Geng Ke,Go Qing,Fei Li,Xiong Hugng,*

aSchool of Electronic and Information Engineering,Beihang University,Beijing 100083,China

bWuhan Maritime Communication Research Institute,Wuhan 430205,China

Relay selection in cooperative communication systems over continuous time-varying fading channel

Geng Kea,Gao Qianga,Fei Lib,Xiong Huaganga,*

aSchool of Electronic and Information Engineering,Beihang University,Beijing 100083,China

bWuhan Maritime Communication Research Institute,Wuhan 430205,China

Channel state information;Cooperative communication;Fading;Relays;Wireless networks

In this paper,we study relay selection under outdated channel state information(CSI)in a decode-and-forward(DF)cooperative system.Unlike previous researches on cooperative communication under outdated CSI,we consider that the channel varies continuously over time,i.e.,the channel not only changes between relay selection and data transmission but also changes during data transmission.Thus the level of accuracy of the CSI used in relay selection degrades with data transmission.We first evaluate the packet error rate(PER)of the cooperative system under continuous time-varying fading channel,and find that the PER performance deteriorates more seriously under continuous time-varying fading channel than when the channel is assumed to be constant during data transmission.Then,we propose a repeated relay selection(RRS)strategy to improve the PER performance,in which the forwarded data is divided into multiple segments and relay is reselected before the transmission of each segment based on the updated CSI.Finally,we propose a combined relay selection(CRS)strategy which takes advantage of three different relay selection strategies to further mitigate the impact of outdated CSI.

1.Introduction

Air traffic is increasing significantly due to the increase of unmanned aerial vehicle(UAV)and small general aviation aircraft.The expected growth in air traffic will lead to the increment in data transmission of aeronautical communication.The high-rate and high-reliability data transmission in wireless channel is needed for future aeronautical communication.Fading in wireless channel tremendously affects the performance of wireless communications.In aeronautical communication,wireless fading is severe since channel coefficients of aeronautical link change frequently.Thus it is imperative to mitigate the impact of wireless impairment in order to improve the performance of aeronautical communication.

Cooperative communication has been shown as a promising approach to combat wireless impairments by exploitingspatial diversity without the need of multiple antennas at one node.1,2In a cooperative communication system,intermediate nodes are utilized as relays to forward data from source to destination over independent wireless channels by two manners,i.e.,the one way relaying and the two way relaying.No matter which manner is chosen,relay selection that instructs a subset of relays in the cooperative system to forward data has been considered as an effective method to improve the performance of cooperative communication.3–7When the nodes in cooperative system have multiple antennas,antenna selection,which has similar influence on the system performance as relay selection,is also investigated.8

Most of the literature dealing with relay selection assumes that the channel state information(CSI)used in the selection procedure is the same as that actually experienced by the data transmitted(i.e.,ideal CSI).However,from a practical point of view,the channel varies over time and a time gap exists between relay selection and data transmission,and thus the CSI used in the selection procedure is not consistent with actual one during data transmission.In other words,the CSI used in relay selection is an outdated version of that during data transmission.As a result,the selected relays may not actually be the best for data transmission.Recently,the impact of outdated CSI on the performance of cooperative communication is investigated.9–13It is found that the outdated CSI results in serious performance degradation.Some relay selection strategies have been proposed to improve the performance of cooperative communication under outdated CSI.14–19Relay is selected based on channel prediction.14–17The relay with the maximal predicted channel strength14,15or the minimal predicted outage probability16,17is selected to forward data.Multiple relays are selected based on the outdated channel strength.18An outage-optimal relay strategy is proposed based on the optimization of the transmitting power of the relays to minimize the conditional outage probability.19

All the above research work implicitly or explicitly assumed a block fading channel where the CSI varies between relay selection and data transmission but maintain constant during data transmission.However,the duration of data transmission is comparable with or even larger than the gap between the relay selection and data transmission.Thus the channel variation during data transmission should be considered in cooperative communication system under outdated CSI,especially for the scenario of aeronautical communication.The correlation between the CSI used in relay selection and that experienced by the data transmitted decreases as the data is being transmitted.In other words,the level of accuracy of the CSI used in relay selection degrades with data transmission.To the best of our knowledge,this issue has not been addressed by the previous researches.

