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Performance analysis with wireless power transfer constraint policies in full-duplex relaying networks.


In wireless communications, full-duplex (FD) transmission mode, which allows the transmitter and receiver to be operated simultaneously in the same frequency band, has attracted much research interest in recent years [1].

In principle, thanks to the use of FD, the spectral efficiency in advanced communication systems can be significantly increased compared to half-duplex (HD) mode. Besides that, FD mode is considered as an attractive mechanism to enhance data rate to satisfy the requirements of high transmission rate. Due to the ability to transfer both information and energy via RF signals at the same time, energy harvesting (EH) plays an important role in simultaneous wireless information and power transfer in the same circuit [2]-[4]. A principal application scenario for simultaneously wireless information and power transfer (SWIPT) so-called wireless-powered relaying (WPR) was put forward, in which a relay powered via RF assists the communication between the destination and the source node. In several previous studies on WPR, they mainly focused on HD relaying and the implementation of two mechanisms, namely time switching-based relaying (TSR) and power splitting-based relaying (PSR) [5]-[7]. The time switchingbased FD wireless-powered transmission was investigated, in [8], [9].

Furthermore, FD mode has more benefits in comparison with HD mode in terms of self-interference. There was a rise in noise floor because of the interfering signal according to the model of self-inference in [10]. In such a model, better self-interference cancellation and self-interference channel estimation are achieved thanks to higher transmit power.

In addition, there are other works on interference cancellation methods which were considered in [11]-[14]. In [11], the authors put forward a scheme in terms of interference aware routing for vehicular networks [12], and they continued proposing a robust scheme for interference mitigation during mobile transmissions in vehicular networks in [13]. Furthermore, power control was evaluated to reduce harmful secondary interference affecting primary users in cognitive networks. In [14], the work focused on combining interference cancellation techniques with access control to reduce the chance of packet loss and packet delay.

However, power allocation was not addressed comprehensively in the aforementioned studies in terms of opportunistic EH-assisted relay schemes. Motivated from these limitations, in this paper, we focus on power supply policies in DF FD relaying networks, where we try to achieve optimal time EH. Therefore, our main contributions can be summarized as follows:

--Closed-form expressions for outage probability and the delay-tolerant and delay-limited throughput over independent and identically distributed Rayleigh fading channels are achieved;

--The simulation results are given in terms of some parameters like self-interference, power allocation

schemes, transmit power at source node and time switching schemes for the EH protocol and FD mode. Additionally, we also compare separated power (SP) with harvested power (HP) mode;

--The proposed EH architecture helps boost the throughput performance. Furthermore, as we derive the optimal time, the optimal transmission rate is derived for HP mode.

The paper is organized as follows. The system model is illustrated in Section II. In Section III, a relaying network is investigated with the optimal power constraints for the relay. We provide the simulation results in Section IV. Finally, Section V draws a conclusion for the paper.

Notation: [gamma] denotes signal-to-noise-ratio (SNR) of specific link. [F.sub.X](*) and [f.sub.X](*) represent the cumulative distribution function (CDF) and probability distribution function (PDF) of the variable X, respectively. Pr (*) is the outage probability function. E (*) illustrates expectation operation and [K.sub.1] (*) is the first order modified Bessel function.


