(EEb(τ, α, µ, ε) + EEh(τ , α, µ, ε),if α†≤α≤1,
EEb(τ , α, µ, ε),otherwise.
(22)
B. Problem Formulation: Energy Efficiency Maximization
In what follows, we describe an optimization problem
in order to determine the optimal values of the parameters
ε,µ,αand τ, such that the energy efficiency of the CR
network is maximized. To this end, we formulate the following
maximization problem, subject to the interference constraint
on the primary network and energy harvesting constraint.
OP : max
τ,µ,α,ε EE(τ, α, µ, ε)
s.t. Pf≤Pf,for some Pf∈(0,1)
Pd≥Pd,for some Pd∈(0,1)
α†≤α≤1,
0≤µ≤1,
0≤τ≤1.(23)
In the next section, we provide the detailed solution of the
above optimization problem.
IV. PER FOR MA N CE A N D ENE RGY EFFI CI E NC Y
OPT IM IZATIO N
In the following theorem, we derive the optimal value of the
detection threshold, ε∗, that satisfies the primary interference
constraint given in problem OP.
Theorem 1. The optimal threshold ε∗for the problem in OP
is obtained when the constraint Pd≥Pdis satisfied with
equality, namely
ε∗=σ2"(γ+1) + s2γ+ 1
(1 −τ)Ns
Q−1Pd#.(24)
Proof. The proof is provided in Appendix A.
In what follows, Theorem 2 shows that when the spectrum
is sensed to be idle, the energy efficiency is maximized when
the ST transmits for the entire data transmission period, that
is, when µ= 1.1
1It is worth noting that in the energy efficiency equation, only
EEh(τ , α, µ, ε∗)depends on µ.
Theorem 2. When α†≤1and α≥α†, the energy efficiency
due to the harvest-and-transmit mode, i.e., EEh(τ , α, µ, ε∗)is
maximum for µ∗= 1.
Proof. The proof is provided in Appendix B.
In the same context, Theorem 3 allows the determination of
the conditions on the backscattering communication rate, such
that an optimal value of α, denoted by α∗, exists between α†
and 1, and provides an analytic expression for α∗, when the
interference from the PU is neglected. The existence of α∗
can be determined similarly for the case that includes the
interference term, but it yields intractable results since the
derivation of a closed form solution is infeasible.
Theorem 3. When α†≤α≤1and the backscatter
transmission rate Bb∈(Bb,LB, Bb,U B ), where
Bb,LB ,P(H0)
P(H1)(1 −Pf)
Pdln 2
×µτ W τPR
(P0−Pc)µτ +Ps(1 −τ) + τPR,(25)
and
Bb,UB ,P(H0)
P(H1)(1 −Pf)
Pdln 2
×µτ W τPR
(P0−Pc)µτ +Ps(1 −τ) + α†τPR,(26)
and the interference from the PU is neglected, then, there exists
an optimal solution α∗∈[α†,1], given by
α∗=P(H0)
P(H1)(1 −Pf)
PdµτW
ln 2
−(P0+Pc)τµ +Ps(1 −τ)
τPR.(27)
Proof. The proof is provided in Appendix C.
Once the optimal values ε∗,µ∗and α∗are determined, we
need to determine the optimal value of τ, denoted by τ∗, which
accounts for the data transmission duration. In the following
theorem, we show that the function EE(τ , α∗, µ∗, ε∗)is
concave in τ, and therefore, τ∗can be determined by standard
methods, such as steepest gradient techniques.
Theorem 4. The function EE(τ , α∗, µ∗, ǫ∗)is concave in τ.
Proof. The proof is provided in Appendix D.
Finally, the maximum energy efficiency can be evaluated as
follows:
EEmax (τ∗, α∗, µ∗, ε∗)
=
max [EEb(τ∗,0, µ∗, ε∗),
EEb(τ∗, α∗, µ∗, ε∗) + EEh(τ∗, α∗, µ∗, ε∗)] ,
if α†≤α∗≤1,
EEb(τ∗,0, µ∗, ε∗),otherwise.
(28)
7
0
6.5
0.4
7
sensing time (1- )
Energy efficiency (Bits/s/Hz/J)
106
0.5
7.5
0.6
Energy harvesting time ( )
8
0.8 1
16.8
7
7.2
7.4
7.6
7.8
8
106
Fig. 2. Variation of energy efficiency with αand τ, for µ∗= 1 and ε∗in
(24). Energy efficiency is concave in both αand τ.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Data transmission time ( )
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
Energy efficiency (bits/s/Hz/J)
106
Fig. 3. Variation of the energy efficiency EE(τ , α∗, µ∗, ε∗)with the data
transmission time, τ, for different SNR values.
V. NUM ERI CA L RESU LTS
In this section, we present the numerical results on the
performance of the ABC-HTT-based CR network. To this end,
we consider the following parameters: the target probability of
detection, Pd, and false-alarm probability, Pf, are set to be
0.9and 0.1, respectively [36], whereas the prior probabilities
P(H0)and P(H1)are set to 0.75 and 0.25, respectively.
