Full-Duplex Cooperative Relaying with Non-Linear Energy Harvesting for Vehicular Communication

Vaijayanti Panse,Tapan Kumar Jain

Abstract—This paper analyses the performance of fullduplex(FD)dual-hop vehicular cooperative network with decode-and-forward (DF) protocol.At FD relay nodes,we examine the effects of non-linear hybrid power time splitting (PTS) based energy harvesting (EH).All three nodes-source (S),relay (R),and destination (D)-are assumed to be moving vehicles.The expressions for the system’s outage probability (OP) over double (cascaded)Rayleigh fading channels are derived.We also analyse the impact of residual self-interference (RSI) caused at FD relay on system’s performance.We compare the performance of system with two relay selection techniques,namely,maximum channel gain-based (Max-G) relay selection and minimum RSI-based(Min-SI)relay selection.This paper considers the joint effect of time splitting ratio and self-interference cancellation (SIC) level to find the optimum EH duration.Additionally,the effect of time splitting ratio and average signal-to-noise ratio (SNR) on outage and throughput performance of the system are also investigated in this paper.The derived expressions are validated through Monte Carlo simulations.

Keywords—Cooperative communication,vehicular networks,energy harvesting,full-duplex,outage probability

I.INTRODUCTION

The use of vehicular communication is a cutting-edge strategy that enables autonomous vehicles and intelligent transportation systems.Vehicle-to-vehicle (V2V) communication is used in the next-generation wireless systems that are being developed to create smart cities,smart transportation,Internet connectivity between vehicles,automated parking,and driver-less experiences.The fading effect brought on by high vehicle speeds,a large number of barriers or scattering elements,and low antenna heights are one of the main challenges in vehicular communication.Additionally,continual energy supply is needed by the vehicular nodes while they are utilizing wireless channels for continuous communication.So,for the purpose of carbon neutrality and energy sustainability,green communications are taken into account in V2V communication systems.To support this scenario,wireless energy transfer has emerged as a recent research trend to provide green energy solutions for future V2V communication.

In literature,different energy harvesting (EH) models are discussed to provide continuous energy supply to the Internet of things(IoT)devices.Ref.[1]discussed the linear EH models based on time splitting(TS)and power splitting(PS)techniques.The linear model,however,is not practical for implementation as it does not consider the sensitivity and saturation thresholds of the harvesting circuit.The non-linear model for EH presented in Ref.[2]takes care of these practical aspects of EH circuits.A hybrid model based on power time splitting(PTS)was presented in Ref.[3],which ensures the reliability of the networks while harvesting more radio frequency (RF)energy.With the advancement in science and technology,almost every device is connected to the Internet leading to big data which is forecast to increase rapidly.The IoT and future wireless networks demand improving the spectrum efficiency of wireless systems.The in-band full-duplex (IBFD) operation has drawn research attention due to the restricted wireless spectrum that is currently available to meet rapidly increasing demands[4].If self-interference(SI)is reduced by around 110 dB,a full-duplex (FD) system can double the spectrum efficiency compared to a half-duplex(HD)system[4-6].Thus,it is encouraging to consider FD vehicular nodes to improve the overall system performance.

Cooperation in wireless communication,using relays,plays a vital role in improving the coverage of wireless network,in addition to allowing nodes to transmit at low powers.Thus,the expansion of the wireless network’s coverage and increased reliability may be accomplished effectively by combining cooperative communication and EH approaches.As a result,many studies focus on performance analysis of radio frequency energy harvesting(RF-EH)cooperative communication systems over Rayleigh as well as Nakagami-mchannels[7-11].As FD systems with sufficient self-interference cancellation (SIC) have better performance as compared to HD,cooperative communication techniques combined with FD-EH nodes have become promising solutions for wireless networks.The outage performance of FD-EH cooperative non-orthogonal multiple access (NOMA) system is analysed in Ref.[12]along with the impact of residual self-interference(RSI).Usage of non-linear EH at FD relay is investigated in Ref.[13]to analyse the effects on the outage,throughput,and error performance of the system.It also discussed the combined effect of RSI and non-linear EH on the system’s performance.Ref.[14]analysed the performance of FD amplifyand-forward (AF) systems with hardware impairments and also studied the effect of RSI on the IBFD-AF relay system.Some recent studies also discussed benefits of harvesting RF energy from SI signal,thus enabling effective utilization of RF signals[15-17].This self-energy recycling also improved the performance of FD relay systems.

