Adaptive Relaying Protocol for Decode and Forward Full-Duplex System over Rician Fading Channel:System Performance Analysis

Tan N.Nguyen,Minh Tran,Thanh-Long Nguyen,Miroslav Voznak

1 Wireless Communications Research Group,Faculty of Electrical and Electronics Engineering,Ton Duc Thang University,Ho Chi Minh City,Vietnam

2 Optoelectronics Research Group,Faculty of Electrical and Electronics Engineering,Ton Duc Thang University,Ho Chi Minh City,Vietnam

3 Center for Information Technology,Ho Chi Minh City University of Food Industry,Ho Chi Minh City,Vietnam

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

Abstract:In this paper,the system performance of a decode-and-forward (DF) full-duplex (FD) adaptive relaying network over the Rician fading environment is proposed,analyzed and demonstrated.In the first stage,the system is presented with the energy harvesting and information transmission processes.After that,the analytical expressions of the achievable throughput,the outage probability,and symbol error ratio (SER) were proposed,analyzed and demonstrated.Finally,the analytical results are also demonstrated by Monte-Carlo simulation in comparison with the closed-form expressions in the influence of the key system parameters.The results show that the analytical and simulated results match for all possible parameter values.

Keywords:relaying network; throughput; outage probability; SER; wireless energy harvesting (EH)

I.INTRODUCTION

Nowadays,energy harvesting has emerged as an alternative solution for prolonging the lifetime of wireless devices and a promising technique for the communication network in the near future.The sources for energy harvesting are very different source such as solar,wind,vibration,radio frequency (RF).However,RF energy harvesting provides key advantages over other energy collection methods due to its predictable and stability,low cost,and small form factor.One of the hottest research categories in the RF energy harvesting area is the wireless powered communication network (WPCN) where network devices harvest energy from the signals transmitted by RF energy sources in the first step and then utilize this harvested energy for their communication needs [1-3].In the last decade,many research papers focused on the WPCN and how to improve its performance and efficiency.This concept of a tradeoff between EH and information transmission in WPCN was considered in [4] and extended in [5].Moreover,the concept of partial network level cooperation for EH networks was introduced in detail in [6],and in [7] wireless EH and information transfer in cognitive relay networks was intensely studied.Then WPCN with RF energy harvesting is the hot research area in this time.

In WPCN,the two traditional time switching (TSP) and power splitting (PSP) protocols have been widely studied in the literature,and many of these studies have compared the performance of the two EH protocols under different scenarios [8-12].From these studies,the TSP and PSP protocols have some drawbacks,for instance,TSP has to lose some information while it switches to the harvesting mode and PSP has a low coverage area.Furthermore,PSP requires a complicated hardware structure to make sure that a proper portion of energy from source signal is extracted for energy harvesting.In contrast,TSP can simplify the hardware at the expense of the throughput or achievable rate of the system.Based on the fact that,both TSP and PSP protocols have their drawbacks,the prospective idea is to combine these two protocols to get the best out of them.This is a solution can obtain in this paper by using an adaptive relaying protocol [10-12].

In this paper,the system performance (in the term the achievable throughput,the outage probability,and symbol errors ratio (SER) of a one-way decode-and-forward (DF) full-duplex (FD) adaptive relaying network over Rician fading channels is proposed,analyzed and demonstrated in details.In the first stage,the analytical expressions of the achievable throughput,outage probability,and SER were proposed and demonstrated.After that,the effect of various system parameters on the system performance is studied with closedform expressions of the system performance.Finally,the analytical results are also demonstrated by Monte-Carlo simulation in comparison with the closed-form expressions.In the numerical results,the effect of various system parameters on the system performance of DF FD adaptive relaying system was demonstrated.The results indicated that the analytical and simulated results match for all possible parameter values.The research results provided the practical solution for the progress of the WPCN in the communication network.The main contributions are summarized as follow:

1) The system model of the adaptive relaying network for the one-way full-duplex system over the Rician fading channels is proposed.

2) The closed-form expressions of the outage probability,achievable throughput,and especially SER of the system model are proposed and derived.

3) Conduct Monte Carlo simulation to verify the analysis results,to compare the performance of TSP,PSP,and Adaptive protocols.