The signal bandwidth and the transmitted power are set to
be 6MHz, and 17 kW, respectively [17]. Also, without a
loss of generality and unless stated otherwise, we assume
the following values: The number of observations is 2000,
Bb= 50 ×103bps, SNR = −10 dB, κ= 1,Ps= 1 mW,
Pc= 0.1mW, δ= 0.6,d= 2.475 km, GT=GR= 6
dBi in the Friis’ equation, such that PR= 0.25 W, and the
path loss and other impairments due to primary interference
Xl= 0.5×10−3.
Figure 2 shows the variation of the energy efficiency with
respect to the parameters αand τ, with µ∗= 1 and ε∗chosen
according to (24). The sampling frequency is chosen such that
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Energy harvesting time ( )
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Energy efficiency (bits/s/Hz/J)
106
Fig. 4. Variation of the energy efficiency EE (τ , α∗, µ∗,ε∗)with α, for
different values of τ.
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4
SNR (dB)
8
8.05
8.1
8.15
8.2
8.25
Optimal energy efficiency (bits/s/Hz/J)
106
Fig. 5. Variation of the optimal energy efficiency EE (τ∗, α∗, µ∗, ε∗)with
SNR, for different values of number of samples Ns. An increase in the
sampling frequency for a fixed τincreases the number of samples.
the number of samples is 1000, and the sensing power Ps=
0.3mW. Also, we set the partial throughput factor, κ= 0.6,
and the energy harvesting efficiency, δ= 0.6. It is evident that
the energy efficiency is concave with respect to both αand
τ. Also, for a small value of α, the energy efficiency is small
since the throughput decreases due to little energy harvesting.
However, if ST spends more time on energy harvesting, i.e., if
αincreases, the energy efficiency decreases further since the
backscattering communication is not efficiently utilized.
Figure 3 illustrates the variation of the value of
EE(τ, α∗, µ∗, ε∗)with τfor different SNR values. As ex-
pected, the energy efficiency increases with SNR. Moreover,
the value of optimum τalso increases with SNR, since a
larger SNR results in lower sensing time required to satisfy
the primary interference constraints and thus, to a higher
data transmission time. Similarly, Figure 4 demonstrates the
variation of the value of EE(τ , α, µ∗, ε∗)for different values
of τ. It is evident that the optimal α∗exists for each τ, and
it decreases with an increase in τ, which is clear from (27).
Moreover, it is intuitive to note that as τincreases, the energy
8
-15 -10 -5 0 5
SNR (dB)
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
Energy Efficiency (bits/s/Hz/J)
106
Fig. 6. Variation of the optimal energy efficiency EE(τ∗, α∗, µ∗, ε∗)with
SNR, for different values of Pd.
-25 -20 -15 -10 -5 0 5 10
SNR in dB
1
2
3
4
5
6
7
8
9
Optimal thoughput (bits/s/Hz)
106
0
0.5
1
1.5
2
2.5
3
Optimal energy consumed (J)
Fig. 7. Variation of the optimal achievable throughput and optimal average
energy consumption with SNR, for different values of Pd. Although a relaxed
constraint with Pdimproves the achievable throughput, it also allows an
increase in the energy consumption due to more transmission opportunities,
which is significant at low SNR values.
efficiency increases.
Figure 5 illustrates the variation of the optimal energy
efficiency for different values of the received SNR at ST, for a
number of samples Ns=500,Ns=1000 and Ns=2000. It is
shown that as the number of samples increases, the detection
accuracy increases, which improves the secondary throughput
and the energy efficiency. Likewise, Figure 6 presents the
variation of the optimal energy efficiency with respect to SNR
for different target probability of detection values, Pd. It is
noted here that the performance is expected to increase with a
decrease in Pd, since a lower tolerance on the probability
of detection improves the average throughput and energy
consumption. However, the plots exhibit a different trend. For
example, Figure 7 reveals that a lower value of Pdimplies
that the PU interference constraint is more relaxed, which in
turn yields a better throughput. However, since a lower value of
Pdalso results in more transmission opportunities, the average
energy consumption also increases, which is significant at the
0 1 2 3 4 5
Transmission rate of backscattering mode Bb (bits/sec) 106
0
2
4
6
8
10
Optimal energy efficiency (bits/s/Hz/J)
106
ABC mode
HTTP mode
ABC mode+HTTP mode
Fig. 8. Variation of the optimal energy efficiency EE (τ∗, α∗, µ∗, ε∗)with
different values of ABC rates, Bb. Using only the HTT mode yields better
performance for small values of Bb. Conversely, using only the ABC mode
performs better for larger values of Bb. Therefore, combining the ABC and
HTT modes yields an overall better performance in terms of energy efficiency,
across all values of Bb.
0 2 4 6 8 10
Transmission rate of backscattering mode Bb (bits/sec) 106
0
2
4
6
8
10
12
14
16
Energy efficiency (bits/s/Hz/J)
106
ABC mode with sensing errors
HTTP mode with sensing errors
ABC mode+HTTP mode with sensing errors
ABC mode without sensing errors
HTTP mode without sensing errors
ABC mode+HTTP mode without sensing errors
Fig. 9. Effect of sensing errors on the optimal energy efficiency. Combining
ABC and HTT modes yields a higher overall energy efficiency.
low SNR regime. Therefore, the trend on variation of EE
with Pddepends largely on the choice of system parameters,
which explains the trend observed in Figure 6. Also, the
optimal energy efficiency saturates after a certain SNR, since
a further improvement in SNR will only improve the detection
performance by a small margin, resulting in little improvement
in the overall energy efficiency.
