Performance analysis of underlay cooperative cognitive full-duplex networks with energy-harvesting relay

Accepted Manuscript

Performance analysis of Underlay Cooperative Cognitive Full-duplex Networks with Energy-Harvesting Relay Pham Ngoc Son, Tran Trung Duy PII: DOI: Reference:

S0140-3664(17)30979-9 10.1016/j.comcom.2018.03.003 COMCOM 5660

To appear in:

Computer Communications

Received date: Revised date: Accepted date:

11 September 2017 22 February 2018 6 March 2018

Please cite this article as: Pham Ngoc Son, Tran Trung Duy, Performance analysis of Underlay Cooperative Cognitive Full-duplex Networks with Energy-Harvesting Relay, Computer Communications (2018), doi: 10.1016/j.comcom.2018.03.003

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Performance analysis of Underlay Cooperative Cognitive Full-duplex Networks with Energy-Harvesting Relay

CR IP T

Pham Ngoc Son1 , Tran Trung Duy2

Abstract

In this paper, we propose an underlay cooperative cognitive network (UCCN), where an energyharvesting (EH) two-antenna relay operating on full-duplex (FD) mode is used to assist a secondary source to forward the data to a secondary destination (FDEHSN protocol). In the FDEHSN protocol, the secondary relay harvests the energy from the radio-frequency signals of the secondary source in the

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first interval before performing simultaneously the receiving and transmitting processes in the remaining interval. We derive asymptotic closed-form expressions of outage probability and throughput over Rayleigh fading channel. Contributions show that the FDEHSN protocol outperforms a conventional full-duplex UCCN without using the EH architecture (WoEH protocol) in terms of outage probability and a conventional half-duplex UCCN with using the EH architecture (UCCN-TS protocol) in terms of throughput. When the EH time ratios are obtained by Golden Section Search approach in order to

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minimize the outage performance for the proposed protocol, the throughput of the FDEHSN protocol is enhanced and exceeds that of the WoEH one while the impacts of residual loopback interference

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are serious. In addition, the effects of the energy conversion efficiency and locations of the primary receiver and the secondary relay on the system performance of the secondary network are presented and discussed. Finally, the asymptotic outage probability and corresponding throughput are valid

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with Monte Carlo simulation results.

Keywords: Full-duplex, energy harvesting, cooperative communication, underlay protocol,

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interference constraint, loopback interference

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1. Introduction

Recently, cognitive radio (CR) and full-duplex (FD) techniques have gained much attention as

being promising solutions to obtain spectrum utilization efficiency. In the CR technique [1, 2, 3], unlicensed users or cognitive users in secondary networks opportunistically access frequency spectrum

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of licensed users in primary networks. Underlay CR has emerged as an efficient spectrum sharing 1 Ho Chi Minh City University of Technology and Education, HoChiMinh city, VietNam E-mail: [email protected] (Corresponding author) 2 Posts and Telecommunications Institute of Technology, HoChiMinh city, VietNam E-mail: [email protected]

Preprint submitted to Journal of LATEX Templates

March 6, 2018

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method in which the cognitive users can utilize the spectrum owned by the primary users at any time provided that the primary networks still guarantee the quality of service (QoS) [4, 5, 6]. In the underlay CR networks, the transmit power of the secondary users must be constrained adaptively with fading effects and interference limits [4, 5, 6]. The interference constraint is set by the primary 10

networks based on the required QoS. For the FD technique [7, 8, 9, 10], the users can simultaneously transmit and receive the signals using the same frequency. Hence, the relay terminals using the FD

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mode can achieve double spectral efficiency, as compared with the half-duplex (HD) mode where the transmitting and receiving operations are performed in the orthogonal time slots. Nevertheless, the FD relaying is suffering from the loopback interferences (or self interferences) which reduces the 15

signal-to-noise ratios (SNRs) received at the receive antennas of the relay node. Cancellation units which operate in domains such as code [7], analogue [8], digitization [8] and space [9] have been considered to mitigate the loopback interferences. However, in practice, these units are not perfect

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[11, 12, 13, 14] and hence, the self interferences may not be fully ignored. In [11], the authors expressed the received signals at the FD nodes with residual loopback interference components caused by the 20

imperfect cancellation. L. J. Rodriguez et al. in [13] also evaluated performance of the FD scheme using the practical cancellation in the presence of this interference.

Transmit power of wireless devices can be limited due to the interference constraint [4, 5, 6] or the

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effect of the loopback interferences in the FD transmission [6, 11, 12, 13, 14], which severely degrades the performance of the secondary networks. To extend the coverage area as well as mitigate the effect 25

of fading channels, cooperative communication has become an effective approach [10, 15, 16, 17]. In

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this technique, the wireless relays can use decode-and-forward (DF) technique [3, 4, 14] or amplify-andforward (AF) technique [2, 12, 13, 14] to relay the source data to the destination. The implementation

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of the DF method is more complex than that of the AF one, however the AF technique creates more noises at the destination due to the amplification of the signals received from the source. 30

Energy harvesting (EH) has been emerged as an effective solution in energy-limited wireless networks

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where it is impossible for wireless devices to replace or recharge their batteries [18, 19, 20]. In [18, 19], the EH techniques were proposed to extend the life time for the energy-limited wireless networks. Published work [20] described an ideal EH receiver that can detect the information. However, it is

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indicated in [21] that the implementation of real physical circuits of such the receiver is a challenging

35

task. Hence, the authors in [21] introduced more practical EH models: time switching (TS) and power splitting (PS). In the TS model, the time is divided into at least two distinct intervals: one interval for the EH process and remaining intervals for processing information [21]. For the PS one, the received signals are separated into lower powered signals for EH and information-related units [21]. A. Related work and motivation.

40

A conventional dual-hop FD relaying network in which an energy constrained relay is powered by radio

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frequency signals from a source using the TS architecture has been investigated in [11]. Multiple-input multiple-output and relaying techniques, called as smart antenna technologies, have been considered to significantly improve the energy efficiency and the spectral efficiency of the wireless EH networks [22]. Using the EH architecture, throughput optimizations were solved in multiple antenna FD re45

lay networks [23]. Also in [23], M. Mohammadi et al. performed loopback interference cancellation techniques in spatial domain. Non-ideal circuit power consumption has studied in [24] with a power-

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supplied base station and multi EH users.