In this paper,we study relay selection under continuous time-varying fading channels in a decode-and-forward(DF)cooperative communication system.The channel not only changes between relay selection and data transmission but also changes during data transmission.We first evaluate the packet error rate(PER)performance of a cooperative system under continuous time-varying fading channel through simulation.It is found that the PER performance of cooperative system deteriorates more seriously under continuous time-varying fading channel than under block fading channel.Then,to improve the PER performance,we propose a repeated relay selection(RRS)strategy,which is a simple but effective approach.The forwarded data is divided into multiple segments.Before the transmission of each segment,the CSI is updated and relay is reselected based on the updated CSI.Finally,to further mitigate the impact of outdated CSI on the PER performance,we propose a combined relay selection(CRS)strategy which takes advantage of three different kinds of the existing relay selection strategies,i.e.,the relay selection strategy based on channel prediction,the multiple relay selection strategy and the repeated relay selection strategy.

2.System model

We consider a DF cooperative system consisting of one source(S),one destination(D),andKhalf-duplex relays,where each node is equipped with only one antenna.The direct link between the source and the destination does not exist,as a result of high shadowing between them.The source wants to transmit a data packet containingNbbits to the destination.The cyclic redundancy check(CRC)bits are included in the transmitted bits for error detection of data reception,but no error correction code(ECC)bit is included.Through modulation with constellation sizeb(i.e.,bbits per symbol),the bit sequence with lengthNbis mapped to a symbol sequence with lengthN=Nb/bfor each packet.

2.1.DF cooperative scheme

The relays in the system assist the source to transmit the data packet to the destination(Fig.1).The cooperation period is divided into three phases.

Data Phase 1:the sourceSbroadcasts the data packet and each relay in the system listens.After receiving the data packet,all relays decode it.With CRC bits,each node knows whether the data packet is decoded correctly or not.The relays that have decoded data correctly(or called decodable relays)are the candidates for data forwarding.

Relay Selection Phase:some of the decodable relays are selected to forward the received data packet based on the channel states between relays and the destinationD.

Data Phase 2:the selected relays forward the received data packet to the destination simultaneously over the orthogonal channels as that in previous works.2,4The destination combines the signals from the relays using a maximal ratio combiner(MRC)and decodes the received data.

The relay selection can beconducted in centralized manner10,11or distributed manner.3,4,18In centralized relay selection,a central unit(e.g.,the destination)in the system collects all information regarding the channel states between the decodable relays and the destination and feeds the selection result back to the relays.In distributed relay selection,each decodable relay competes to participate in data forwarding based on a timer whose duration is inversely proportional to the quality of the link between relay and the destination.In this paper,to simplify the notation,we adopt the centralized manner in relay selection.The distributed manner obeys the same rules and formulations.

Concerning power allocation,we assume that the source consumes a half of the total transmitting power of the system to transmit its data,while the rest of the transmitting power is evenly distributed among the selected relays to forward data.4

2.2.Continuous time-varying channel model

(1)Generate a complex Gaussian process with variance 1(the real and imaginary parts each have variance 1/2).

(3)Interpolate the discrete-time filtered Gaussian noise(FGN)process to match the input signal sampling rate,using a combination of polyphase and linear interpolation filtering.

where ρkis the correlation coef ficient betweenh(k0

D)andh(k1D).It is given by

2.3.Packet error rate

A data packet is in error when at least one of the symbols is decoded incorrectly.Each symbol in the data packet is decoded based on the channel response it experienced.Since this paper focuses on the relay selection,the receiver is assumed to know the precise channel responses of the received symbols.9–18

Under the continuous time-varying channel modeled in this paper,the packet error rate(PER)of the data transmission from nodeAtoBis related to the symbol error rate(SER)as