Figure 8 demonstrates the variation of the optimal en-
ergy efficiency EE(τ∗, α∗, µ∗, ε∗)with different values of
backscattering communication rates, Bbfor the indicative
values of Ns= 1000, and PR= 1 W. It is evident that the
achievable rate due to energy harvesting is not dependent upon
Bb. Also, for lower values of Bb, using the HTT mode alone
yields a better energy efficiency, whereas for larger values of
Bb, the ABC mode exhibits a better performance. Therefore,
9
operating the CR network in a combination of the ABC and
HTT modes yields an improvement in the overall performance
in terms of energy efficiency, across all values of Bb.
Finally, Figure 9 illustrates the effect of sensing errors on the
performance of the ABC-HTT-based CR network. In order to
calculate the performance of the system without sensing errors,
we follow the procedure described in [17], which considers the
simplistic case of no sensing errors. By choosing the indicative
values Ns= 2000, and PR= 1 W, it is shown that the
optimal energy efficiency achieved with no sensing errors is,
as expected, higher than the realistic case with present sensing
errors. Additionally, we observe that the energy efficiency
increases in both cases, due to the use of both ABC and HTT
modes. That is, as expected, the energy efficiency achieved due
to only ABC or HTT mode is lower than that obtained by com-
bining the two modes, in the presence and absence of sensing
errors. Moreover, it is recalled that we have set κ= 1. In terms
of energy efficiency, this corresponds to the best possible case
from the CR network point of view. In our formulation, the
choice of κonly affects the average achievable throughput, and
not the energy consumption. Therefore, the energy efficiency
performance deviation in Fig. 9 – between the ABC and HTT
modes with and without sensing errors – constitutes a lower
bound. In fact, choosing any other value of κwill result in a
larger performance deviation.
VI. CO NCL USI ON
We investigated the performance of ABC-HTT-based cog-
nitive radio networks in terms of energy efficiency in the
presence of sensing errors as they are encountered in realistic
wireless communication scenarios. In this context, we derived
novel analytic expressions for the average achievable through-
put, average energy consumption and energy efficiency of
the considered network. Then, we formulated an optimization
problem that maximizes the energy efficiency of the CR net-
work operating in ABC and HTT modes, for a given set of con-
straints including the primary interference constraint. Finally,
we derived the optimal set of parameters that maximize the
energy efficiency of the CR system. Capitalizing on the offered
results, we quantified the performance of the CR network
under the considered setup and demonstrated the performance
improvement achieved in the CR network when incorporating
a combination of ABC and HTT modes. The offered results
provided interesting theoretical and technical insights on the
behavior of backscatter systems that are expected to be useful
in the design and deployment of future systems in the context
of various wireless applications of interest.
APP EN D IX A
PROO F OF THE ORE M 1
In order to establish that the constraint Pd≥Pd
is satisfied with equality, it is sufficient to show that
∂EE(τ, α, µ, ε)/∂ε ≥0, for all ε. To this end, we observe
that
∂EE(τ, α, µ, ε)
∂ε =
∂R(τ ,α,µ,ε)
∂ε E(τ , α, µ, ε)
[E(τ, α, µ, ε)]2
−R(τ, α, µ, ε)∂ E(τ ,α,µ,ε)
∂ε
[E(τ, α, µ, ε)]2.(29)
Furthermore, taking the first derivative of (10) with respect to
ǫ, namely
R(τ, α, µ, ε) = P(H1)Pd(1−α)τBb+κP (H1)(1 −Pd)
µτ W log21+ Ptr
ZIPT,P U +P0
+P(H0)(1 −Pf)µτ W log21+Ptr
P0,(30)
yields
∂R(τ , α, µ, ε)
∂ε =P(H1)(1 −α)τ Bb
∂Pd
∂ε −κµτ W P (H1)
log21+ Ptr
ZIPT,P U +P0
∂Pd
∂ε
−µτ W P (H0) log21+Ptr
P0∂Pf
∂ε ,(31)
and
∂E(τ , α, µ, ε)
∂ε =−µτ Ptr P(H1)∂Pd
∂ǫ +P(H0)∂Pf
∂ǫ .