For cognitive networks, the authors in [25] have proposed an EH-based HD underlay relay network in which the secondary transmitters exploited signals received from the primary networks to charge their 50

batteries during the spectrum sharing operation. A TS-architecture EH relay is charged in a required number of energy subslots which are fed back to a secondary source after the first energy subslot [26]. In [27], an underlay multi-hop EH cognitive radio network with time division multiple access is inves-

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tigated to lower the transmit powers of secondary users. In [18], optimal transmission and harvesting durations have been obtained to maximize throughput of energy-harvesting CR networks while pro55

tecting primary users. In [6], opportunistic FD relay selection in an underlay cognitive network without the EH architecture has been studied to diminish impacts of residual self-interferences. Recently, a FD transmission has been studied at energy access points which are equipped by multi transmitting

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and receiving antennas, and also operate as a DF relay for one primary transmitter-receiver pair [28]. The energy access points and the primary transmitter supply energy to a power-limited secondary 60

transmitter to enhance performance of one secondary multi-antenna transmitter-receiver pair.

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Inspired by the current works on wireless-powered HD cognitive networks, in this paper, we propose an underlay cooperative protocol in the secondary network (SN) where a two-antenna secondary EH

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relay operating on the FD mode is employed to forward data from a one-antenna secondary source to a one-antenna secondary destination (denoted by FDEHSN protocol). In the proposed protocol, 65

the EH process is realized based on the TS method in which the relay harvests energy from radio-

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frequency (RF) signals of the source in the first interval and simultaneously performs the receiving and transmitting processes in the remaining time interval. B. Contributions

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The system performances of the proposed FDEHSN protocol are analyzed in terms of asymptotic out-

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age probability and throughput over Rayleigh fading channel, in the joint impact of the interference constraint required by the primary network, the loopback interference caused by the FD operation, and the EH time ratio. Moreover, we perform Golden Section Search algorithm [29] to determine the optimal value for the EH time ratio, subject to the minimum outage probability. For comparison purposes, a corresponding FD cognitive protocol without using the EH architecture at the relay node

75

(denoted by WoEH protocol) is also considered [6]. In addition, a UCCN-TS protocol in [30] which

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has the same system model with the proposed FDEHSN protocol but operates in HD communication mode is also referred. Computer simulations using Monte Carlo method are presented to verify the theoretical results. The main contributions of this paper are as follows: 80

• We analyze the system performance of the FD modes with (the proposed FDEHSN protocol) and

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without using the EH architecture (the WoEH protocol) in the underlay cooperative network, and find that the proposed FDEHSN protocol can obtain better performance in terms of outage probability. In the case that we derive the optimal EH time ratios by the Golden Section Search, the throughput of the proposed FDEHSN protocol is increased and outperforms that 85

of the WoEH protocol. The throughput analyses are performed in the serious impacts of the residual loopback interference at the secondary relay.

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• We take simulation and analysis results of our published UCCN-TS protocol in the same scene with the proposed protocol to compare the EH-FD and EH-HD relaying modes, our results show that the throughput of the EH-FD mode outperforms that of the EH-HD one. 90

• Considering about impacts of the primary receiver, both protocols FDEHSN and WoEH achieve better system performances when the primary receiver is close the secondary relay and far from

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the secondary source. In addition, with a fixed location of the primary receiver, the proposed FDEHSN protocol achieves the minimum outage probability when the secondary relay is close

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the secondary destination.

• We corroborate suitability of the asymptotic outage probability and throughput results with Monte Carlo simulation ones, and show mutual relations between the system performances and

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the energy conversion efficiencies of the EH architecture. C. Paper outline

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The rest of this paper is organized as follows. In Section 2, the system model and operation principles of the FDEHSN and WoEH protocols are described. In Section 3, asymptotic closed-form expressions

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of the outage probability and throughput are derived. Section 4 presents numerical evaluations as well as Monte Carlo simulation results. Section 5 summarizes the conclusions of this paper.

2. System Model and Operation Principles Figure 1 presents the system model of the FDEHSN protocol in which the secondary source (S) attempts to transmit its data to the secondary destination (D) via the help of the secondary relay (R). The source and destination nodes are equipped with a single antenna, while the relay has two antennas and operates on the FD mode. Furthermore, this relay is the energy-constrained terminal which uses 4

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h4

h1

h2 h5

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h3

1  D T

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DT

Figure 1: System model of the cooperative system with the FD wireless relay in the underlay CR networks.

the harvest-use category to harvest the energy from the RF signals of the source [11, 23, 27, 31],[32, Fig. 1(a)]. The harvested energy can be stored in a supercapacitor and then is used immediately. However,

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the supercapacitor also suffers from high self-discharge [27]. For example, the EH architecture with the harvest-use category can be installed into wireless sensors which are very small devices and are distributed in the large regions. We assume that the relay only has enough energy to reply on the

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pilot massages in the set-up phase and the source cannot transmit signals directly to the destination due to far distance or deep shadow fading. In the underlay CR networks, the transmitters S and R

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must dynamically adapt their transmit power to satisfy the interference constraint set by the primary receiver (PR). We also assume that the primary transmitters which are not showed in Fig. 1 locate sufficiently far from the secondary network so that the co-channel interference caused by their data

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transmission can be ignored in comparison with other terms in the received signals at the relay and destination nodes [33, 34], or can be lumped together with additive noises following a Gaussian distribution [35, 36]. In the EH phase, the relay uses its receive antenna to harvest energy from the

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RF signals of the source during the time αT , where T is total communication period used to relay the data from the source to the destination. The remaining time (1 − α) T is used for receiving and transmitting the data simultaneously. In addition, the DF relaying technique is applied by the relay R, i.e., it decodes the current data of the source and forwards the previously decoded data to the destination using the energy harvested in the EH phase. In Fig. 1, h1 , h2 , h3 and h5 denote the Rayleigh fading channel coefficients of the S → R, R → D, S → PR and R → PR, respectively, while h4 models the residual loopback Rayleigh interference

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channel due to the full-duplex operation with imperfect cancellation at the relay R [11, 14]. The selfinterference cancellation in the relay R cannot consume energy by using passive isolation techniques such as placing RF absorber material between antennas, deploying of directional antennas [23, 37] or using very small energy consumption micro controllers [23, 38]. The channel coefficients h3 , h4 , and h5 are described as co-channel interferences in which h3 and h5 act on the primary network   2 whereas h4 influences back to the relay of the secondary network. The channel gains gi gi = |hi |

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are exponentially distributed random variables (RVs) [2, 3, 33], where i ∈ {1, 2, 3, 4, 5}. Therefore, the probability density function (PDF) and the cumulative distribution function (CDF) of the exponential RV , i.e., g, can be expressed by fg (x) =

    x x 1 exp − , Fg (x) = 1 − exp − , µ µ µ

(1)

where µ = E {g} is the expected value of g, and E is the expectation operator. Let us denote µi as

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the expected values of the exponential RVs gi .