3.PER evaluation

In this section,the PER performance of the cooperative system under the continuous time-varying channel is evaluated through simulation.The performance of the cooperative system is related to the relay selection strategy.We adopt the opportunistic relay selection(ORS)strategy3,4to select relay.The ORS strategy is one of the most common relay selection strategies since it can achieve excellent performance and even the optimal performance for DF cooperative system under ideal CSI,and it has been extensively studied under block fading channel model.By the ORS strategy,the decodable relay with the strongest instantaneous channel strength is selected to forward data,which can be expressed as

where D denotes the set of the decodable relays.We set the simulation scenario according to the situation that small aircrafts fly in formation at low altitude.In the simulation,5 relays are used in the cooperative system(K=5).To simplify the setting of the simulation scenario without loss of generality,we assume thatdSk=dkD=1000 m fork=1,2,···,5 and the maximum Doppler frequency shifts for all pairs of nodes are equal,i.e.,fAB=f0(i.e.,all the channels in the system are independent and identically distributed4,9).The simulation results for independent and non-identically distributed channels will be given at the end of this paper.The bits transmitted are modulated by binary phase shift keying(BPSK)to map to symbols,i.e.,b=1.The transmission rate of the symbols is set to be 1 MBaud.Other system parameters,in line with previous works,4,9,14,15are summarized in Table 1.

Fig.2 shows the PER performance of the cooperative system over average received signal-to-noise ratio(SNR)under different channel models.It can be found that PER performance of the cooperative system deteriorates more seriously under continuous time-varying fading channel than under block fading channel,where the channel remains constant during data transmission.This indicates that the variation of channel during data transmission has significant impact on the performance of the cooperative system.The impact comes from two aspects.On the one hand,the correlation between the CSI used in relay selection and that experienced by the data transmitted decreases with data transmission.On the other hand,the correlation between the channel responses experienced by any two symbols decreases,and hence all the symbols are more impossibly correctly decoded together.To investigate which aspect has larger influence on the PER performance,we simulate the cooperative system when the channel varies continuously over time,but the relay is selected accurately based on the CSI of each symbol.The corresponding PER performance is plotted in this figure using a dash line marked by circle.It can be seen that the PER performance under this situation is close to that under ideal channel model(channel remains constant during the whole cooperation period)while far away from that under continuous time-varying fading channel.This implies that the level of accuracy of the CSI used in relay selection influences the PER performance of the cooperative system more largely.

In the following,we will study the influence of the system parameters on the PER performance of the cooperative system.Fig.3 shows the PER performance over the length of the data packet(cf.Fig.3(a)),the Doppler frequency(cf.Fig.3(b))and the time duration of relay selection phase(cf.Fig.3(c))under different channel models.

In Fig.3(a),it can be found that the PER performance under continuous time-varying fading channel becomes away from that under block fading channel as the length of the data packet increases.This is because the channel during data transmission changes slightly when the data packet is short,while it changes more remarkably for longer data packet.Additionally,a gap always exists between the PER performance under continuous time-varying fading channel(or under the block fading channel)and that under ideal channel model since the CSI used in the relay selection is outdated when the channel varies over time.

In Fig.3(b),it can be found that the PER performance under continuous time-varying fading channel becomes away from that under block fading channel as the Doppler frequency increases,while approaches to it when the Dopplerfrequency is higher than a certain value.This can be explained as follows.When the Doppler frequency is low,its increase makes the channel change more remarkably,and thus the PER performance deteriorates more seriously under continuous time-varying fading channel.When the Doppler frequency is higher than a certain value,the CSI used in the relay selection is almost independent of that experienced by the data packet no matter under which channel model.The impacts of outdated CSI on the PER performance under different channel models tend to be the same.Thus the PER performance under continuous time-varying fading channel approaches to that under block fading channel.However,a gap always exists between the PER performance under these two channel models,since the correlation between the channel responses experienced by any two symbols decreases under continuous time-varying fading channel and all the symbols are more impossibly correctly decoded together.Note that under ideal channel model the PER performance does not change with the increase of the Doppler frequency since the channel is assumed to remain constant during the whole cooperation period.

Table 1 System parameters.

In Fig.3(c),it can be found that the PER performance under continuous time-varying fading channel becomes close to that under block fading channel as the time duration of relay selection phase increases.This is because for longer time duration of the relay selection phase,the CSI used in the relay selection and that experienced by the data packet are more inclined to be independent no matter under which channel model,and the impacts of outdated CSI on the PER performance under different channel models tend to be the same.Similar with Fig.3(b),a gap always exists between the PER performance under these two channel models.