(32)
Using the above, and substituting (31) and (32) in (29), and
carrying out some algebraic manipulations, one obtains
∂EE(τ, α, µ, ε)
∂ε =∂Pd
∂ε
P(H1)(1 −α)τBb
E(τ, α, µ, ε)
−∂Pd
∂ε P(H1)κµτ W log21 + Ptr
ZIPT,P U +P0
+∂Pd
∂ε µτ PtrP(H1)R(τ, α, µ, ε)
E(τ, α, µ, ε)2
−∂Pf
∂ε P(H0)µτ W log21 + Ptr
P0+µτPtr P(H0)
R(τ, α, µ, ε)
E(τ, α, µ, ε)2.(33)
In addition, it is noted that
∂Pf
∂ε =−exp −(1 −τ)Ns(ǫ
σ2−1)2
2pNs(1 −τ)
√2πσ2≤0,
(34)
and
∂Pd
∂ε =−exp −(1 −τ)Ns(ǫ
σ2−γ−1)2
2(1 + 2γ)qNs(1−τ)
1+2γ
√2πσ2≤0,
(35)
with ∂Pd/∂ε ≥∂Pf/∂ε. Following these results, (33) can be
further simplified and shown to be non-negative if
P(H1)κµτW log21 + Ptr
ZIPT,P U +P0
−1
EP(H1)(1 −α)τBb−µτPtr P(H1)R
E2>0.(36)
10
It is easy to verify that the above requirement holds when W
and Ptr are selected such that
W κ log 1 + Ptr
P0≥1
Eµ (1 −α)Bb+Ptr
R
E2,(37)
in which case, ∂EE/∂ε ≥0, for all ε. Based on this result,
it is sufficient to choose the value of εwhen Pd=Pdis
satisfied.
APP EN D IX B
PROO F OF THE ORE M 2
As mentioned earlier, we consider only the term
EEh(τ , α, µ, ε∗), since EEb(τ, α, µ, ε∗)is independent of µ.
Next, it is noted that which upon substituting the expression
for Ptr from (5) yields (39). Compactly, (39) can be re-written
as
EEh(τ , α, µ, ε∗) =
X1µlog2hB+A
µi+X2µlog2hD+C
µi
X3+X4µ,
(40)
where
X1,κP (H1)(1−Pd)τW, (41)
X2,P(H0)(1−Pf)τW, (42)
X3,Ps(1 −τ),(43)
X4,τPtr {P(H1)(1 −Pd) + P(H0)(1 −Pf)},(44)
A,αPR−Ps(1−τ)
[ZIPT,P U +P0]τ,(45)
B,1−Pc
[ZIPT,P U +P0],(46)
C,ατPR−Ps(1 −τ)
P0τ,(47)
and
D,1−Pc
P0
,(48)
such that X1,X2,X3,X4,A,B,Cand Dare posi-
tive constants. Next, by evaluating the first derivative of
EEh(τ , α, µ, ε∗)with respect to µit follows that
∂EEh(τ, α, µ, ε∗)
∂µ =
∂Rh(τ ,α,µ,ε∗)
∂µ Eh(τ , α, µ, ε∗)
[Eh(τ, α, µ, ε∗)]2
−Rh(τ, α, µ, ε∗)
∂Eh(τ ,α,µ,ε∗)
∂µ
[Eh(τ, α, µ, ε∗)]2,(49)
where
∂Rh(τ , α, µ, ε∗)
∂µ =X1(−A
µ(B+A
µ) ln(2)+log2B+A
µ)
+X2(−C
µ(D+C
µ) ln(2)+log2D+C
µ),(50)
and
∂Eh(τ , α, µ, ε∗)
∂µ =τ Pt1−P(H1)Pd−P(H0)Pf.(51)
Substituting (50) and (51) in (49), we get
∂EEh(τ, α, µ, ε∗)
∂µ =
X1−A
µ(B+A
µ) ln(2)+log2B+A
µ
(X3+X4µ)2
+
X2−C
µ(D+C
µ) ln(2)+log2D+C
µ
(X3+X4µ)2.(52)
Based on this, we observe that
lim
µ→+∞
∂EEh(τ, α, µ, ε∗)
∂µ
= lim
µ→+∞
(X1+X2)X3
µ+X4(X1+X2) + X1+X2
µPs(1−τ)
µ+X4µ2= 0.
(53)
Moreover, the second derivative of EEh(τ, α, µ, ε∗)with
respect to µcan be expressed as follows:
∂2EEh(τ , α, µ, ε∗)
∂µ2
=−x1A
E(A+Bµ) ln 2 +
x1τW log2A
µ+B
E
−x2C
E(C+Dµ) ln 2 +
x2τW log2C
µ+D
E
−
x4nx1µlog(A
µ+B) + x2µlog( C
µ+D)o
[x3+µx4]2.(54)
Carrying out some long but straightforward algebraic manip-
ulations, it can be shown that ∂2EEh(τ ,α,µ,ε∗)
∂µ2≤0. Hence,
EEh(τ , α, µ, ε∗)is an increasing function of µ, which implies
that µ∗= 1.