We consider the quasi-static (block) fading model in which the channel coefficients hi remain constant during the period T , and change to a new independent value in the next period [39]. Because the PR receives the interferences from the source S and the relay R simultaneously, the transmit powers of the source and relay nodes must be constrained as in [6, 10]:

(2)

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PS |h3 |2 + PR |h5 |2 ≤ I,

where PS and PR are transmit power of the source and the relay, respectively, and I is the maximum

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interference threshold set by the PR.

Prior to data transmission and harvesting energy, a connection is established according to the Medium Access Control (MAC) protocol specified in [40]. The secondary source S and the secondary relay R

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can know the channel state information (CSI) h3 and h5 , respectively, by directly the feedback channel from the PR [41] or by indirectly the feedback channel from a third party [42]. Unlike the complex optimal power allocation method proposed in [10], this paper considers a simple power allocation

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strategy as follows:

PS ≤

I Ith I Ith = , PR ≤ = , 2|h3 |2 g3 2|h5 |2 g5

(3)

where Ith = I/2. Next, let us consider the operation principle of the FDEHSN protocol which is divided into two phases: EH phase and data transmission phase with respective time intervals αT and (1 − α) T, where α (0 < α < 1) is a designed parameter. In the EH phase, the relay uses its receive antenna to harvest the energy from the RF signals of the source. The RF signal received at the relay can be expressed as yR =

p

PS h1 xe + ηR , 6

(4)

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where xe is energy symbol with E {xe } = 1, and ηR denotes as Additive White Gaussian Noise (AWGN) at the relay with zero mean and variance N0 . Then, the energy harvested by the relay during the EH phase is given by 2

Eh = ηPS |h1 | (αT) = ηαTPS g1 ,

(5)

where η (0 < η ≤ 1) is the energy conversion efficiency. Then, the harvested energy Eh is used to power of the relay in the second phase can be obtained as Peh R =

ηαPS g1 Eh = . (1 − α) T 1−α

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forward the successfully decoded data of the source during the interval (1 − α) T . Hence, the transmit

(6)

From (3) and (6), the maximum transmit power of the source and the relay can be calculated, respec-

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tively as PS =

PR = min



Ith eh ,P g5 R



Ith , g3

= min



Ith ηαPS g1 , g5 1−α



.

(7)

(8)

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In (8), because of using the harvest-use category of the relay R, if PR = Ith /g5 < PReh , then remaining
power PReh − Ith /g5 cannot be utilized in the next T period [27] due to the leakage of the supercapacitor in the relay R.

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After adjusting the transmit power as in (7) and (8), the source and the relay starts to transmit the data in the second phase. Due to the FD operation, the receive antenna at the relay receives two signals: the desired signal from the source S and the loopback interference signal from its transmit

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antenna. Hence, the received signals at the relay can be given as zR =

p

PS h1 xS +

p PR h4 xR + υR .

(9)

In (9), xS and xR are the signals currently transmitted by the source and the relay, respectively, where E {xS } = E {xR } = 1. The term υR in (9) denotes the AWGN noise at the relay with zero

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mean and variance N0 . Here, we note that xR is the source signal that is decoded successfully at the previous time slots and now it is forwarded to the destination [11]. In addition, the power for decoding operation of xS is small when comparing with the transmit power PR as in [38]. It is also noted that

for ease of presentation, we ignore the time index. From (9), the signal-to-interference-plus-noise ratio (SINR) received at the relay, with respect to the signal xS , is obtained by 2

γ1 =

PS |h1 | 2

PR |h4 | + N0

7

.

(10)

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Substituting (7) and (8) into (10), the SINR γ1 can be rewritten as γ1 =

g3 min

n

Ith g1 Ith ηαIth g1 g5 , g3 (1−α)

where Q = Ith /N0 and κ = ηα/(1 − α).

o

= g4 + g3 N0

Qg1 , Q min {g3 /g5 , κg1 } g4 + g3

(11)

Next, the received signal at the destination, due to the transmission of the relay, is formulated by p

PR h2 xR + υD ,

(12)

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zD =

where υD is the AWGN noise at the destination with zero mean and variance N0 . From (8) and (12), the SINR received at the destination D can be given as 2

PR |h2 | γ2 = = Qg2 min N0



1 κg1 , g5 g3



.

(13)

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With the DF relaying scheme, the end-to-end SINR of the FDEHSN protocol can be expressed as FDEHSN γe2e = min (γ1 , γ2 ) .

(14)

For performance comparison, we consider the corresponding FD protocol in the underlay CR networks without using the EH technique at the cooperative relay (denoted by WoEH protocol) [6]. In this

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protocol, the relay is the energy sufficient device and it does not need to harvest the energy from the RF signals of the source. Hence, the operation of the WoEH protocol during the interval T is performed only in the data transmission phase. Without the EH architecture, the transmit power of

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the relay in the WoEH protocol is PR = Ith /g5 . We should note that the transmit power of the source in this protocol is also given by (7).

Similar to (11) and (13), the SINRs at the relay R and the destination D in the WoEH protocol can

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be formulated, respectively as

2

γ3 =

PS |h1 | 2

PR |h4 | + N0

=

Qg1 /g3 , Qg4 /g5 + 1

(15)

2

γ4 =

PR |h2 | g2 =Q . N0 g5

(16)

Then, the end-to-end SINR of the WoEH protocol can be obtained by WoEH γe2e = min (γ3 , γ4 ) .

(17)

To take distances and path-loss exponent into account, the expected values µi can be expressed as 105

µi = d−β [2, 3, 5, 30], where di are normalized link distances between nodes corresponding with the i expected values µi , β is the path-loss exponent, and i ∈ {1, 2, 3, 5}.

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3. Outage Probability and Throughput In this section, we derive expressions of the outage probability and throughput for the considered protocols. The outage probability is the probability that the end-to-end SINR is less than a predetermined positive threshold denoted by γth . Mathematically speaking, the outage probability of the FDEHSN and WoEH protocols can be expressed, respectively by

OPWoEH = Pr [min {γ3 , γ4 } < γth ] .

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OPFDEHSN = Pr [min {γ1 , γ2 } < γth ] ,

(18)

Next, we formulate the average throughput for the FDEHSN and WoEH protocols as follows: TpFDEHSN = (1 − α) (1 − OPFDEHSN ) Rth , TpWoEH = (1 − OPWoEH ) Rth ,

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(19)

where Rth is the target data rate and is given by Rth = log2 (1 + γth ) [21]. 3.1. The FDEHSN Protocol

Firstly, we rewrite the outage probability of the proposed FDEHSN protocol under the following

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form:

OPFDEHSN = 1 − Pr [γ1 ≥ γth , γ2 ≥ γth ] .

(20)

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Substituting (11) and (13) into (20), we obtain OPFDEHSN = 1 − Pr

h

Qg1 Q min{g3 /g5 , κg1 }g4 +g3

i

κQg1 g2 2 ≥ γth , Qg ≥ γth g5 ≥ γth , g3

.