From the simulation results shown in Figs.2 and 3,we can also see that the PER performance of the cooperative system deteriorates largely under continuous time-varying fading channel compared with that under ideal channel model.This implies that wireless fading is more severe for the aeronautical link whose channel coefficients change more frequently than other slow fading channels.Thus new cooperative strategies combating the wireless fading are needed to guarantee the reliability of aeronautical communication,which can in turn improve the data rate.

4.Proposed relay selection strategies

In this section,to improve the PER performance under the continuous time-varying channel,we propose a repeated relay selection(RRS)strategy that updates the selected relay to adapt to the channel variation.We also propose a combined relay selection(CRS)strategy which takes advantage of three different kinds of the existing relay selection strategies.

4.1.Strategy description

Because the selected relay by the traditional ORS strategy cannot adapt to the channel variation during data transmission,the PER performance of the cooperative system deteriorates largely.To improve the PER performance,we propose a RRS strategy.In this strategy,the cooperation period is divided into two phases,i.e.,data broadcast phase and relay selection/data forwarding phase,while the relay selection/data forwarding phase is divided into multiple sub-phases(cf.Fig.4).Each sub-phase is further divided into two parts as follows:

Part 1:the latest CSI between the decodable relays and the destination is acquired and the decodable relay with the strongest instantaneous channel strength obtained from the updated CSI is selected.

Part 2:a segment of the data packet is forwarded by the selected relay.

The division of the data packet can be preset in the system as parameters or determined by the source temporarily and informed to the nodes in the system by packaging in the data.Since the reselected relay is one of the decodable relays,it has the segment of the data packet that need to be forwarded.By this strategy,the time for redoing the relay selection is reduced and the fact that the PER performance of cooperative communication can be improved largely though this strategy originates from a simple idea.

There are some other strategies given in the literature to select relays under outdated CSI.14–18These relay selection strategies can be classified into two categories.The first kind selects single relay based on some channel prediction methods.14–17The relay with the maximal predicted channel strength14,15or the minimal predicted outage probability16,17is selected to forward data.The second kind relaxes the constraint of single relay selection and allows more relays to forward data.In previous work,18a so-called N+NT-ORS strategy is proposed,where multiple relays are selected based on the outdated channel strength.

If we take advantage of the two kinds of the relay selection strategies in the literature and the proposed RRS strategy to select relays,the impact of the continuous time-varying channel on the performance of cooperative system will be mitigated more effectively.To further improve the PER performance,we propose a CRS strategy by combining the MOP strategy,16N+NT-ORS strategy18and RRS strategy proposed in this paper.The cooperation period is divided as in RRS strategy.The relay selection is performed as follows:

(1)Nbest relays are selected out of the decodable relays,with respect to the predicted outage probability given in previous work.16

(2)The ratio of the predicted outage probability on theNth best relay to that of the rest of the decodable relays is tested against a normalized threshold μ∈[0,1]and only those relays passing this test are selected in addition to theNbest relays.

The setting of normalized threshold μ in CRS strategy is on the basis ofN+NT-ORS strategy in previous work.18Under this strategy,the relays that are not theNbest ones but also have good channel quality can be selected,and the number of selected relays can be adjusted dynamically to adapt to the channel variant for each cooperative transmission.The value of the threshold influences the number of the selected relays and the transmitting power of each selected relay,and hence,has impact on the system performance.For lower threshold,more relays can be selected to participate in the cooperation,but each selected relay uses lower power to forward data due to the total power constraint.If the threshold becomes higher,the number of selected relays decreases,but the transmitting power of each relay becomes higher.Thus the threshold can be optimized to further improve the system performance,and we will investigate it in the future.

4.2.Simulation results

The PER performance of the proposed RRS and CRS strategies under the continuous time-varying channel is evaluated through simulation.The data packet is evenly divided intoMsegments to be forwarded inMsub-phases.The parameters used are chosen from Table 1.

Fig.5 shows the PER performance of RRS strategy over average received SNR under different number of the subphasesM.It can be seen that the PER performance can be improved noticeably by dividing the data packet into multiple segments for high SNR region(e.g.,SNR larger than 15 dB),while the extent of the PER improvement decreases as the number of the sub-phasesMincreases.For low SNR region,the PER improvement is not noticeable and the PER performance is even worse by dividing the data packet into multiple segments.This implies that increasing the number of the subphases cannot always improve the PER performance.There is an optimal number of sub-phasesM*for minimal PER.