APP EN D IX C
PROO F OF THE ORE M 3
Let us define
y1,1−Pcµτ
[ZIPT,P U +P0]τ µ ,(55)
y2,τPR−Ps(1 −τ)
[ZIPT,P U +P0]τ µ ,(56)
y3,1−Pc
P0−Ps(1 −τ)
P0τµ ,(57)
and
y4,τPR
P0τ µ ,(58)
11
EEh(τ , α, µ, ε∗) =
κP (H1)(1 −Pd)µτ W log21+ Ptr
ZIPT,P U +P0
Ps(1−τ)+µτPt{1−P(H1)Pd−P(H0)Pf}
+
P(H0)(1 −Pf)µτ W log21+Ptr
P0
Ps(1−τ)+µτPt{1−P(H1)Pd−P(H0)Pf}.(38)
EEh(τ , α, µ, ε∗) =
κP (H1)(1 −Pd)µτ W log21 + ατ PR−µτ Pc−Ps(1−τ)
[ZIPT,P U +P0]τ µ
Ps(1−τ)+µτPt{1−P(H1)Pd−P(H0)Pf}
+
P(H0)(1 −Pf)µτ W log21 + ατ PR−µτ Pc−Ps(1−τ)
[P0]τ µ
Ps(1−τ)+µτPt{1−P(H1)Pd−P(H0)Pf}.(39)
such that y1,y2,y3, and y4are positive constants. Then, the
expression for energy efficiency is expressed as
EE(τ, α, µ∗, ε∗) = EEb(τ, α, µ∗, ε∗)+EEh(τ, α, µ∗, ε∗),
=Rb(τ, α, µ∗, ε∗)
E(τ, α, µ∗, ε∗)+Rh(τ , α, µ∗, ε∗)
E(τ, α, µ∗, ε∗)
=P(H1)Pd(1 −α)τBb
E(τ, α, µ∗, ε∗)
+P(H1)(1 −Pd)κµτW log2[y1+αy2]
E(τ, α, µ∗, ε∗)
+P(H0)(1 −Pf)µτW log2[y3+αy4]
E(τ, α, µ∗, ε∗).(59)
Now, consider the first derivative of EE (τ , α, µ∗, ε∗)with
respect to α, that is, ∂EE(τ , α, µ∗, ε∗)/∂α, which is given
by
∂EE(τ, α, µ∗, ε∗)
∂α =P(H1)(1 −Pd)κµτ W
ln 2
y2
y1+αy2
E(τ, α, µ∗, ε∗)
−P(H1)PdτBb
E(τ, α, µ∗, ε∗)+P(H0)(1 −Pf)µτ W
ln 2
y3
y1+αy4
E(τ, α, µ∗, ε∗).(60)
Likewise, the second derivative of EE (τ , α, µ∗, ε∗)is given
by
∂2EE(τ, α, µ∗, ε∗)
∂α2=∂2EEh(τ, α, µ∗, ε∗)
∂α2,
=−P(H1(1 −Pd)κ
E
µτW
ln 2
y2
2
(y1+αy2)2
−P(H0)(1 −Pf)
E
µτW
ln 2
y2
4
(y1+αy2)2<0(61)
From (60) and (61), we can infer that ∂EE(τ, α, µ∗, ε∗)/∂α
is a decreasing function of α. Furthermore, to guaran-
tee that there exist a value of α∈[α†,1] such that
EE′
ABC (τ, α, µ∗, ε∗) = 0, we calculate the following bound-
ary values. To this effect, observing that when α=α†, it
follows that
∂EE(τ, α†, µ∗, ε∗)
∂α =P(H1)(1 −Pd)κµτ W
ln 2
y2
y1+α†y2
E(τ, α, µ∗, ε∗)
−P(H1)PdτBb
E(τ, α, µ∗, ε∗)+P(H0)(1 −Pf)µτ W
ln 2
y3
y1+α†y4
E(τ, α, µ∗, ε∗)≥0,
(62)
whereas when α= 1, we get
∂EE(τ, 1, µ∗, ε∗)
∂α =P(H1)(1 −Pd)κµτ W
ln 2
y2
y1+y2
E(τ, α, µ∗, ε∗)
−P(H1)PdτBb
E(τ, α, µ∗, ε∗)+P(H0)(1 −Pf)µτ W
ln 2
y3
y1+y4
E(τ, α, µ∗, ε∗)≤0.
(63)
Therefore, there exists an α∗∈[α†,1] where the derivative
∂EE(τ, α†, µ∗, ε∗)
∂α is exactly 0. Thus, the bounds on Bb
are obtained by equating the expression in (60) to zero,
and rearranging accordingly, yielding Eq.(64). If the effective
interference from the PU is neglected, then
Bb=P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2
×τPR
(P0−Pc)µτ +Ps(1 −τ) + ατPR
.(65)
Now, the upper and lower bounds on Bb, namely, Bb,LB and
Bb,UB can be obtained by substituting for the value of α
corresponding to the two extreme cases 1and α†, respectively.