(21)

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The probability expression in (21) has complex form related to five RVs g1 , g2 , g3 , g4 and g5 , and with our best experiments, it is impossible to obtain the exact closed-form expression for (21).As a way to

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analyze equivalently, we attempt to derive the asymptotic one for OPFDEHSN at high Q values, i.e., Q → +∞. Indeed, we have the approximation: Q min {g3 /g5 , κg1 } g4 +g3

Q→+∞

≈

Q min {g3 /g5 , κg1 } g4 ,

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which yields

OPFDEHSN

Q→+∞

≈

1 − Pr

h

g1 min{g3 /g5 ,κg1 }g4

i

κQg1 g2 2 ≥ γth , Qg ≥ γth g5 ≥ γth , g3

.

(22)

By considering two cases, i.e., g3 /g5 ≤ κg1 and g3 /g5 > κg1 , equation (22) can be rewritten as follows: OPFDEHSN

Q→+∞

≈

1 − Pr | − Pr |

h

g3 g5

h

g3 g5

≤ κg1 , gg31 gg45 ≥ γth , {z

Qg2 g5

≥ γth , gg1 3g2 ≥

γth κQ

J1

> κg1 , g4 ≤

Qg2 1 κγth , g5

{z

J2

9

≥ γth , g1g3g2 ≥

γth κQ

i

}

i }

.

(23)

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Our next objective is to calculate the probability J1 and J2 as remarked in (23). Before calculating the probabilities, let us consider a RV X: X = g1 /g3 . By using [3, eq. (68-69)], the CDF and PDF of X can be given, respectively as µ3 x 1 = , µ1 + µ3 x 1 + µ1 /(µ3 x)

(24)

µ1 µ3 ∂FX (x) = 2. ∂x (µ3 x + µ1 )

(25)

fX (x) =

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FX (x) =

Using Appendix A, the probability J1 is obtained as        µ2 Q µ3 ϕ ϕ 1 J1 = µ2 Q+µ − 1 − exp − × exp − E 1 µ1 µ5 κ κγth 5 γth  µ4 κγth  κγth   µ3 µ4 µ3 µ4 1 1 − µ1 µ5 (ϕµ4 −1) × exp − µ4 κγth − µ µ (ϕµ −1)2 E1 µ4 κγth   1 5 4    ϕµ4 −1 ϕµ4 −1 1 3 µ4 + µ µ µ(ϕµ 1 − × exp E 1 κϕγth , µ4 κγth µ4 κγth −1)2 5

4

where E1 (x) = −Ei(−x) =

R +∞ x

1 t

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1

(26)

exp (−t) dt is the exponential integral function [43], and ϕ=

µ3 γth (µ2 Q + µ5 γth ) . µ1 µ2 µ5 Q

Next, the probability J2 in (23) is derived from Appendix B as

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       h   µ5 γth µ5 γth 1 E ψ 1 + J2 = 1 − exp − µ4 κγ × ψ exp ψ 1 + 1 µ2 Q µ2 Q th    i   −Ω exp (Ω) E1 (Ω) − Ω exp Ω 1 + µµ51γQth E1 Ω 1 + µµ51γQth ,

(27)

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where ψ = µ3 /(µ1 µ5 κ), and Ω = µ3 γth /(µ1 µ2 κQ).

Plugging (23), (26) and (27) together, we obtain the asymptotic expression of the outage performance for the proposed protocol.

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Next, the throughput of the FDEHSN protocol in (19) can be approximated by ≈

(1 − α) (J1 + J2 ) log2 (1 + γth ) .

(28)

3.2. The WoEH Protocol From (15)-(18), the outage probability of the WoEH protocol can be formulated as   (Qg1 /g3 ) Qg2 OPWoEH = 1 − Pr [γ3 ≥ γth , γ4 ≥ γth ] = 1 − Pr ≥ γth , ≥ γth . (Qg4 /g5 ) + 1 g5

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110

Q→+∞

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TpFDEHSN

10

(29)

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+

Z

+∞

|0

Z

+∞

0

Z

J3

2 Qxy /γth

fX (x)fg2 (y) fg4 (z) Fg5 {z

0

J4

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Next, at high Q values, the outage probability OPWoEH is approximated as   Q→+∞ γth g4 Qg2 ≤ g5 ≤ OPWoEH ≈ 1 − Pr X γth 2    Z +∞ Z +∞ Z Qxy/γth  γ z  Q→+∞ Qy th ≈ 1− fX (x)fg2 (y) fg4 (z) Fg5 dzdydx − Fg5 γth x 0 0 0 2   Z +∞ Z +∞ Z Qxy/γth Q→+∞ Qy ≈ 1− fX (x)fg2 (y) fg4 (z) Fg5 dzdydx γth 0 0 {z } |0 γ z  th dzdydx . x }

(30)

 2 By setting ϑ = µ3 µ4 γth /(µ1 µ5 ), ω1 = µ1 /µ3 , ω2 = γth (µ2 Q), and using Appendix C, we obtain the cases as • Case 1: ω1 = ω2 = ω Q→+∞

≈

1−

−

µ1 2µ3 ω

+

µ2 µ5 γth Q+µ2 µ5 γth

−

1 2 1+Q/(µ2 µ5 γth )−Qµ1 µ2 /(µ3 µ4 γth )

Qµ1 µ2 2 2 2 µ3 µ4 γth )) (1+Q/(µ2 µ5 γth )−Qµ1 µ2 /(µ3 µ4 γth

• Case 2: ω1 6= ω2 OPWoEH

+

Q→+∞

≈

1−

−ϑ+1+ϑ ln ϑ (ϑ−1)2

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−ϑ+1+ϑ ln ϑ (ϑ−1)2

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OPWoEH

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asymptotic closed-form expression of the outage probability OPWoEH for the WoEH protocol in two

µ2 µ5 γth + Q+µ − 2 µ5 γth

+

µ1 ω2 µ3

h

1 (ω2 −ω1 )ω1

ln



+

1 (ω2 −ω1 )2

ln

1 2 1+Q/(µ2 µ5 γth )−Qµ1 µ2 /(µ3 µ4 γth )

Qµ1 µ2 − 2 2 2 µ3 µ4 γth )) (1+Q/(µ2 µ5 γth )−Qµ1 µ2 /(µ3 µ4 γth

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2 Qµ1 µ2 /(µ3 µ4 γth ) 1+Q/(µ2 µ5 γth )

ln





ω1 ω2



(31)

.

i

2 Qµ1 µ2 /(µ3 µ4 γth ) 1+Q/(µ2 µ5 γth )



(32) .