While using multiple relay nodes in a multi-hop cooperative communication network,it is very crucial to select the best relay node for communicating the information to the destination.The method used to choose a relay node has a big infuence on the system performance[18].In the literature,many relay selection methods have been described based on various selection criteria.Refs.[10]and[11]discussed the selection of relays in a dual-hop cooperative network based on first hop channel gain.Some papers also discussed the impact of relay selection based on signal-to-noise ratio (SNR)[19-20].However,selecting the best relay in the FD relay network in presence of RSI is relatively difficult.Ref.[21]provided three relay selection strategies based on optimal relay selection,maximum harvested energy relay selection,and lowest SI relay selection to optimize the harvested energy in FD relaying networks.

A combination of cooperative communication and FD-EH technique is an exciting research direction that can be explored for V2V communication.FD-EH cooperative communication is a promising technique for intelligent transportation systems (ITS) because of its various advantages such as reduced end-to-end delay times,spectrum efficiency,and ensuring continuous power supply to power-constrained nodes.In literature,the recent research is focused on the applications,channel models,and protocols of V2V communication.Considering the severe fading in case of V2V communication,the cascaded Rayleigh fading channel is mostly used in literature for implementing vehicular communication scenarios.Recently,while using RF-EH for V2V communication,the bit error probability(BEP)of a dual-hop decode-and-forward(DF)relaying system is calculated based on how antennas are used at the relay.The antennas are utilized considering the modes with dedicated antenna for EH and linear/ non-linear EH models[22].NOMA technique in cooperative V2V communication employed in Ref.[23]considers a practical scenario with double Rayleigh fading between the communicating vehicles (near and far) with the base station.The system performance is analysed for outage probability(OP)and ergodic capacity in case of near and far users.The FD-EH in V2V communication is studied in Ref.[24]considering double-cascaded Rayleigh fading where energy is harvested from a power beacon (PB) using time splitting EH protocol.The performance of dual-hop FD relaying in V2V communication with single relay node is analysed in Ref.[25].The performance analysis of vehicular networks with EH and cooperative relaying have been analysed to obtain closed-form expressions for OP and symbol error rate(SER)over cascaded Rayleigh channels.Ref.[26]discussed the outage performance of dual-hop cooperative communication over cascaded Rayleigh fading channels between the vehicles with multiple access points(APs).The exact expressions were obtained for OP and SER considering two scenarios with different channel models.Ref.[27]investigated the ergodic capacity (EC)of dual-hop FD-EH relaying for V2V communication.The source node was assumed to be stationary while relay and destination were moving vehicles.The closed-form expression for EC was derived and the impact of RSI for both AF and DF relaying was studied.The V2V communication along with the effect of RSI and hardware impairments is investigated in Ref.[28].The performance is compared with the traditional systems where the negative impact of above factors is justified.

A.Motivation and Contribution

Due to complexity of modeling the channels for V2V communication,there is still a scope for research to analyse the performance of FD-V2V communication in terms of OP,error,and throughput.Motivated by this,this paper proposes a dual-hop FD-EH system with multiple relay nodes for vehicular communication.This system utilizes non-linear hybrid PTS-based energy harvesting at the relay nodes.Also,unlike other related works,we present a practical scenario when all the nodes(source(S),relay(R),and destination(D))are moving vehicles.We derive the expression for OP and the system is analysed over double Rayleigh fading channels between all the nodes.Following are the main contributions of this paper.

•We investigate the outage and throughput performance of dual-hop FD-EH V2V network where all the nodes are assumed to be moving vehicles and all the channels are modelled by double Rayleigh fading channels.Thus,this system model represents a practical scenario for vehicular communication.

•We derive the expression for OP of a non-linear hybrid PTS-based energy harvester system over cascaded Rayleigh fading channels.The significant impact of RSI at FD relay nodes is also investigated.

•The system performance is studied for maximum channel gain-based relay selection (Max-G) and minimum RSIbased relay selection(Min-SI).

•This paper investigates the combined effect of RSI and EH duration on system performance to find the optimum EH duration based on the level of RSI.In addition to this,the impact of time splitting ratio and average SNR on the outage and throughput performance of the system are also studied in this paper.

The rest of this paper is organized as follows.Section II describes the system and channel models.Section III presents the operation of a non-linear hybrid PTS-based energy harvester.Section IV presents the performance analysis of the considered system in terms of OP and throughput.Finally,section V presents the numerical findings,and section VI wraps up this paper.