The structure of the rest of this paper is organized as follows.Sections II presents the system model of one-way FD adaptive relaying (ARP) network over Rician Fading Channels.Sections III proposed the system performance of the model system in details.Section IV provides the numerical results and some discussions.Finally,Section V concludes the paper.

In this paper,the system performance of the adaptive relaying full-duplex decode-and-forward network over the Rician Fading Channel has been proposed,analyzed and demonstrated.

II.SYSTEM MODEL

In this section,DF adaptive relaying protocol for one-way full-duplex system network over Rician fading channel is proposed and presented in figure 1.In figure 1,the information and energy are transferred between the source (S) and the relay (R) in one-way with the full-duplex system.The energy harvesting and information processing of the adaptive relaying network are proposed in figure 2.Total interval time for the energy harvesting and information processing is denoted by T,which is divided into three intervals.The first portion of timeαTis used for energy harvesting at R from the source S.The the second interval (1-α)T/2is used for energy harvesting the powerρ PSfrom the source S signal by the relay node.In the remaining interval time (1-α)T/2,a fraction power(1-ρ)PSis used for information transmission from the source to relay and after that from the relay to the destination.In this model,0 ≤ α ＜ 1and0 ≤ ρ ＜1.Ifα=0,this scheme becomes PSP.Ifρ=0then it becomes the TSP.

2.1 Energy harvesting process

During the energy harvesting phase at the relay node,the received signal can be expressed as:

In this equation,xsis the energy-transmitted signal from sources withi s the zero-mean additive white Gaussian noise (AWGN) at R with zero mean and varianceσr2.Here E{.} denotes the expectation operation.

The energy harvested at the relay node is the combination of two components:the first one is the received energy during the first interval αT(from TSP),while the second one comes from the PSP interval (1-α)T/2.The amount of harvested energy can be given by the below equation:

whereηα,ηρrepresent the EH efficiency of the two stages TSP and PSP,respectively,0＜ηα＜1 and 0＜ηρ＜1.

Finally,the received power at the relay node can be computed as:

Fig.1.System model.

Fig.2.The energy harvesting and information processing.

2.2 Information transmission process

In this subsection,the information transmission phase is considered.The received signal at the relay can be expressed as (5):

wherenrdenotes the AWGN noise at the relay node.Moreover,xris the loopback interference due to full-duplex relaying and satisfiesdenotes the loopback interference channel.

Now,the end-to-end signal-to-noise(SNR)for S to R link can be calculated by (10):

Replace Prto (6) we have (7):

The received signal at the destination node is given by:

wherendis the additive white Gaussian noise (AWGN) atRwith zero mean and varianceσd2.The equation (8) can be reformulated as:

Here,we assume that the distance of loopback channel between two antennas at the relay is small.Therefore,f belongs to Rayleigh fading channel,the channels from S to R and from R to D are Rician fading channels.Moreover,we denote

The probability density function (PDF) of random variable (RV)φiis [13],wherei∈(1,2).

λiis the mean value of RVφi.For more reformulation,we assume thatλ1=λ2.In the equation (10),K is the Rician K-factor defined as the ratio of the power of the line-of-sight (LOS) component to the scattered components andI0(·) is the zero-th order modified Bessel function of the first kind.

The equation (10) can be rewritten as follows:

The cumulative density function(CDF) of RVφ1can be computed as in [14].

The probability density function (PDF) of random variable (RV)φ3can be formulated as:

where 1/λ3is the mean value of RVφ3.Then the cumulative density function(CDF) of RVφ3can be computed as the following equation:

More details of the analytical model for the proposed system is presented in details in the following sections [15-22].

III.THE SYSTEM PERFORMANCE

Based on the system model on above section,the system performance of the relay network is presented,analyzed and demonstrated in this section.In this section,the outage probability,throughput performance,and Symbol error ratio analysis (SER) of the proposed system are proposed and derived.