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Finally, the average throughput can be computed approximated as TpWoEH

Q→+∞

≈

(1 − α) (J3 + J4 ) log2 (1 + γth ) ,

(33)

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where J3 and J4 are obtained in Appendix C. 4. Numerical Results and Discussion In this section, the system performances of the secondary network in the protocols FDEHSN and

WoEH are analyzed and evaluated by using the asymptotic theoretical analyses and the Monte Carlo 120

simulation results of the outage probability and throughput. In addition, simulation and analysis results of our UCCN-TS protocol in [30] are also referred to compare with the proposed FDEHSN protocol. The UCCN-TS protocol has the same system model with the FDEHSN protocol but operates 11

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in HD communication mode. The Q (dB) values along horizontal axis are defined as Q = Ith /N0 . We note that at the high Q values, the QoS of the primary network is low, and thus the transmission 125

opportunity with the high QoS of the secondary network increases. We assume that the target data rate, Rth , is equal to 1 (bits/s/Hz). Figure 2 presents the outage probability and the throughput of the FDEHSN, WoEH and UCCNTS protocols as a function of Q in dB when η = 0.9, α = 0.3, µ1 = µ2 = 1, µ3 = µ5 = 0.5 and

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µ4 = 0.1. The high energy conversion efficiency η is referred in [21, 44](η is set to 1), [45](η is set to 0.8) and [30] (η is set to 0.9). From Fig. 2, when the value Q increases, the outage probability of the FDEHSN protocol decreases whereas that of the WoEH protocol moves to the saturate values (at Q > 20 dB). It is due to the fact that the decoding capacity of the protocols FDEHSN and WoEH is strongly effected by the signal qualities in the first hop (SINRs γ1 and γ3 suffer from the loopback interferences), and the SINR γ3 in the WoEH protocol does not depend on Q (dB) at high Q values whereas the transmit power of the loopback interference is more effected by the harvested energy

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than the interference constraint in the FDEHSN protocol. In addition, the decoding performance of the proposed FDEHSN protocol is better than that of the WoEH protocol when Q > 12 dB where the WoEH protocol begins movement to the saturate region. Considering the spectrum utilization efficiency, the throughput of the proposed FDEHSN protocol is inferior to that of the WoEH protocol because of the small efficiency transmission time (1 − α). Comparing with the UCCN-TS protocol

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in [30] in which the energy-harvesting relay does not suffer from the loopback interferences, the throughput outperforms whereas the outage probability of the FDEHSN protocol is larger than those

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of the UCCN-TS protocol. Finally, the asymptotic outage probability expressions of the protocols FDEHSN and WoEH are valid with the simulation results. Figure 3 presents the outage probability and throughput of the FDEHSN, WoEH and UCCN-TS

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protocols as a function of η when α = 0.3, Q = 20 (dB), µ1 = µ2 = 1, µ3 = µ5 = 0.5, and µ4 = 0.1. From Fig. 3, the outage probability of the proposed FDEHSN protocol is declined and the

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throughput of the FDEHSN protocol is slightly increased due to the large harvested energies as in (5) corresponding to increase of the energy conversion efficiencies η, whereas the WoEH protocol does 150

not depend on η. Once more, although obtaining larger outage probabilities, the proposed full-duplex

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FDEHSN protocol achieves better throughputs than that of the HD UCCN-TS protocol. In addition, in spite of impact of the fixed time efficiency (α = 0.3), the throughput of the FDEHSN protocol can move forward that of the WoEH protocol. Figure 4 presents the outage probability and throughput of the FDEHSN, WoEH and UCCN-TS

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protocols as a function of α when η = 0.9, Q = 20 (dB), µ1 = µ2 = 1, µ3 = µ5 = 0.5 and µ4 = 0.1. In Fig. 4, the WoEH protocol does not depend on α, thus the outage probability and the throughput are constants. For the proposed FDEHSN protocol, the outage probability achieves the smallest value

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Tp 10-1

10-2

FDEHSN-Sim (OP) WoEH-Sim (OP) UCCN-TS-Simu (OP) FDEHSN-Sim (Tp) WoEH-Sim (Tp) UCCN-TS-Simu (Tp) Approximate theory Exact theory

10-3

10-4 0

5

10

15

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OP

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Outage probability (OP) & Throughput (Tp)

100

20

25 Q (dB)

30

35

40

45

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Figure 2: The outage probabilities and the throughputs in the protocols FDEHSN, WoEH and UCCN-TS versus Q (dB) when η = 0.9, α = 0.3, µ1 = µ2 = 1, µ3 = µ5 = 0.5, and µ4 = 0.1.

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at optimal α (denoted as αopt and αopt ≈ 0.65 in Fig. 4). This optimal value can be obtained by

the Golden Section Search (GSS) approach [29] with a small tolerance interval ε = 10−5 . The result 160

about the survey of the outage probability versus α can be explained as follows. When the value

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α is smaller than the optimal value αopt , the small harvested energy Eh in (5) can make the small loopback interference power PR in (8). The high SINR at the relay R in (11) causes the smaller outage

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probability of the FDEHSN protocol. On the other hand, when α is higher than αopt , the SINRs γ1 and γ3 move to γ2 and γ4 , respectively, hence causing the higher outage probability. At the optimal 165

value αopt , the FDEHSN protocol can balance the loopback interference of itself and the interference

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constraint of the primary network. Again, comparing with the WoEH and UCCN-TS protocols, the throughput of the proposed FDEHSN protocol is smaller than that of the WoEH protocol because of the loss of the time for the EH, and is larger than that of the UCCN-TS protocol due to increasing of the bandwidth utilization efficiency.

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Figure 5 presents the outage probability and throughput of the FDEHSN and WoEH protocols as a function of µ4 when η = 0.9, Q = 20 (dB), µ1 = µ2 = 1 and µ3 = µ5 = 0.5. The time ratio α is set to the optimal value αopt for each µ4 value. This optimal value αopt is obtained by the GSS approach with the small tolerance parameter ε = 10−5 . From Fig. 5, due to additive loopback interference, the 13

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0.9

0.7 FDEHSN-Sim (OP) WoEH-Sim (OP) UCCN-TS-Simu (OP) FDEHSN-Sim (Tp) WoEH-Sim (Tp) UCCN-TS-Simu (Tp) Approximate theory Exact theory

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Tp 0.5 0.4 0.3

OP

0.2 0.1 0 0.1

0.2

0.3

0.4

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Outage probability (OP) & Throughput (Tp)

0.8

0.5

0.6

0.7

0.8

0.9

1

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η

Figure 3: The outage probabilities and the throughputs in the protocols FDEHSN, WoEH and UCCN-TS versus η when

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α = 0.3, Q = 20 (dB), µ1 = µ2 = 1, µ3 = µ5 = 0.5, and µ4 = 0.1.

outage probability of both protocols FDEHSN and WoEH increase when µ4 increases. In addition, it 175

is worth noting from this figure that because of the optimal value αopt in the FDEHSN protocol, the

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throughput of the proposed method is enhanced, while that of the WoEH one is declined when the impact of the residual loopback interference channel is serious (µ4 increases).