II.SYSTEM MODEL

Fig.1 shows the system model for dual-hop FD-EH vehicular network with multiple relay vehicles.All the nodes (S,R,andD)are assumed as moving vehicles.TheSandDoperate in HD mode and have a direct path between them.TheSvehicle node communicates withDwith the help of multiple relay nodes.The system consists of a set of FD relay vehiclesRn(n ∈{1,2,···,N}).Each relay vehicle has two antennas and a non-linear hybrid PTS-based energy harvester.The best relay vehicle node is selected based on two selection schemes namely,Max-G and Min-SI.We consider DF relaying protocol where the selected relay vehicle node decodes the signal and forwards it to the destination.Since,all the nodes are moving considering the realistic scenario,the channels between the nodes are characterized by double(cascaded) Rayleigh fading distribution.The channel betweenStojth relay is denoted byh1jand the channel betweenjth relay andDis denoted byh2j,indicating first hop and second hop,respectively.After selecting the best relay(Ri),the channel from sourceSto the best relayRi(RitoD)is indicated byhSR(hRD).

Fig.1 Full-duplex dual-hop vehicular network

The link betweenSandDis represented as,hSD.d1represents the distances betweenStoRi,d2is the distance betweenRitoD,andd3represents distance betweenStoD,respectively.Because of simultaneous transmission and reception of signal,a strong SI is caused at the FD relay,indicated byhRR.However,a number of SIC techniques may be used to reduce the SI to the noise foor.We assume the RSI still exists at the FD relay due to imperfect SIC.All channels are assumed to exhibit cascaded Rayleigh fading distribution whose probability density function (PDF) and cumulative distribution function(CDF)are represented as follows[25,27].

wherepq ∈{SR,RD,SD},K0(·)represents zero-order modified Bessel functions of the second kind andK1(·)represents the first-order modified Bessel functions of the second kind,respectively[29].

III.OPERATION OF NON-LINEAR HYBRID PTS-BASED ENERGY HARVESTER

Fig.2 illustrates the non-linear hybrid PTS-based energy harvester[3]at the FD relay vehicle node.The non-linear EH model takes care of the practical aspects of EH circuits,such as,sensitivity and saturation thresholds,thus allowing more realistic implementation[2].In addition to this,we are using a hybrid PTS-based protocol which provides better harvested energy while handling reliability issues simultaneously.Using the time splitting ratio(α),the complete transmission time in Fig.2 is separated into two time slots.In the first time slot,αT,the relay performs pure EH while in the remaining time slot,(1-α)T,the relay utilizes PS to harvest the energy as well as perform information transmission.The PS is performed for harvesting the RF energy according to PS ratioρ ∈{0,1}.Energy harvesting is performed inρfraction of received signal power and the remaining fraction of (1-ρ)is utilized for decoding the information.We assume that different active and passive SIC techniques are implemented on FD relay nodes to cancel the SI.However,due to imperfect SI cancellation at the relay,RSI is still assumed to be present.The decoded signal is then forwarded toD.We consider DF relaying in this system.

Fig.2 Hybrid PTS-based energy harvester

During first time slot,the signal fromStoRiis given as

we also assume direct path to be present betweenSandD.The signal received atDthrough directS-Dpath is given as

wherePsis the source transmit power,xsrepresents the normalized signal of transmission,withE[xs]2=1,mdenotes the path loss exponent and,wRrepresents additive white Gaussian noise (AWGN) atRiandwDdenotes the AWGN atD,such that,wR～C N(0,) andwD～C N(0,σD2),whereC N(·) represents circularly symmetric complex Gaussian noise.The strong SI channel at the FD relay is denoted ashRR.It is assumed that the SI channel exhibits frequency,nonselective Rayleigh block fading with=E[|hRR|2].

Considering DF relaying protocol,Ridecodes the signal and sends it on to D.The signal received atDthrough relaying path is given as

wherexRstands for the decoded signal atRiandPRstands for the transmission power ofRi.

Assuming negligible energy harvested from SI signal,the input signal power at relay will bePin=Ps|hSR|2.

Using a non-linear hybrid PTS-based protocol,the total amount of energy thatRihas harvested will be determined as

wherea1=αTη+(1-α)Tηρ.

So,the expression for the transmission power ofRiis

From(3)-(6),and(8)and assuming significant RSI after SIC,the instantaneous SNR expressions can be written as

whereγSRis instantaneous SNR betweenSandRi,γRDrepresents instantaneous SNR betweenRiandD,andγSDrepresents instantaneous SNR betweenStoDlink.Herea2=(1-ρ)(1-α)Tanda3=

The partial relay selection (PRS) strategy utilised in Ref.[10]is the basis for the Max-G relay selection scheme employed in this paper.According to Max-G,Schooses the optimal relayRidepending on the first hop channel gains,which is represented as,

In this case,it is possible to derive the PDF of|hSR|2usingNth order statistics[32].The PDF of|hSR|2is provided as given below considering the channel coefficients|h1j|2to be independent random variables.

The PDF of the instantaneous SNR of the chosenS-Rilink,|hSR|2,will be derived by substituting the values of the PDF and CDF of|h1j|2from(1)and(2)into the equation above.