In Fig. 1, a two-hop system is considered, in which a power constrained relay (R) assists the communication between a source (S) and a destination node (D) due to the impossible communication between (S) and (D). It is assumed that one antenna is equipped at (S) and (D) node while (R) consists of one receiving and one transmitting antenna. The channel coefficients of three different links, including S-R (SR), R-D (RD) and the residual loopinterference (LI) are denoted as h, g and f, respectively. The channel power gains [[absolute value of h].sup.2]2, [[absolute value of g].sup.2], [[absolute value of f].sup.2] are exponentially distributed random variables (RVs) with means = dS-Rm, [[OMEGA].sub.g] = [d.sup.-m.sub.RD], and [[OMEGA].sub.f] = [d.sup.-m.sub.LI]. Let us denote the distances between (S) and (R), (R) and (D) as [d.sub.SR], [d.sub.RD], respectively. Meanwhile, dLI is denoted as the distance between two antennas at (R), and m is the path-loss exponent. It is assumed that all nodes are affected by the additive white Gaussian noise (AWGN) which is [N.sub.0] with variance [[sigma].sup.2]. Furthermore, the quasi-static channel model with ideal channel state information (CSI) is also assumed at (S) and (R). In principle, CSI could be achieved by various techniques, e.g., the pilot assisted channel reverse channel training. Note that receiving and transmitting information at (R) are carried out at the same frequency band, which leads to residual self-interference, [[absolute value of f].sup.2] regardless of the deployment of self-interference cancellation at (R).

In this paper, TSR protocol for EH is considered, in which T denotes the time block for an information transfer period. During the first phase, transmitting energy accounts for [alpha]T , in which the EH receiver exploits the RF signal and stores the direct current to the capacitor, while in the second phase, the residual amount of time, (1 -[alpha])T is used for transmitting information. Simultaneously, the received signal is decoded before transmitting antenna forwards the decoded signal to (D). Each variable corresponds with the SNR, in which single-hop transmission is carried out over the distinct channel to optimize energy efficiency.

We denote [P.sub.S] and [P.sub.R] as the transmit power at (S) and (R), respectively. Besides, they are considered as individual constraints, i.e., [P.sub.S] [less than or equal to] 1 and [P.sub.R] [less than or equal to] 1, respectively. In conventional networks, the received signal at the relay can be computed as

[y.sub.R] = h[x.sub.S] + f[x.sub.R] + [N.sub.0], (1)

where energy symbols of both source and relay are denoted by E{[[absolute value of [x.sub.s]].sup.2]} = [P.sub.S], E{[[absolute value of [x.sub.R]].sup.2]} = [P.sub.R], respectively. Each variable corresponds with the SNR, in which single-hop transmission is carried out over the distinct channel to optimize energy efficiency.

Regarding the cellular down-link transmission, the high SNR at relay node in case of small noise term can be computed as [15]

[[gamma].sub.R] = [P.sub.S][[absolute value of h].sup.2]/[P.sub.R][[absolute value of f].sup.2] + [[sigma].sup.2] = [P.sub.S][[absolute value of h].sup.2]/[P.sub.R][[absolute value of f].sup.2]. (2)

Likewise, the received SNR at the destination node can be written as

[[gamma].sub.D] = [P.sub.R][[absolute value of g].sup.2]/[[sigma].sup.2]. (3)

After deploying DF relay-assisted protocol, the overall end-to-end SNR can be expressed by

[[gamma].sub.eq] = min {[[gamma].sub.R],[[gamma].sub.D]}. (4)

III. Wireless Power Supply Policies For Relay Node

In practice, optimal power constraints at (S) and (R) are separated. Conventionally, we set the transmit power at (S) and (R) as {[P.sub.S] = 1, [P.sub.R] = 1}. Therefore, the instantaneous rate of FD relaying in DF protocol can be calculated as

[R.sub.1] = B[beta] [log.sub.2] (1 + [[]gamma.sub.eq]), (5)

where [beta] = 1/2 and [beta] = (1-[alpha]) are for SP and HP mode, respectively and B is the signal bandwidth.

In terms of the outage probability performance analysis, [P.sub.out], if the given target rate is higher than the system data rate. Consequently, the outage probability corresponds with the given target rate [R.sub.0] (bps/Hz) which can be given by


where we determine two cases, including SP and HP. This condition is modelled as the SNR threshold, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

A. Separated Power (SP) Mode

By using optimal power constraints, we can optimize the instantaneous rate. Due to the high transmission rate, the optimal power at (S), [P.sup.*.sub.S] and at (R), [P.sup.*.sub.R] can be derived by solving the optimization below