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Figure 6 presents the outage probability (Fig. 6a) and the throughput (Fig. 6b) of the protocols FDEHSN and WoEH as a function of Q (dB) when η = 0.9, α = 0.3, µ1 = µ2 = 1, µ4 = 0.1, and two 180

locations of the primary receiver PR: 1) the PR is close to the secondary source S and far from the

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secondary relay R, a case (µ3 , µ5 ) = (1, 0.2); and 2) the PR is close to the secondary relay R and far

from the secondary source S, a case (µ3 , µ5 ) = (0.2, 1). From Fig. 6a (outage probability) and Fig. 6b

(throughput), both protocols FDEHSN and WoEH have the system performance in terms of the outage probability and the throughput are better when the primary receiver PR is close to the secondary

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relay R (the case (µ3 , µ5 ) = (0.2, 1)) because of allocation of the loopback interference power by (8). When the primary receiver PR is close the secondary source S and far the secondary relay R, the maximum transmit power of the secondary source S is limited to a minimum value as in (7), and as a result, the maximum transmit power of the relay can take a small value as in (8). In addition, the 14

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Tp

10-2

10-3 0.1

FDEHSN-Sim (OP) WoEH-Sim (OP) UCCN-TS-Simu (OP) FDEHSN-Sim (Tp) WoEH-Sim (Tp) UCCN-TS-Simu (Tp) Approximate theory Exact theory

0.2

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OP

10-1

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Outage probability (OP) & Throughput (Tp)

100

0.4

0.5

0.6

0.7

0.8

0.9

α

Figure 4: The outage probabilities and the throughputs in the protocols FDEHSN, WoEH and UCCN-TS versus α when η = 0.9, Q = 20 (dB), µ1 = µ2 = 1, µ3 = µ5 = 0.5, and µ4 = 0.1.

-1

M OP

PT

10

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Tp

AC

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Outage probability (OP) & Throughput (Tp)

10 0

FDEHSN-Sim (OP) WoEH-Sim (OP) FDEHSN-Sim (Tp) WoEH-Sim (Tp) Approximate theory

10 -2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

µ4

Figure 5: The outage probabilities and the throughputs in the protocols FDEHSN and WoEH versus µ4 when η = 0.9, Q = 20 (dB), µ1 = µ2 = 1, and µ3 = µ5 = 0.5.

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100

0.9 0.8

10-1

0.6

10-2

FDEHSN-Sim: (µ3 , µ5 ) = (1, 0.2) WoEH-Sim: (µ3 , µ5 ) = (1, 0.2) FDEHSN-Sim: (µ3 , µ5 ) = (0.2, 1) WoEH-Sim: (µ3 , µ5 ) = (0.2, 1) Approximate theory

10-3

0

5

10

15

20

25

30

0.5

PR is close to S 0.4

0.3

FDEHSN-Sim: (µ3 , µ5 ) = (1, 0.2) WoEH-Sim: (µ3 , µ5 ) = (1, 0.2) FDEHSN-Sim: (µ3 , µ5 ) = (0.2, 1) WoEH-Sim: (µ3 , µ5 ) = (0.2, 1) Approximate theory

0.2

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40

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25 Q (dB) b)

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Q (dB) a)

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PR is close to R

10-4

PR is close to R

0.7

Throughput (Tp)

Outage probability (OP)

PR is close to S

Figure 6: The outage probabilities (Fig. 6a) and the throughputs (Fig. 6b) in the protocols FDEHSN and WoEH versus Q (dB) when η = 0.9, α = 0.3, µ1 = µ2 = 1, µ4 = 0.1, and two cases: (µ3 , µ5 ) = (1, 0.2) and (µ3 , µ5 ) = (0.2, 1).

proposed FDEHSN protocol can achieve better throughputs than the WoEH protocol at Q > 15 (dB) 190

when the primary receiver PR is close to the secondary source S (the case (µ3 , µ5 ) = (1, 0.2)). In order to survey impacts of distances on the system performance of the FDEHSN and WoEH

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protocols, we set the coordinates of the secondary and primary nodes as S(0, 0), D(1, 0), R(xR , 0) and PR(0.5, 0.5) in the two-dimensional plane, where 0 < xR < 1. As a result, the distances of links

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S-R (d1 ), R-D (d2 ), S-PR (d3 ) and R-PR (d5 ) are obtained respectively as d1 = xR , d2 = 1 − xR , q p 2 d3 = 0.52 + 0.52 = 0.71, and d5 = (0.5 − xR ) + 0.52 . In addition, we can assume that the path-

loss exponent is fixed to a constant, β = 3. Figure 7 presents the outage probability and throughput

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of the FDEHSN and WoEH protocols as a function of the locations of the secondary relay R on the x-axis (xR ) when η = 0.9, Q = 20 (dB), α = 0.3, µ3 = d−β = 2.83, µ4 = 0.1, µi = d−β 3 i , and the

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coordinate xR of the secondary relay is shifted from 0.1 to 0.9, where i ∈ {1, 2, 5}. As plotted in Fig. 7, the outage probability of the FDEHSN protocol is smaller than that of the WoEH protocol, and can achieve a minimum value at xR = 0.7. Also at xR = 0.7, the throughput of the FDEHSN protocol

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reaches to a maximum value because of balance of SINRs γ1 and γ2 of two hops in which the SINR γ1

includes the loopback interference. For the WoEH protocol, the outage probability increases and the respective throughput decreases when the secondary relay R moves toward the secondary destination

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D (xR increases).

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Tp

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FDEHSN (OP WoEH (OP) FDEHSN (Tp) WoEH (Tp)

10-1

OP

10-2 0.1

0.2

0.3

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Outage probability (OP) & Throughput (Tp)

100

0.4

0.5

0.6

0.7

0.8

0.9

xR

Figure 7: The outage probabilities and the throughputs in the protocols FDEHSN and WoEH versus xR when η = 0.9,

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Q = 20 (dB), α = 0.3, µ4 = 0.1, µi = d−β i , i ∈ {1, 2, 3, 5}.