3.1 Outage probability

whereγth=2R-1,in which R is the source rate.The equation (15) can be rewritten as:

In this session,we consider:

Using equation (14) we have:

We denote:

Using equation (11) and (12),the equation (20) can be rewritten as the following:

Using Table of Integral Eq[3.471,9] in [16],the equation (23) can be rewritten as:

Finally,the outage probability can be calculated as:

3.2 Achievable throughput:

The achievable throughput at the destination node can compute by:

3.3 Symbol error ratio analysis

In this section,we obtain new expressions for the Signal Error Rate (SER) at the destination.We first consider the outage probability,which was obtained in [18].Thus,we have

whereγ=min(γr,γd) and

Q(t)=is the Gaussian Q-function,ωandθare constants which is specific for modulation type.(ω,θ)=(1,1) for BPSK and (ω,θ)=(1,2) for QPSK.As a result,before obtaining the BER performance,the distribution function ofγis expected.Then,we begin rewriting the SER expression given in (14) directly regarding outage probability at the source by using integration,as follows

Using equation (20),we obtain (31) shown in the bottom at this page.

We denote:

Using table of integral eq(3.361,1) in [16],we have:

Here we employ following equations (6.643,3) in [16]

Where Γ(·) is the gamma function andW(·) is the Whittaker function.

We apply Taylor series:

Equation (25) can be recomputed (43) shown in the bottom at this page.

Proof similar with I2,we have:

Fig.3.Outage probability (a) and achievable throughput (b) of the system model versus ρ and α.

We obtain SER as following equation:

IV.NUMERICAL RESULTS AND DISCUSSION

In this section,Monte Carlo simulation was conducted to verify the analysis developed in the previous section by generating random channel responses.For simplicity,in our simulation model,we assume that the source-relay and relay-destination distances are both normalized to unit value.For this model,the outage probability,achievable throughput,and SER are analyzed in details.The main simulation parameters are listed in table 1.

Firstly,in order to verify the effectiveness of the time switching factorαand the power splitting factorρon the outage probability and the throughput of the system model,we present the outage probability concerningαandρ,as shown in figure 3 for ARP,TSP and PSP protocols.In figure 3a,we investigate the outage probability of the model system versus the power and time factors.In this research,we assume that the source powerPs=10 dB,0＜α＜1,and 0＜ρ＜1.The simulation results indicate that the analytical expression agreed fully with the Monter Carlo simulation results.In addition,it is noted that the outage probability decreased in the beginning values of the power and time factor and after that,it had a huge increase.For other cases,the outage probability is always minimized whenρ=0.5-0.7 andα=0.4-0.6.Similarity,Fig.3b shows the effect of power and time factor on the achievable throughput of the network system with the same parameters like in the figure 3a.The simulation results show that the Monter Carlo simulations have been performed,which validates the correctness of the analytical results in the previous section.

Fig.4.Outage probability (a) and achievable throughput (b) of the system model versus K.

Fig.5.Outage probability (a) and achievable throughput (b) of the system mode versus ratio PS.

Figure 4a and 4b demonstrate the influence of the K-Rician factor on the outage probability and the throughput,respectively.Here we assume thatα=0.3,ρ=0.3,and the source power Ps=15 dB.The simulation results indicated that the outage probability falls and the throughput rises up when theKvaried from 0 to 5.The optimal simulation results match up with the theoretical optimal results perfectly.

Figure 5a and 5b show the relationship between the outage and the throughput with the source powerPs,respectively.In this case,Psvaries from 0 to 20 dB.On the other hand,we investigate the effect of R on the outage and throughput of the system in the Fig 6a and 6b.In all Figs we assume thatα=0.3,ρ=0.3,andPs=15 dB.From the results,the Monter Carlo simulation results totally confirm the correctness of the analytical expressions on above section.

Fig.6.Outage probability (a) and achievable throughput (b) of the system mode versus R.

Fig.7.SER versus PS.

Finally,Fig.7 studies the SER of the model system in connection with the source power Psin all ARP,TSP and PSP protocols.From the research results,it is clearly observed that the Monte Carlo simulations guarantee the correctness of the analytical results.

V.CONCLUSIONS

In this paper,the system performance of the adaptive relaying full-duplex decode-and-forward network over the Rician Fading Channel has been proposed,analyzed and demonstrated.Firstly,the analytical analysis of the model system is demonstrated.After that,the closed form expressions of the outage probability,achievable throughput,and SER are proposed and derived.Finally,the numerical results show that the analytical expression and the simulation results using Monter Carlo method are totally matched each other.Moreover,this paper has provided practical insights into the effect of various system parameters on the system performance of the model network and the comparison between the adaptive,the time switching and power splitting relaying network.The results could provide the prospective solution for the communication network in the near future.