XIAO Shu-yan(),LI Shi-yin()(),CUI Jie( ),ZHANG Xiao-guang()

1 School of Information and Electrical Engineering,China University of Mining & Technology,Xuzhou 221116,China

2 Unit No.91469 PLA,Beijing 100841,China

Introduction

With the ever-increasing demand for high data rate communications and wider bandwidth,the frequency spectrum bands become more and more scarce.However,restricted by the static spectrum assignment policy,a large portion of spectrums are not being used efficiently,resulting in serious spectrum band congestion.Cognitive radio (CR) technology proposed by Mitolaetal.[1]has been considered as a potential technology to improve spectrum utilization by sharing the spectrum band.Spectrum sensing is one of the major functions of CR to discover available spectrum bands for cognitive (unlicensed) users (CUs) without interfering in the transmissions of primary (licensed) users (PUs).Standalone spectrum sensing[2]based on single user can be divided into three categories: energy detection,matched filter detection,and cyclostationary detection.If CU has limited information on the PU signals,energy detector[3]is optimal.But it’s deeply affected by hidden terminal due to the pass loss and shadowing.As a further development of standalone sensing,cooperative spectrum sensing (CSS) schemes[4-7]have received great attention.There are many research achievements about CSS methods divided into two categories: hard combination (HC) algorithms[8]and soft combination (SC) algorithms[9].HC methods include such as “AND” rule,“OR” rule,and “K out of N” rule.But,they are not efficient enough to meet the demanded performance of spectrum sensing.SC methods are the ones that can fuse the information sensed by CUs.Spectrum sensing scheme based on Dempster-Shafer (D-S) theory in Ref.[10] is a typical SC algorithm for the consideration of reliability degree of different CUs and introduction of reliability function which can acquire more accuracy.

However,requiring CUs to behave in a synchronous way,all the CSS algorithms mentioned above assume that CUs sense and send the results to fusion center (FC) simultaneously by stopping their own transmissions.In practice,the reports of CUs do not always arrive at FC at the same time even cannot arrive because of the shadowing and uncertainty of wireless channels.The synchronization requirement may not be practical.Asynchronous cooperative spectrum sensing (ACSS) method is addressed in Ref.[11],in which the FC using “OR” rule to improve the ability of sensing cannot achieve perfect performance because of the HC of “OR” rule.ACSS scheme proposed in Ref.[12] considers the transformation rate of the PUs and the difference of the sensing time and assigns differential weight of sensing information according to differential credibility on the results of cooperation.Sliding-window ACSS algorithm proposed in Ref.[13] can improve the sensitivity by fusing sensing results in real time,but at the same time computational complexity is increased in FC.Reference [14] raised an ACSS algorithm based on probability,in which fusion always begins after the sensing information from CUs is collected.Usually the collection process is time-consuming,so it loses the advantage of asynchronous schemes: timeliness.

In this paper,a triggered ACSS scheme based on D-S theory is proposed.The main innovative points of this paper are as follows: (1) when the FC receives useful sensing information,the fusion process is triggered,which can ensure FC fuses the sensing information in real time; (2) each cognitive user calculates the reliability function with the double threshold spectrum sensing method to improve the local sensing accuracy; (3) different from the ACSS schemes mentioned above,the proposed scheme can increase sensing accuracy by D-S theory and decrease the calculation complexity of FC by screening useless sensing reports.

1 System Description

The system model of ACSS is made up of PUs,CUs,FC,base station of PU,etc.Figure 1 shows a CR system with one PU,three CUs,and one FC,in which there is shadow effect between CU1and PU while multipath effect between CU2and PU.The sensing time lengths (STLs) of CU1,CU2,and CU3are identified asts1,ts2,andts3while the arrival time of CUs to the FC ast1,t2,andt3respectively.The confidence measure functions can be obtained by utilizing double threshold spectrum sensing method.FC makes the decision whether PU signal is present according to the reports receiving at different time.