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5. Conclusions

An underlay cooperative cognitive network model with a full-duplex communication method based on EH was proposed and investigated, denoted as the FDEHSN protocol. The two-antenna secondary

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relay harvested energy of the radio-frequency signals from the one-antenna secondary source in the first interval per the total communication period, and performed receiving and transmitting of data

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simultaneously in the remaining time interval. Performance evaluations were derived in terms of outage probability and throughput in the joint presence of the interference constraint, the loopback interference, and harvesting time ratio. Optimal harvesting time ratios, which satisfied the minimal

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outage probabilities of the proposed FDEHSN protocol, were obtained by the Golden Section Search

215

approach. In addition, the proposed FDEHSN protocol was compared with the conventional fullduplex cognitive network model where the secondary network also suffered the interference constraints of the primary receiver but did not apply the EH architecture at the cooperative relay, denoted as the WoEH protocol. The published UCCN-TS protocol where the underlay cooperative cognitive network with the EH architecture operates in the half-duplex mode was referred to compare with the

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proposed FDEHSN protocol. The Monte Carlo simulation method was used to confirm validation of the asymptotic theory expressions. Our interesting outcomes about the proposed FDEHSN protocol 17

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included that 1) the outage probability of the FDEHSN protocol is smaller than that of the WoEH protocol; 2) The throughput of the proposed FDEHSN protocol outperforms that of the UCCNTS protocol; 3) Both protocols FDEHSN and WoEH achieve better system performances when the 225

primary receiver is close the secondary relay and far from the secondary source; 4) By considering the optimal harvesting time ratios, the throughput of the FDEHSN protocol can be higher than that of the conventional WoEH protocol, which means that the proposed method can obtain higher time

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utilization efficiency; 5) The proposed FDEHSN protocol is improved as increasing of the energy conversion efficiency and achieves the minimum outage probability when the secondary relay is close 230

the secondary destination; Finally, the asymptotic analyzes are valid with the simulation results, which verifies our derivations.

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Appendix A: Solving the probability J1 in (23)

(A.1)

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The probability J1 in (23) is rewritten by the following expression:   γth g4 γth g2 γth 1 ,X ≥ ,X ≥ , ≥ J1 = Pr X ≥ κg5 g5 κQg2 g5 Q     1 γth g4 γth γth = Pr X ≥ max g5 , g2 ≥ , , κg5 g5 κQg2 Q     1 γth g4 γth g5 . = Pr X ≥ max , , g2 ≥ κg5 g5 Q

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Then, by considering two cases, i.e., g4 ≤ 1/(κγth ) and g4 > 1/(κγth ), we can rewrite (A.1) by   1 1 γth J1 = Pr g4 ≤ g5 ,X ≥ , g2 ≥ κγth κg5 Q {z } | L1

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  1 γth g4 γth g5 . + Pr g4 > ,X ≥ , g2 ≥ κγth g5 Q {z } | L2

Let us consider the probability L1 in (A.2), which can be formulated as     1 1 γth L1 = Pr g4 ≤ Pr X ≥ , g2 ≥ g5 κγth κg5 Q   Z +∞       1 1 γth = Fg4 × fg5 (x) 1 − FX 1 − Fg2 x dx. κγth κx Q 0

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(A.2)

(A.3)

Substituting the PDF of g5 given as in (1), the CDF of g2 given as in (1) and the CDF of X given in (24) into (A.3), after some careful manipulations, we obtain    1 L1 = 1 − exp − × µ4 κγth h     i (µ2 Q+µ5 γth )µ3 µ2 Q µ3 5 γth )µ3 , E1 (µ2µQ+µ µ2 Q+µ5 γth − µ1 µ5 κ exp − µ1 µ2 µ5 κQ 1 µ2 µ5 κQ 18

(A.4)

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where E1 (x) = −Ei(−x) =

R +∞ x

1 t

exp (−t) dt is the exponential integral function [43].

For the probability L2 in (A.2), we can formulate it by       Z +∞ Z +∞ γth x γth fg4 (x) fg5 (y) 1 − FX L2 = × 1 − Fg2 y dydx. y Q 1/κγth 0

(A.5)

Substituting the CDFs of the RVs X and g2 ; and the PDFs of the RVs g4 and g5 into (A.5), we can obtain (A.6) as  1−

Z

+∞

Z

+∞

where ϕ=

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1 µ4 µ5

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   µ3 γth x x (µ2 Q + µ5 γth ) exp − − y dydx µ3 γth x + µ1 y µ4 µ2 µ5 Q 1/(κγth ) 0   Z +∞ x µ2 Q exp − = dx µ4 (µ2 Q + µ5 γth ) 1/(κγth ) µ4     Z +∞ µ3 γth (µ2 Q + µ5 γth ) µ3 γth x µ3 γth (µ2 Q + µ5 γth ) x exp − x− E1 x dx µ1 µ4 µ5 1/(κγth ) µ1 µ2 µ5 Q µ4 µ1 µ2 µ5 Q     Z +∞ 1 µ2 Q µ3 γth x exp − = − x exp ϕx − E1 (ϕx) dx, (A.6) (µ2 Q + µ5 γth ) µ4 κγth µ1 µ4 µ5 1/(κγth ) µ4

L2 =

µ3 γth (µ2 Q + µ5 γth ) . µ1 µ2 µ5 Q

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By using [43, eq. (5.221.5)] for the integral in (A.6), the closed-form expression of L2 is given as     µ2 Q 1 1 µ3 µ4 L2 = exp − exp − − (µ2 Q + µ5 γth ) µ4 κγth µ1 µ5 (ϕµ4 − 1) µ4 κγth       ϕµ4 − 1 µ3 µ4 ϕµ4 − 1 1 1 − + × exp E 1 2 µ4 κγth µ4 κγth κϕγth µ1 µ5 (ϕµ4 − 1)   1 µ3 µ4 − . (A.7) 2 E1 µ4 κγth µ1 µ5 (ϕµ4 − 1)

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Substituting (A.4) and (A.7) into (A.2), the probability J1 is solved as in (26).

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Appendix B: Solving the probability J2 in (23)

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The probability J2 in (23) is rewritten by     γth 1 g2 γth 1 Pr ≤X< , ≥ J2 = Pr g4 ≤ κγth κQg2 κg5 g5 Q    1 = 1 − exp − × (B.1) µ4 κγth   Z     Z +∞ Z Qx/γth +∞ Z Qx/γth 1 γth fg2 (x) fg5 (y) FX dydx − fg2 (x) fg5 (y) FX dydx   κy κQx  0 . 0 0 0 | {z } | {z } L3

L4

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The integral L3 in (B.1) can be expressed by

    x y µ3 exp − exp − dydx L3 = µ2 µ5 (µ3 + µ1 κy) µ2 µ5 0 0    Z +∞       µ3 x µ3 µ3 µ3 µ1 κQx = exp − exp × E1 − E1 1+ dx µ1 µ2 µ5 κ µ1 µ5 κ µ2 µ1 µ5 κ µ1 µ5 κ µ3 γth 0     Z +∞ x Q ψ (B.2) exp (ψ) exp − E1 ψ + x dx, = ψ exp (ψ) E1 (ψ) − µ2 µ2 µ5 γth {z } |0 +∞

Z

Qx/γth

Int1

where ψ = µ3 /(µ1 µ5 κ).