These bounds are given by
Bb,LB ,P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2 (66)
×τPR
(P0−Pc)µτ +Ps(1 −τ) + τPR
,
Bb,UB ,P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2
×τPR
(P0−Pc)µτ +Ps(1 −τ) + α†τPR
.(67)
Therefore, when Bb∈(Bb,LB , Bb,U B ),EE(τ, α, µ∗, ε∗)is
concave in α. Finally, the optimal α∗∈[α†,1], can be obtained
12
Bb=1−Pd
Pd
κµτW
ln 2
τPR−Ps(1 −τ)
[ZIPT,P U +P0−Pc]τµ +α(τ PR−Ps(1 −τ))
+P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2
τPR
(P0−Pc)µτ +Ps(1 −τ) + ατPR
.(64)
∂EEb(τ, α∗, µ∗, ε∗)
∂τ =
P(H1)PdBbn1−α−τ∂α∗
∂τ o
[E(τ, α∗, µ∗, ε∗)]
+P(H1)Pd(1 −α)τBbn−Ps+µPtr hP(H1)(1 −Pd)κ−P(H0)τ∂Pf
∂τ +P(H0)(1 −Pf)io
[E(τ, α∗, µ∗, ε∗)]2.(82)
∂EEh(τ, α∗, µ∗, ε∗)
∂τ =1
E(τ, α∗, µ∗, ε∗)P(H1)(1 −Pd)κµW w2
2
τw1−w2
+ log(w1−w2
τ)
−1
E(τ, α∗, µ∗, ε∗)(1 −Pf)w4w3
ln 2(τw3−w4)2−1
E(τ, α∗, µ∗, ε∗∂ Pf
∂τ w4
ln 2(τw3−w4)
−1
E(τ, α∗, µ∗, ε∗)∂Pf
∂τ log(w3−w4
τ) + 1
E(τ, α∗, µ∗, ε∗)(1 −Pf)w4
τ(τw3−w4)τln 2
−1
E(τ, α∗, µ∗, ε∗)2−Ps+µPtr P(H1)(1 −Pd)κ−P(H0)τ∂Pf
∂τ +P(H0)(1 −Pf)
nP(H1)(1 −Pd)κµτW log2hw1−w2
τi+P(H0)(1 −Pf)µτW log2hw3−w4
τio.(83)
by neglecting the interference term and equating the first
derivative to zero, which is expressed as
α∗=P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2 −y3
y4
,(68)
for Bb∈(Bb,LB , Bb,UB ). Based on this, by substituting for y3
and y4, we obtain
α∗=P(H0)
P(H1)
(1 −Pf)
Pd
µτW
ln 2
−(P0+Pc)τµ +Ps(1 −τ)
τPR
.(69)
APP EN D IX D
PROO F OF THE ORE M 4
Let us define
w1,1 + αPR−µPc+Ps
[ZIPT,P U +P0]µ,(70)
w2,Ps
[ZIPT,P U +P0]µ,(71)
w3,1 + αPR−µPc+Ps
P0µ,(72)
and
w4,Ps
P0µ,(73)
such that w1,w2,w3, and w4are positive constants. Then, the
expression for energy efficiency can be simplified as
EE(τ, α∗, µ∗, ε∗) = P(H1)Pd(1 −α∗)τBb
E(τ, α, µ∗, ε∗)
+P(H1)(1 −Pd)κµτW log2w1−w2
τ
E(τ, α, µ∗, ε∗)
+P(H0)(1 −Pf)µτW log2w3−w4
τ
E(τ, α, µ∗, ε∗).
(74)
Next, we determine the first derivative of EE(τ, α∗, µ∗, ε∗))
with respect to τi.e. ∂EE(τ, α∗, µ∗, ε∗)/∂τ, upon which it
is clear that
∂EE(τ, α∗, µ∗, ε∗)
∂τ =∂EEb(τ, α∗, µ∗, ε∗)
∂τ
+∂EEh(τ, α∗, µ∗, ε∗)
∂τ .(75)
By rewriting α∗in (27) in terms of τas
α∗=L1
(1 −Pf)
Pd
τ−L2−L31
τ−1,(76)
where
L1,P(H0)
P(H1)
µW
ln2≥0,(77)
L2,(P0+Pc)µ
PR≥0,(78)
and
L3,Ps
PR≥0,(79)
13
the derivative of α∗can be calculated as
∂α∗
∂τ =−L1P′
f
Pd−L1(1 −Pf)P′
d
P2
d
+L3
τ2.(80)
Substituting (76) and (80) in (75), and observing that
Pd=Pdat ε=ε∗,we obtain ∂EEb(τ , α∗, µ∗, ε∗)/∂τ and
∂EEh(τ, α∗, µ∗, ε∗)/∂τ, as given in (82) and (83), respec-
tively. In addition, it is straightforward to calculate the first
derivative of Pfwith respect to τas
∂Pf
∂τ =ε∗
σ2−1
p8π2Ns(1−τ)exp −Ns(1−τ)
2ε∗
σ2−12!,
(81)
and it is intuitive that the second derivative of Pfwith respect
to τwould be negative, since Pfis concave in τ. Utilizing
this result, the rest of the proof involves calculation of the sec-
ond derivatives of EEb(τ , α∗, µ∗, ε∗)and EEh(τ, α∗, µ∗, ε∗),
and showing them to be negative. Therefore, the second
derivative of EE(τ , α∗, µ∗, ε∗)is also negative, and hence
EE(τ, α∗, µ∗, ε∗)is concave in τ. The corresponding details
lead to expressions that are rather lengthy, which are omitted
for brevity.
REF ERE NC ES
[1] R. Kishore, S. Gurugopinath, P. C. Sofotasios, S. Muhaidat, and
N. Al-Dhahir, “Opportunistic ambient backscatter communication in RF-
powered cognitive radio networks,” in 2016 IEEE Wireless Communi-
cations and Networking Conference (WCNC), Apr. 2019, pp. 1–6.