Fig.6 shows the PER performance of RRS strategy over the number of the sub-phasesM(SNR equal to 15 dB).It is clear that the optimal number of sub-phasesM*exists for minimal PER.If the data phase is divided into more sub-phases,the CSI used in the relay selection is updated more frequently and can adapt to the channel variation;therefore the PER decreases with the increasing number of the sub-phases when data phase is divided into few sub-phases.On the other hand,as the number of sub-phases increases,more time gaps are introduced among the data segments.This will cause that the correlation between the channel responses experienced by any two data segments decreases and all the segments are more impossibly correctly decoded together.Thus the PER will increase after the number of sub-phases exceeds a certain value.To obtain the optimal number of sub-phasesM*,it is necessary to derive the PER of RRS strategy,which is a function of the number of sub-phasesM,and then establish the minimization problem of the PER with the variableM.The optimal solutionM*can be obtained using some optimization algorithms,e.g.,the brute-force search method.Unfortunately,the calculation of PER is too complex to be dealt with,and thus the optimal number of sub-phasesM*is found through simulation method in this paper.

Fig.7 shows the PER performance comparison among the existing relay selection strategies including the traditional ORS strategy,MOP strategy,16N+NT-ORS strategy,17RRS strategy and CRS strategy proposed in this paper.We simulate these strategies in two scenarios,i.e.,all the channels in the system are independent and identically distributed(i.i.d)and they are independent and non-identically distributed(i.ni.d).For i.i.d scenario,the system is set as given in Section 3,while for i.ni.d scenario the relays are distributed randomly in a 2000 m×2000 m square area and the source and the destination are located at the middle of one side and the opposite side respectively.The number of the sub-phases in the RRS and CRS strategies is set to be 2,and the parametersNand μ used in CRS andN+NT-ORS strategies are set to make the average number of the selected relays be equal to 2.From this figure,we can see that the proposed CRS strategy achieves large improvement of the PER performance compared with other strategies,and the proposed RRS strategy outperforms the traditional ORS strategy and the MOP strategy.According to the simulation parameter settings,the maximum relative speedv=λf0between arbitrary two nodes is about 110 km/h,which is a typical speed for small aircrafts at low altitude.As the speed increases,the Doppler frequency shifts will increase,while the performance improvements of the proposed strategies are similar(Fig.7).We omit the simulation results for other Doppler frequency shifts due to limited space of this paper.

Note that there are some costs for each of the relay selection strategies under outdated CSI given in the literature and proposed in this paper.For MOP strategy,the statistical information of the channel state is needed to predict the outage probability.ForN+NT-ORS strategy,multiple orthogonal channels are needed to be allocated to the multiple relays selected.For RRS strategy,a longer delay of the data transmission is inevitable due to the multiple relay selection parts introduced in the cooperation period.The CRS strategy has all the above costs since it combines these strategies.In a practical system,it is necessary to consider the system constraints,the performance improvement of these relay selection strategies and their costs in order to choose an appropriate relay selection strategy to combat the impact of the channel variation on the system performance.

5.Conclusions

In this paper,we study the relay selection under continuous time-varying fading channels in a DF cooperative communication system.We first evaluate the PER performance of cooper-ative system under continuous time-varying fading channel.It is found that the PER performance of the cooperative system deteriorates more seriously under continuous time-varying fading channel than when the channel remains constant during data transmission.Then,to improve the PER performance,we propose a repeated relay selection(RRS)strategy that updates the selected relay to adapt to the channel variation.It outperforms the traditional ORS strategy.Finally,to further mitigate the impact of channel variation on the PER performance,we propose a combined relay selection(CRS)strategy by taking advantage of three different kinds of the existing relay selection strategies.The CRS strategy achieves large improvement of the PER performance compared with other strategies.

As we have seen,the number of the sub-phases introduced in the RRS strategy and the threshold used in the CRS strategy affect the PER performance of the cooperative system in complex ways,and the optimization problem of these parameters can be studied to minimize the PER of the system.We leave this to future research.

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9 March 2016;revised 29 May 2016;accepted 30 June 2016

Available online 21 December 2016

?2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is anopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:hgxiong@buaa.edu.cn(H.Xiong).

Peer review under responsibility of Editorial Committee of CJA.