Fig.1 The system model of ACSS

Supposing that there areiCUs sending the local sensing report and STLtsito FC.Meanwhile,FC records the momenttiwhen thei-th report arrives in FC.The delay of transmitting duration can be ignored because it’s relatively momentary compared with the STL.We can obtain the detection time of thei-th CUtdiis

tdi=ti-tsi.

(1)

FC can make a judgment whether thei-th report sensed by thei-th CU is overdue according to thei-th CU’s detection time.

2 Proposed ACSS Scheme

Figure 2 presents the flow chart of the proposed ACSS scheme.And the sensing processes are as follows.

Process 1: every CU employs energy detector to sense local information with double threshold.

Process 2: every CU transmits the local sensing result to FC.

Fig.2 The flow chart of ACSS scheme based on D-S theory

Process 3: when FC receives a report from CU,a judgment will be made by FC,and the result will be abandoned if it’s overdue; if not,the FC will continue to judge whether the sensing information is the same as the former one received,if not,the data fusing process is triggered,otherwise the sensing result will be abandoned.

Triggered ACSS scheme based on D-S theory proposed in this paper includes three parts: local sensing with double threshold,selection of useful sensing information,and triggering fusion process,fusing useful report based on D-S theory.

2.1 Local sensing with double threshold

The detection problem for local sensing at CUs can be stated in terms of a binary hypothesis test,with the hypothesisH0identifying PU signal being absent,and alternative hypothesisH1representing PU signal being present,as

(2)

The energyXreceived by a single CU is

N=2TW,

(3)

where,Tis the sensing time,andWrepresents the sensing bandwidth.WhenN>200，Xcan be approximated as a Gaussian random variable under both hypothesesH0andH1,with meansμ0,μ1and variancesσ0,σ1respectively[11].

(4)

whereSNRis the signal to noise ratio of the PU transmitting signal at CU.

In conventional energy detection[3],every CU compares the energyXreceived from PU with the thresholdη0: ifXis greater thanη0,we identify the PU being present; if not we obtain the PU being absent.Proposed in Ref.[15],energy detection with double threshold needs to set two thresholdsη0,η1compared with energyX.

In energy detection with double threshold[15],false alarm probabilityPf,probability of detectionPd,and probability of miss detectionPmare identified as follows

(5)

(6)

(7)

whereη0,η1are two thresholds of the energy detection with double threshold,and Γ(.),Γ(.,.) are the incomplete gamma function and the gamma function respectively whileQ(.,.) is the generalized MarcumQ-function.

In ACSS based on D-S theory with double threshold,every CU estimates the reliability functionsmi(H0),mi(H1) according to its local sensing informationXi,as follows

mi(H0)=P{Xi<η0|H0}+P{η0≤Xi<η1|H0}=

(8)

mi(H1)=P{Xi>η1|H1}+P{η0≤Xi<η1|H1}=

(9)

whereμ0,μ1are means ofXandσ0,σ1are variances ofXunder hypothesesH0andH1,respectively.

2.2 Select useful information triggering fusion

Every CU employs energy detection to sense the local information and then transmits sensing resultsmi(H0),mi(H1) and STLtsito FC.At the same time,FC records the momenttiwhen thei-th user’s sensing information is received.Then FC screens the useful sensing results.

(1) Overdue screen: when fusion center receives CU’s sensing report,FC should make a judgment,whether the report is overdue.“Overdue” means the detection time of the result is earlier than the time when a final decision is made last time.We can calculate the detection time from Eq.(1).

(2) Further screen: adopt run-length coding (RLC) method to screen sensing results and trigger fusion.