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Z

Our next objective is to calculate the single integral Int1 marked in (B.2). By setting y = ψ +

(B.3)

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Qx/(µ5 γth ), this integral can be rewritten by   Z +∞   µ5 γth µ5 γth ψ µ5 γth Int1 = exp exp − y E1 (y) dy. × Q µ2 Q µ2 Q ψ

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Using integration by parts with t = E1 (y) and dv = exp (−µ5 γth y/(µ2 Q)) dy, we obtain Z +∞ +∞ Int1 = (tv)ψ − vdt ψ   h       i R +∞ 1 µ5 γth ψ µ5 γth ψ µ2 Q µ5 γth exp × µµ52γQ exp − µ5µγ2th = dy E (ψ) − exp − 1 + y 1 Q µ γ y µ Q ψ 5 th 2 th Q µ2 Q      µ5 γth ψ µ5 γth E1 ψ 1 + . (B.4) = µ2 E1 (ψ) − µ2 exp µ2 Q µ2 Q

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Substituting (B.4) into (B.2), the close-form expression of L3 can be provided by       µ5 γth µ5 γth L3 = ψ exp ψ 1 + E1 ψ 1 + . µ2 Q µ2 Q

(B.5)

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Similarly, we can express the probability L4 in (B.1) by the exact closed-form expression as follows:     Z +∞ Qx γth L4 = fg2 (x) Fg5 FX dx γth κQx 0     Z +∞ 1 x Qx 1 = exp − 1 − exp − × dx µ2 µ2 µ5 γth 1 + µ1 κQxµ1 κQx (µ3 γth ) (µ3 γth ) 0       µ1 Q µ1 Q = Ω exp (Ω) E1 (Ω) − Ω exp Ω 1 + E1 Ω 1 + , (B.6) µ5 γth µ5 γth where Ω = µ3 γth /(µ1 µ2 κQ).

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Finally, substituting (B.5) and (B.6) into (B.1), the probability J2 is obtained in the exact closed-form expression as in (27).

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Appendix C: Solving the outage probability OPWoEH in (30)

0

Moreover, at high Q region, we have the following approximation:

µ2 µ5 Q 2 Q→+∞ µ2 µ5 Q 2 ≈ µ5 x + x x . 2 2 γth γth

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µ4 γth + µ5 x +

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Using the available CDFs and PDFs, the integral J3 in (30) can be computed as    Z +∞ Z +∞ µ5 x µ5 x Qxy fX (x) fg2 (y) 1 − exp − 2 . dydx J3 = µ4 γth + µ5 x γth µ4 γth + µ5 x 0 0 Z +∞ µ1 µ3 µ5 x = 2 dx (µ4 γth + µ5 x) (µ3 x + µ1 ) 0     Z +∞ Z +∞ µ1 µ3 µ5 x 1 µ5 x Qxy exp − × − + y dydx 2 2 µ2 γth µ4 γth + µ5 x µ2 (µ4 γth + µ5 x) (µ3 x + µ1 ) 0 0 Z∞ µ1 µ3 µ5 x −ϑ + 1 + ϑ ln ϑ − (C.1) =  2 dx. 2 2 (ϑ − 1) (µ3 x + µ1 ) γth µ4 + µ5 x + (µ2 µ5 Qx2 ) γth (C.2)

Therefore, we can approximate J3 in (C.1) as J3

Q→+∞

≈

−ϑ + 1 + ϑ ln ϑ (ϑ − 1)

2

−

Z∞

µ1 µ3 µ5 x n 2 (µ x + µ ) µ5 + 3 1 0 {z |

µ2 µ5 Q x 2 γth

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Int2

(C.3)

}

(C.4)

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Let us consider the integral Int2 in (C.3), which can be rewritten as Z µ1 ω2 +∞ 1 Int2 = dx. 2 µ3 0 (x + ω1 ) (x + ω2 )

o dx .

Then, we have to consider two cases as follows: • Case 1: ω1 = ω2 = ω

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In this case, the integral Int2 can be calculated by Z µ1 ω +∞ 1 µ1 Int2 = 3 dx = 2µ ω . µ3 0 3 (x + ω)

(C.5)

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• Case 2: ω1 6= ω2

In this case, we can obtain Int2 as " # Z µ1 ω2 +∞ 1 1 1 1 1 1 Int2 = − + dx 2 2 µ3 0 ω2 − ω1 (x + ω1 )2 (ω2 − ω1 ) x + ω1 (ω2 − ω1 ) x + ω2 "  # µ1 ω2 ω1 1 1 = + . 2 ln ω µ3 (ω2 − ω1 ) ω1 2 (ω2 − ω1 )

21

(C.6)

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Similarly, the probability J4 in (30) can be computed exactly as       Z +∞ Z +∞ 1 1 Q Qxy fX (x) exp − + y 1 − exp − dxdy J4 = 2 µ2 µ2 µ5 γth µ4 γth 0 0 Z∞ µ2 µ5 γth µ1 µ3 = −   dx 2 2 ) Q + µ2 µ5 γth µ2 (µ3 x + µ1 ) 1/µ2 + Q (µ5 γth ) + Qx (µ4 γth 0

µ2 µ5 γth 1  = − 2 ) Q + µ2 µ5 γth 1 + Q/(µ2 µ5 γth ) − Qµ1 µ2 (µ3 µ4 γth 
ln 2 1 + Q/(µ µ γ ) − Qµ µ (µ µ γ 2 ) 2 µ3 µ4 γth 2 5 th 1 2 3 4 th


! 2 Qµ1 µ2 µ3 µ4 γth . 1 + Q/(µ2 µ5 γth )

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−

Qµ1 µ2

(C.7)

Combining (C.5) and (C.6) into (C.3), and then substituting (C.3) and (C.7) into (30), the outage

References 245

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probability OPWoEH for the WoEH protocol is solved as in (31) and (32).

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interference constraints, IEEE Transactions on Wireless Communications 10 (2) (2011) 390–395. doi:10.1109/TWC.2010.120310.090852. [5] H.-V. Khuong, Outage analysis in cooperative cognitive networks with opportunistic relay se-

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Communications 69 (11) (2015) 1700–1708. doi:10.1016/j.aeue.2015.08.004. [6] B. Zhong, Z. Zhang, X. Chai, Z. Pan, K. Long, H. Cao, Performance analysis for opportunistic fullduplex relay selection in underlay cognitive networks, IEEE Transactions on Vehicular Technology

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