([P.sup.*.sub.S] [P.sup.*.sub.R]) = argmax ([R.sub.1]), (7)

where 0 [less than or equal to] ([P.sub.S], [P.sub.R]) [less than or equal to] 1. It is assumed that CSI is known at (R) and each SNR value stems from the average received power at (R). Therefore, the above expression can be rewritten as:


The proposed optimization problem can be solved as


Likewise, we obtain the average optimal transmit power at relay as


Proposition 1: For system performance analysis, the outage probability can be analytically calculated by

[P.sup.SP.sub.out] ([[gamma].sub.0]) = [P.sub.S][[OMEGA].sub.h]/[P.sub.S][[OMEGA].sub.h] + [P.sub.R][[OMEGA].sub.f] [[gamma].sub.0]exp([[sigma].sup.2][[gamma].sub.0]/[P.sub.R][[OMEGA].sub.g]). (11)

Proof: See in Appendix A.

B. Harvested Power (HP) Assisted Relay

Let us consider the second phase, where the received signal is forwarded to (D) after being decoded by (R). In such scenario, (R) is capable of scavenging energy from the received RF signal due to not having any fixed power supplies (i.e. batteries). Thus the received signal at (R) can be computed as [6]

[P.sub.R] = [E.sub.h]/(1-[alpha])T = [rho][P.sub.S][[absolute value of h].sup.2], (12)

where the energy conversion efficiency is denoted by 0 < [eta] < 1. In addition, this coefficient illustrates the impact of EH circuitry, the harvested energy is denoted by [E.sub.h] = [eta][alpha][P.sub.S] [[absolute value of h].sup.2]T, and [rho] = [rho][alpha][(1-[alpha]).sup.-1].

Based on (2), the high SNR at relay can be rewritten as

[[gamma].sub.R] = [P.sub.S][[absolute value of h].sup.2]/[rho][P.sub.S][[absolute value of h].sup.2] [[absolute value of f].sup.2]. (13)

Next, the end-to-end SNR can be computed as [21]

[[gamma].sup.HP.sub.eq] = min{[[gamma].sub.R],[[gamma].sub.D]} = min{1/[rho][[absolute value of f].sup.2], [rho][P.sub.S]/[[sigma].sup.2][[abolute value of h].sup.2][[absolute value of g].sup.2]}. (14)

To achieve optimal transmission rate, we have

1/[eta][alpha](1-[alpha])[[absolute value of f].sup.2] = [eta][alpha](1-[alpha])[P.sub.S]/[[sigma].sup.2] [[absolute value of h].sup.2] [[absolute value of g].sup.2]. (15)

After some simple manipulations, the optimal time switching coefficient can be determined as


Remark 1: By choosing the value of [[alpha].sub.opt] and its effect

on the instantaneous rate of the network, the (S) and (R) can harvest more energy but reduce the throughput at (D).

Proposition 2: The outage probability in EH-assisted networks can be calculated as

[P.sup.HP.sub.out]([[gamma].sub.0]) = 1-L x [PSI][K.sub.1](PSI), (17)

where [PSI]= 2[[sigma].sup.2][square root of ([[gamma].sub.0][([rho][P.sub.S][[OMEGA].sub.h][[OMEGA].sub.g]).sup.-1])], L = 1-exp(-1/[rho][[gamma].sub.0][[OMEGA].sub.f]).

Proof: See in Appendix B.

C. Asymptotic Outage Probability Analysis

So as to simplify the approximation, upper bounds in case of SP and HP for outage probability are derived. First let us start with SP case.