[2] J. Mitola and G. Q. Maguire, “Cognitive radio: Making software radios
more personal,” IEEE Personal Commun. Mag., vol. 6, no. 4, pp. 13–18,
Aug. 1999.
[3] E. Axell, G. Leus, E. G. Larsson, and H. V. Poor, “Spectrum sensing
for cognitive radio : State-of-the-art and recent advances,” IEEE Signal
Process. Mag., vol. 29, no. 3, pp. 101–116, May 2012.
[4] O. Altrad, S. Muhaidat, A. Al-Dweik, A. Shami, and P. D. Yoo, “Op-
portunistic spectrum access in cognitive radio networks under imperfect
spectrum sensing,” IEEE Trans. Veh. Technol., vol. 63, no. 2, pp. 920–
925, Feb. 2014.
[5] N. U. Hasan, W. Ejaz, N. Ejaz, H. S. Kim, A. Anpalagan, and M. Jo,
“Network selection and channel allocation for spectrum sharing in 5G
heterogeneous networks,” IEEE Access, vol. 4, pp. 980–992, Feb. 2016.
[6] M. Usman and I. Koo, “Access strategy for hybrid underlay-overlay
cognitive radios with energy harvesting,” IEEE Sensors J., vol. 14, no. 9,
pp. 3164–3173, Sep. 2014.
[7] A. Goldsmith, S. A. Jafar, I. Maric, and S. Srinivasa, “Breaking spectrum
gridlock with cognitive radios: An information theoretic perspective,”
Proc. IEEE, vol. 97, no. 5, pp. 894–914, May 2009.
[8] M. Costa and A. Ephremides, “Energy efficiency versus performance
in cognitive wireless networks,” IEEE J. Sel. Areas Commun., vol. 34,
no. 5, pp. 1336–1347, May 2016.
[9] L. Zhang, M. Xiao, G. Wu, S. Li, and Y. C. Liang, “Energy-efficient
cognitive transmission with imperfect spectrum sensing,” IEEE J. Sel.
Areas Commun., vol. 34, no. 5, pp. 1320–1335, May 2016.
[10] M. R. Mili, L. Musavian, K. A. Hamdi, and F. Marvasti, “How to
increase energy efficiency in cognitive radio networks,” IEEE Trans.
Commun., vol. 64, no. 5, pp. 1829–1843, May 2016.
[11] R. Kishore, C. K. Ramesha, S. Gurugopinath, and K. R. Anupama,
“Performance analysis of superior selective reporting-based energy ef-
ficient cooperative spectrum sensing in cognitive radio networks,” Ad
Hoc Networks, vol. 65, pp. 99 – 116, Oct. 2017.
[12] H. Hu, H. Zhang, and Y. C. Liang, “On the spectrum- and energy-
efficiency tradeoff in cognitive radio networks,” IEEE Trans. Commun.,
vol. 64, no. 2, pp. 490–501, Feb. 2016.
[13] N. I. Miridakis, T. A. Tsiftsis, G. C. Alexandropoulos, and M. Debbah,
“Green cognitive relaying: Opportunistically switching between data
transmission and energy harvesting,” IEEE J. Sel. Areas Commun.,
vol. 34, no. 12, pp. 3725–3738, Dec. 2016.
[14] A. E. Shafie, N. Al-Dhahir, and R. Hamila, “A sparsity-aware coop-
erative protocol for cognitive radio networks with energy-harvesting
primary user,” IEEE Trans. Commun., vol. 63, no. 9, pp. 3118–3131,
Sep. 2015.
[15] J. Ren, J. Hu, D. Zhang, H. Guo, Y. Zhang, and X. Shen, “RF energy
harvesting and transfer in cognitive radio sensor networks: Opportunities
and challenges,” IEEE Commun. Mag., vol. 56, no. 1, pp. 104–110, Jan.
2018.
[16] S. H. Kim and D. I. Kim, “Hybrid backscatter communication for
wireless-powered heterogeneous networks,” IEEE Trans. Wireless Com-
mun., vol. 16, no. 10, pp. 6557–6570, Oct. 2017.
[17] D. T. Hoang, D. Niyato, P. Wang, D. I. Kim, and Z. Han, “Ambient
backscatter: A new approach to improve network performance for RF-
powered cognitive radio networks,” IEEE Trans. Commun., vol. 65,
no. 9, pp. 3659–3674, Sep. 2017.
[18] L. R. Varshney, “Transporting information and energy simultaneously,”
in Proc. IEEE Int. Symp. Inf. Theory, Jul. 2008, pp. 1612–1616.
[19] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networks
with RF energy harvesting: A contemporary survey,” IEEE Commun.
Surveys Tuts., vol. 17, no. 2, pp. 757–789, Nov. 2015.
[20] T. D. P. Perera, D. N. K. Jayakody, S. K. Sharma, S. Chatzinotas, and
J. Li, “Simultaneous wireless information and power transfer (SWIPT):
Recent advances and future challenges,” IEEE Commun. Surveys Tuts.,
vol. 20, no. 1, pp. 264–302, Dec. 2018.
[21] J. Yan and Y. Liu, “A dynamic SWIPT approach for cooperative
cognitive radio networks,” IEEE Trans. Veh. Commun., vol. 66, no. 12,
pp. 11 122–11 136, Dec. 2017.