We also use Min-SI relay selection scheme in this paper which is based on minimum SI present at the relay node.The relay with the lowest SI is chosen as the best relay in this scheme.Here,we assume SI to be Rayleigh distributed,the PDF of minimum of SI signals can be obtained from order statistics as given in Ref.[32].However,the selectedS-Rilink in this case will follow a cascaded Rayleigh distribution whose PDF is as defined in (1).Thus,while performing outage analysis of the system,the PDF of|hSR|2should be used accordingly.

IV.PERFORMANCE ANALYSIS

A.Outage Performance Analysis

This section derives a mathematical expression for OP of the FD dual-hop vehicular network with hybrid PTS-based energy harvesting.The probability that the throughput is lower than the desired target rate is known as the OP.The throughput fromStoDfor relaying path and direct path can be expressed as[2,33]

Assuming selection combining (SC) at D,the probability that the maximum throughput for relaying and direct links will be less than the desired rate is known as the OP.Consequently,OP may be represented as[8]

The outage analysis for the considered system is analysed in this section.The following is the mathematical formula for outage probability.

For the proof of OP,please refer to the appendix.

B.Throughput Analysis

The system’s throughput is the highest rate that it is capable of achieving with successful transmission.The network throughput can be defined in terms of OP as follows[33].

wherer0is the source transmission target rate and(1-α)is total transmission time.

The analytical expression for the throughput can thus be obtained by substituting the expression for OP in terms ofO1andO2.Thus,analytical expression can be simply represented as

V.NUMERICAL RESULTS

This section presents the numerical results which analyse the performance of the dual-hop FD vehicular network considering non-linear EH.The parameters used in this paper are as indicated in Tab.1.

Tab.1 Performance parameters

Fig.3 compares the system’s outage performance for different levels of SIC levels.It can be observed that the system’s performance is significantly impacted by the SIC level.With increasing the amount of SIC at the selected relay,the system’s outage performance improves.

Fig.3 Effect of SIC level on outage performance of system

Fig.4 shows the effect of energy harvesting duration on system performance with different SIC levels.

Fig.4 Joint effect of α and SIC level on outage of system

It has been shown that the amount of SIC applied to the relay has an impact on the optimal value ofαas well.Thus,Fig.4 illustrates the combined effect ofαand SIC levels.As the amount of SIC increases,it is shown that the optimal value ofαalso increases.This is because as more SI is suppressed,the instantaneous SNR of the relaying path increases which allows the use of more time duration for pure EH.The optimumαfor maximum SIC of 100 dB is observed to be 0.3.

Fig.5 compares the system’s performance with different relay selection schemes.It can be observed that selection of relay also affects the system’s performance.As seen from Fig.5,Max-G relay selection gives better performance as compared to Min-SI scheme.This is because Max-G ensures the best channel link betweenS-Ri.However,selecting a relay based on its SI level,as in Min-SI,does not guarantee an optimumS-Rilink,which results in poor performance.

Fig.5 Impact of relay selection scheme on system performance

Fig.6 shows the system’s throughput performance for different values ofα.As the value ofαis increased,the system throughput decreases.This is because,asαis increased,more energy will be harvested.But,at the same time,the duration(1-α)required for information decoding will be decreased,which reduces the system throughput.There is no optimum value ofαfor maximising the throughput performance.

Fig.6 Effect of energy harvesting duration on system’s throughput

VI.CONCLUSION

This paper analysed the outage and throughput performance of FD vehicular cooperative relaying with hybrid PTSbased non-linear energy harvester.We derived the equations for OP over cascaded Rayleigh channels under the assumption that all nodes are moving vehicles.This paper analysed the significant effects caused by the FD relay node’s RSI on OP.We compared the outage performance of the system for Max-G and Min-SI based relay selection to observe its impact on the system’s performance.This paper also studied the joint effect of SIC level and duration of energy harvesting on outage performance of the system.Results indicated that SIC level is also one of the important factors in determining the optimal time splitting ratio.This paper also presented the impact of time splitting ratio on system’s performance in terms of throughput.

APPENDIX

A)There are two independent possibilities for the relaying path and direct path SNR’s to fall below the threshold SNR.Consequently,

Solving forO1,we get,

From(20),O2,is given as

We will first solve forI1.From(23),I1can be obtained as

Case I:C ＜A:I11can be written as

Case II:C ＞A:I12can be written as

Thus,I1will be calculated as

From(23),the expression forI2is obtained as

Case I:B ＞C:I21is written as

Case II:B ＜C:I22can be written as

Thus,I2will be calculated as

Substituting the values ofI1andI2from (25) and (27) in(23),the value ofO2can be obtained.