1) SP Case

In order to provide some practical insights into the fundamental impact of self-interference, we now expand the low interference system. In an ideal scenario of FD systems, we assume that without significant loss of generality, ([[OMEGA].sub.f] [right arrow] 0). Therefore, the outage probability can be upper bounded as

[P.sup.PS_Upper.sub.out]([[gamma].sub.0])[approximately equal to]1-exp(-[[sigma].sup.2][[gamma].sub.0] /[P.sub.R][[OMEGA].sub.g]). (18)

2) HP Case

In the high-power regime, ([P.sub.S] [right arrow] [infinity]), we apply the approximation of [PSI][K.sub.1]([PSI])[approximately equal to][PSI]1/[PSI]=1 according to ([PSI] [right arrow] 0). Thus, we can upper bound the outage probability as follows

[P.sup.HP_Upper.sub.out]([[gamma].sub.0])[approximately equal to]exp(-1/[rho][[gamma].sub.0][[omega].sub.f]). (19)

D. Throughput Performance

1) Delay-Limited Transmission

We first consider the delay-limited throughput, we have to evaluate the outage probability. As a result, at the fixed rate, [R.sub.0], we have


2) Delay-Tolerant Transmission

Regarding the delay-tolerant throughput, we calculate the ergodic capacity, [C.sup.k],k [member of] {SP,HP} at (D). Note that (S) requires less transmission rate than or equal to the derived ergodic capacity. Thus, it does not require CSI at either (S) or (R) to achieve ergodic capacity. The obtained fixed transmission rate at (S) corresponds with the ergodic capacity. Therefore, the throughput, [[tau].sup.k.sub.TO], at (D) can be written as



It is noted that ergodic capacity at (D) can be computed as



Some numerical results in these experiments are presented to confirm the analytical expressions derived in the above sections and the optimal throughput for the optimal power constraints with different parameters. To analyse the outage performance, the source transmission rate is set to fixed rate, e.g., [R.sub.0] = 2(bps/Hz) and hence the SNR threshold causing outage is given by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The transmit power at (S) is [P.sub.S] = 1. The EH efficiency is set [eta] = 0.5. Besides, a normalized system bandwidth, is set B = 1.

For simplicity, similar noise variances are assumed at all nodes, i.e., [[sigma].sup.2] = 0.5. In these simulations, we denote [[bar.[gamma]].sub.SR] = [[OMEGA].sub.h], [[bar.[gamma]].sub.RD] = [[OMEGA].sub.g] and [[bar.[gamma]].sub.LI] = [[OMEGA].sub.f].

In Fig. 2 and Fig. 3, the analytical results for throughput are depicted under different SNRs of the (S)-(R) hop with [[bar.[gamma]].sub.SR] = [[bar.[gammma]].sub.RD]. In case of SP, we consider [alpha] = 0.5 while with HP mode, optimal time switching-based [[alpha].sub.opt] is chosen for performance evaluation.

Considering the impact of time switching coefficients, Fig. 4 and Fig. 5 illustrate the optimal throughput obtained with the optimal time factor of HP and also the delay-limited throughput and delay-tolerant throughput, respectively under different time allocation coefficients.

In the considered protocol, there is an increase in throughput when a climbs from 0 to the optimal value, [alpha] = 0.1, contributing to best performance compared to SP [a,lpha] = 0.5. However, it begins falling, as [alpha] rises from the optimal value. As the values of [alpha] are smaller than the optimal time, [[alpha].sub.opt], less time is utilized for EH.

These figures confirm that self-interference factors have an important impact on throughout at every value of time factors. Interestingly, in both transmission modes, a reasonable choice of [alpha] for HP is to enable the considered protocol to satisfy a better throughput performance in many cases of self-interference.

Furthermore, the performance of HP reaches the peak and then declines slightly. Figure 6 considers the throughput performance under different transmit power at (S). It is clear that the highest throughput can be obtained regardless of the increase in the transmit power at (S), and the tight upper bound is close to the simulation results. The throughput performance changes considerably, if we choose different values of the SNR threshold. As a result, the relay with EH circuitry can satisfy proper applications for wireless communications with an acceptable SNR level.

Similarly, we consider the throughput performance under the impact of self-interference in Fig. 7. It is clear that the throughput declines as self-interference increases compared to SP's upper bound which is equal to 0. The performance is limited by both SNR threshold, at 0 dB and 2 dB, respectively.