RLC is a simple technology to realize lossless compression,especially suitable for binary sequence of compression.In this paper,RLC method is adopted to screen the sensing result in FC.When the CU’s sensing results received by FC are not overdue,it should also make a judgment,whether the report is the same with the last received one.Firstly,we make a local decision: ifmi(H0)>mi(H1),“0” is decided,and “1” is decided ifmi(H1)≥mi(H0).If CU transmits continuous“0” or “1” to FC,it means this CU considers the same state of PU inH0orH1.When FC receives no report from CU,FC also considers the state of the observing spectrum has not changed.In other words,if FC receives continuous“0” or “1”,FC doesn’t acquire any useful information about PU being present or absent.At the same time there are redundancy data in FC.So when FC receives the report different withRlastrepresenting the last receiving report,a fusion process is triggered in FC.Otherwise it has to abandon this report and wait for the next one.

2.3 D-S fusion

In cooperative spectrum sensing scheme based on D-S theory,receiving reliability functions {mi(H0),mi(H1)} from each CU,FC combines all the reliability functions and makes the final decision with Eqs.(10)-(12) as shown in Fig.3.

Fig.3 The diagram of fusion by D-S theory

The frame of discernment,Θis a finite set of mutually exclusive and exhaustive hypotheses.AnyA?Θ,m(A) represents the basic probability assignment (BPA) ofA,which also can be called evidence ofA.Assumem1andm2are two independent basic probability assignments.Through D-S theory,we can achieve a new BPA

(10)

In this paper,Θ={H0,H1} are defined to characterize the uncertainty and the support of certain hypotheses.In FC,decisions associated with credibility from distributed CUs are combined using Eq.(10) according to D-S theory of combination,resulting in final credibility of CR system for each hypothesis in the form of BPA,namelym(H0) andm(H1),as

(11)

(12)

By comparingm(H0) andm(H1),the final decision is made upon a following simple strategy

(13)

whereγ0andγ1are the final decision thresholds.

3 Performance Evaluation and Simulation Results

(14)

In this section,we compare our scheme with some typical asynchronous and synchronous algorithms: the sliding-window algorithm in Ref.[13],the D-S scheme in Ref.[10],and the“AND”，“K out of N” algorithms in Ref.[8].We compare the detection probabilityPd,and the receiver operating characteristics (ROC) curves.

As shown in Fig.4,it depicts the curves between detection probabilityPdand the SNR.When the SNR increases,Pdof this five schemes are all increasing.AndPdrises up to 1.0 when the SNR is greater than -5 dB for all of the five schemes.In addition,when the SNR is low,the proposed scheme can obtain a significant performance compared with the other four schemes.This also shows the superiority of the double threshold spectrum sensing method.Seen from the simulation result,it is obvious that the detection performance of the scheme proposed in this paper is better than the other four schemes when the SNR changes.

Fig.4 The curves of the detection probability under different SNR

Figure 5 refers to a more practical environment: SNR of 12 CUs is different from each other.And SNR ranges from -20 dB to -10 dB.As shown in Fig.5,it depicts the ROC curves.We obtain the ROC curves of the proposed scheme by changing the decision thresholdsγ0,γ1while we get ROC curves of the algorithms of Refs.[10,13] by changing the detection thresholds of energy detection.The performance of the proposed scheme increases obviously.This also demonstrates that the double threshold judgment and screening out useless information have greater performance gain to comprehensive decision.

Fig.5 The curves of ROC

In Fig.6,as the number of CU increases,the total time cost of the three algorithms,the proposed scheme in this paper,sliding-window algorithms in Ref.[13],and D-S method in Ref.[10],increase smoothly.But the total time cost calculation amount of the proposed scheme is obviously lower than that of the other two methods.

Fig.6 The curves of the time consumption under different number of CU

4 Conclusions

By combining local reliability function,taking history credibilityRlastand the detection timetditogether into consideration and screening out useless information with RLC method,the detection performance of proposed scheme is superior to the previous schemes.The proposed scheme in this paper guarantees the accuracy and real-time performance of the ACSS while reduces the time cost and the calculation amount of FC.As a whole,this scheme does well in overcoming the limitation in practical application.Not needing CUs to behave in a synchronous way,ACSS algorithm is easier to be implemented,and more sensitive than ACSS scheme.But at the same time it is more complex than ACSS scheme.

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