[22] F. Benkhelifa, K. Tourki, and M. S. Alouini, “Proactive spectrum sharing
for SWIPT in MIMO cognitive radio systems using antenna switching
technique,” IEEE Trans. Green Commun. Netw., vol. 1, no. 2, pp. 204–
222, Jun. 2017.
[23] A. A. Al-habob, A. M. Salhab, S. A. Zummo, and M. S. Alouini, “Multi-
destination cognitive radio relay network with SWIPT and multiple
primary receivers,” in Proc. WCNC, Mar. 2017, pp. 1–6.
[24] J. F. Ensworth and M. S. Reynolds, “BLE-Backscatter: Ultralow-power
IoT nodes compatible with bluetooth 4.0 low energy (BLE) smartphones
and tablets,” IEEE Trans. Microw. Theory Tech., vol. 65, no. 9, pp. 3360–
3368, Sep. 2017.
[25] S. Shao, A. Khreishah, and H. Elgala, “Pixelated VLC-backscattering for
self-charging indoor IoT devices,” IEEE Photon. Technol. Lett., vol. 29,
no. 2, pp. 177–180, Jan. 2017.
[26] N. V. Huynh, D. T. Hoang, X. Lu, D. Niyato, P. Wang, and D. I. Kim,
“Ambient backscatter communications: A contemporary survey,” IEEE
Commun. Surveys Tuts., vol. 20, no. 4, pp. 2889–2922, Fourthquarter
2018.
[27] J. Ren, J. Hu, D. Zhang, H. Guo, Y. Zhang, and X. Shen, “RF energy
harvesting and transfer in cognitive radio sensor networks: Opportunities
and challenges,” IEEE Commun. Mag., vol. 56, no. 1, pp. 104–110, Jan.
2018.
[28] M. E. Ahmed, D. I. Kim, and K. W. Choi, “Traffic-aware optimal
spectral access in wireless powered cognitive radio networks,” IEEE
Trans. Mobile Comput., vol. 17, no. 3, pp. 733–745, Mar. 2018.
[29] F. Benkhelifa and M. S. Alouini, “Prioritizing data/energy thresholding-
based antenna switching for SWIPT-enabled secondary receiver in cog-
nitive radio networks,” IEEE Trans. Cognitive Commun. Netw., vol. 3,
no. 4, pp. 782–800, Dec. 2017.
[30] Y. Wang, Y. Wang, F. Zhou, Y. Wu, and H. Zhou, “Resource allocation
in wireless powered cognitive radio networks based on a practical non-
linear energy harvesting model,” IEEE Access, vol. 5, pp. 17 618–17 626,
Jun. 2017.
[31] B. Clerckx, Z. B. Zawawi, and K. Huang, “Wirelessly powered backscat-
ter communications: Waveform design and SNR-energy tradeoff,” IEEE
Commun. Lett., vol. 21, no. 10, pp. 2234–2237, Oct. 2017.
[32] X. Lu, D. Niyato, H. Jiang, D. I. Kim, Y. Xiao, and Z. Han, “Ambient
backscatter assisted wireless powered communications,” IEEE Trans.
Wireless Commun., vol. PP, no. 99, pp. 2–9, Jan. 2018.
[33] D. Darsena, G. Gelli, and F. Verde, “Modeling and performance analysis
of wireless networks with ambient backscatter devices,” IEEE Trans.
Commun., vol. 65, no. 4, pp. 1797–1814, Apr. 2017.
[34] S. Althunibat, “Towards Energy Efficient Cooperative Spectrum Sensing
in Cognitive Radio Networks,” Ph.D thesis, University of Trento, Trento,
Italy, 2014.
[35] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for
cognitive radio applications,” IEEE Commun. Surveys Tuts., vol. 11,
no. 1, pp. 116–130, Mar. 2009.
14
[36] Y. C. Liang, Y. Zeng, E. C. Y. Peh, and A. T. Hoang, “Sensing-
throughput tradeoff for cognitive radio networks,” IEEE Trans. Wireless
Commun., vol. 7, no. 4, pp. 1326–1337, Apr. 2008.
[37] W. Ejaz, G. A. Shah, N. U. Hasan, and H. S. Kim, “Energy and
throughput efficient cooperative spectrum sensing in cognitive radio
sensor networks,” Trans. Emerging Tel. Tech.,, vol. 26, no. 7, pp. 1019–
1030, Mar. 2015.
[38] S. Althunibat, M. D. Renzo, and F. Granelli, “Optimizing the k-out-of-n
rule for cooperative spectrum sensing in cognitive radio networks,” in
Proc. GLOBECOM, Dec. 2013, pp. 1607–1611.
[39] V. Liu, A. Parks, V. Talla, S. Gollakota, D. Wetherall, and J. R.
Smith, “Ambient backscatter: Wireless communication out of thin air,”
SIGCOMM Comput. Commun. Rev., vol. 43, no. 4, pp. 39–50, Aug.
2013.
[40] C. A. Balanis, Antenna Theory: Analysis and Design. Wiley-
Interscience, 2005.