Finally, Fig. 8 illustrates the transmission rate in terms of the optimal time switching coefficients. In case of SP, since it cannot harvest energy to assist the communication process, the transmission rate remains unchanged. Thanks to EH capacity and the installation of battery store at (R), HP outperforms SP in terms of higher transmit power.


In this paper, we propose wireless power supply policies in FD relaying networks. In particular, in HP mode, the choice of optimal time with the help of the EH protocol assist the relay in sharing energy without consuming totally it like SP. The exact expressions for outage probability and throughput are provided.

Numerical results confirm that the simulation results match well with the exact expression for outage probability. Besides that, the numerical results help gain an acceptable outage performance between HP and SP mode. We give some valuable insights into the impact of self-interference, time switching coefficients and the transmit power on the system throughput.


Proof of Proposition 1

This appendix derives the outage probability at (D) for TSR protocol. We obtain the PDF and CDF of SNR in the first hop as below.

The PDF is given by


where x [graeter than or equal to] 0. The CDF can be computed as


We have the distribution function of self-interference as below


Next, we calculate the outage probability of the overall system as


It is noted that end-to-end SNR in DF scheme can be calculated as Y = min{[[gamma].sub.R],[[gamma].sub.D]}. We have the general outage probability



This ends the proof for Proposition 1.


Proof of Proposition 2

Similarly, we first have PDF of the SNR for selfinterference


The CDF of the SNR at relay node as


Using the integral identity [16], the outage probability can be calculated as


Finally, we compute the overall outage probability as


This ends the proof for Proposition 2.

Manuscript received 16 October, 2016; accepted 21 May, 2017.

The research received a financial support from the SGS grant No. SP2017/174, VSB-Technical University of Ostrava, Czech Republic.


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Hoang-Sy Nguyen (1,2), Miroslav Voznak (1,2), Minh-Tung Nguyen (3), Lukas Sevcik (2)

(1) Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, 19 Nguyen Huu Tho St., Tan Phong Ward, Dist. 7, Ho ChiMinh City, Vietnam

(2) Faculty of Electrical Engineering and Computer Science, Technical University of Ostrava, 17. listopadu 2172/15, 708 33 Ostrava-Poruba, Czech Republic

(3) Binh Duong University, Binh Duong Province, Vietnam

Caption: Fig. 1. The system model for the energy harvesting FD relaying networks.

Caption: Fig. 2. Theory and simulation results of throughput vs. rSR under different impacts of self-interference [[bar.[gamma]].sub.LI] = 5 dB or [[bar.[gamma]].sub.LI] = 10 dB and [[alpha].sub.opt], [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] (Delay-limited mode).

Caption: Fig. 3. Theory and simulation results of throughput vs. [[bar.[gamma]].sub.SR] under different impacts of self-interference [[bar.[gamma]].sub.LI] = 5 dB or [[bar.[gamma]].sub.LI] = 10 dB and [[alpha].sub.opt], [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] (Delay-tolerant mode).

Caption: Fig. 4. Throughput performance versus time switching coefficients with [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] = 10 dB in the delay-limited mode.

Caption: Fig. 5. Throughput performance versus time switching coefficients with [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] = 10 dB in the delay-tolerant mode.

Caption: Fig. 6. The asymptotic throughput performance with performance with different transmit power in the delay-limited mode and [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] = 10 dB, [[bar.[gamma]].sub.LI] = 5 dB.

Caption: Fig. 7. The asymptotic throughput performance under impact of selfinterference with [bar.[gamma]]SR = [bar.[gamma]]RD = 20 dB.

Caption: Fig. 8. The transmission rate vs [P.sub.S] other parameters: [[bar.[gamma]].sub.LI] = 5 dB, [[bar.[gamma]].sub.SR] = [[bar.[gamma]].sub.RD] = 20 dB, [alpha] = 0.1 and [[alpha].sub.opt].
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Author:Nguyen, Hoang-Sy; Voznak, Miroslav; Nguyen, Minh-Tung; Sevcik, Lukas
Publication:Elektronika ir Elektrotechnika
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Date:Aug 1, 2017
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