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呻西逼怯 China Communlcations 

Determination of Threshold for 

Energy Detection in Cognitive 

Rad io Sensor Networks 

Hao Jianjun,Li Jin 

School of Information and Communication Engineering,Beijing University of Posts and Telecommunications 

Beijing 1 00876.P R.China 

Abstract:The Internet of Things(1oT)is called the 

I。INTRODUCTlON 

world’S third wave of the information industry.As 

the core technology of IoT,Cognitive Radio Sensor 

The Internet of Things(IoT)is called the world's 

Networks(CRSN)technology can improve spec— 

third wave of the information industry foHoWing the 

trtma utilization efficiency and lay a sofid foundation 

computer and the Internet.It has attracted increas. 

for large—scale application of IoT.Reliable spectrum 

nig attention in many countries[1_3].In China,na- 

sensi’ng is a crucial task of the CR.For energy de— 

tional leaders give it high priority.1oT has been a— 

tection,threshold Will determine the probability of 

dopted as a national strate ̄j. 

detection(Po)and the probability of false alarm Pf at 

Sensor network,the core technology of IoT, 

the same time.、Ⅳhfie the trheshold increases P and 

plays an extremely important role in promotnig the 

Pf will both decrease.In this Paper we foCUS on the 

development of IoT.In the future,IoT Will be Wide— 

maximum of the difference of Pd and Pf,and try to lV used.and the end product Will reach severaI 

fmd out how to determine the trheshold with this 

times or even hundreds of times larger than the cur— 

precondition.Simulation resuks show that the pro— 

rent Internet.Sensor networks are typically used in 

posed method can effectively approach the ideal op— 

ISM bands.such as the 2.4 GHz which is a very 

timal resuk. 

crowded spectrum resource restricting large—scale 

Key words:Internet of 

Things;Cognitive Radio 

sensor network applications. Sensor networks 

Sensor Networks;energy 

detection;threshold 

based on cognitive radio(Cognitive Radio Sensor 

Networks)technology can 

14 2011l1 

RESEARCH PAPER 

沦艾集锦 

improve spectrum utilization efficiency and lay a 

solid foundation for large—scale application of IoT 

tional conlmunications system.such as Matched 

Filter Detection,Energy Detection and Cyclostation— 

[4—8]. 

Akey sisue in CR is spectnma sensing,i.e.the relia- 

ble detection ofthose spectral ranges that are current— 

ary Feature Detection,also can be used in spectrum 

sensing.The following is a briefdescription. 

2.1 Energy Detection 

yl accessed by PUs.The second part ofthis paper will 

briefly describe the existing CR frequency spectrum 

If SUS cannot gather enough PUs’sinalg informa— 

tion.the sub—optimal detection scheme iS energy de- 

detection of several major.For energy detection,the 

decision threshold is a very important factor which in— 

lfuences the probability of detection )and probabili- 

ty of false alarm(尸f).The third part balances be— 

tween two probabilities and discusses the differnet 

SNRs’decision to set a reasonable threshold.Finny, 

detailed simulation of theoretical results and actual re— 

suits will he compared. 

I1.SPECTRUM SENSING 

Spectrum sensing capacity is one of the most im— 

portant preconditions for CR's proper working.The 

SUs must be able to immediately detect the pres- 

ence/absence of PUs and use the spectrum only if 

communication does not interfere with any PUs. 

The PUs have no obligation to change their own 

structures and the cognitive radio network to share 

the specturm.The most effectvie way to detect 

spectrum holes is to detect the PUs receiving data 

within their operatnig range.SUs monitor the radio 

spectrum environment to detect the frequency 

bands that are not accessed by PUs.Spectrum 

sensing scheme may consist of single--node detec・- 

tion and multi—node joint detection. 

Single—node detection model can be used under 

the basic assumption that Eq.(1)description: 

)= 州 ) (1) 

where f)is the signal received by SUs; (f)is the 

singal transmitted to PUs; ( )is additive white 

Gaussian noise;the case that the PUs are inactive is 

referred to as hypothesis/40;hypothesis refers to 

another case that the PUS are actvie.The most pop— 

ular techniques used in singal processing by tradi一 

tection.To measure the received singal energy,we 

need to calculate the square of the output singal of 

band_。pass filter with bandwidth Wand integral with—- 

ni the tmie period T.Compared with the decision 

threshold,we can determine whether there are PUS. 

The main advantage of the energy detection algo— 

rithm is simple.but the drawback is poor perform— 

ance.Through the singal energy or power spec— 

trum,it does not differentiate between singal and 

noise and distinguish different communications 

system’s singa1. 

2.2 Matehed r Deteclion 

For SUs detecting the singal of PUs,the optimal de- 

tector is the ideal matched fdter,because it allows 

the received Singal to Noise Ratio(SNR)maximiza— 

tion.The greatest advantage of matched fdter is that 

it can have high processing gains in a very sh0n 

time.However,it must effectively demoduhte the 

singal of PUs which means that it requires prior 

knowledge ofthe singal ofPUs,such as modulation 

method and order,pulse shaping,and data packet 

format.A clear disadvantage of matched filter de— 

tection is that SUs would require a dedicated receiv— 

er for each type of PU 

2.3 Cyclostationary Feature Detection 

Reference[9一l0]proposes a spectrum sensing 

scheme called cyclostationary feature detection. 

Modulated singals are in general coupled with sine 

wave carriers,pulse sequences,repeating spreading, 

rfequency hopping and cyclic prefixes which result 

ni built—in periodicity.Although the data is stationary 

random,however,the statistics of these modulated 

singals,mean and autocorrelation are cyclical in na— 

ture and therefore called cyclostationary.By analy— 

zing the spectral autocorrelation function we can 

2011 1 

1 5 

呻西遏镊 china Communications 

detect these features.Through spectrum autocorre— 

altion function,we Call differentiate modulated sig— 

nals,interference and noise in low SNR.Of course, 

it is more complex than the energy detcteor and re— 

Pf=P( )>£I )=J P。( ) (3) 

When the PU is actve,accordiing to Ref.[121, 

there si E(T)=txl=(入+1)6:,D(T)= =(2A+ 

quires a longer observation time. 

Ⅲ。SINGLE NODE DETECTION 

Energy detection has been extensively used in CR. 

Decision threshokt plays a very important role in de— 

termining the probability ofdetection and false alarm 

ni energy detectoin.The probability of detection and 

false alarm will be up and down while the decision 

threshold increases and decreases.Obviously,for 

atl optimal decision trheshold,the detection proba— 

b should be sa h as possible while the false a— 

lann probability should be sa low as poss ̄le.Based 

on this consideration,this paper will balance be— 

tween detcetion probability and false alarm probabil一 

and determine a reasonable decision threshold by 

maximizing the difference between Pd and尸f[11]. 

3.1 System model 

As a result of Eq.(1),the signal received by SU 

while PUis active can be represented as 

f)= (f)+ (f) 

sAsuming: 

l1 Noise signal is real Gaussian white noise with 

zero—mean and varianceD[凡(f)]= . 

2)The PU adopted BPSK singal,h denotes the re— 

ceived SNR while the PU si active. 

3)In energy detection,the test statistic is TO,)= 

∑ I 1),(D 1 ,where N is the sample number ni 

SU 

According to the i.i.d central limit theorem, 

when N si large,TO,)approximates the Gaussian. 

In the absence ofthe PU, )= o= ,D(T)= 

= 

4 /Ⅳ.The probability density function(PDF)of 

T can be written as 

)=e一 /( 27rfi。) (2) 

If the detection threshold is .then the probabili- 

ty of false alarm is given by 

1 6 2011 

1)6 ̄/N.The PDF of T can be represented by 

Pl )一e- / 6 ) (4) 

If the detection threshold is ,then the probabili- 

ty of detection can be represented by 

Pd P(T(V)>sl )=j P )dx (5) 

3.2 Determination of thres11oId 

The detection trheshold s will determine the proba— 

bility of detection and the probabiliyt of false alarm 

at the same time.Thus,when the SNR is constant, 

there is a that maximizes the difference between 

Pd and Pf,i.e.satsifies 

) P(H)I P- ) 

尸( )I Po ) 一max (6) 

Differentiating )with respect to ,by judging 

the relationship between the difference and zero to 

determine the monotony of the situation,then 

厂(8) 尸( ( )一尸(H0 。 ) 

= 

— =__2 w60  

e~一 

一—=二_ 2

e 

l J

 

丌6 

Determination of the relationship between the 

厂 )and 0,can be equivalently converted to deter- 

mination of the relationship between Eq.(8)and 1. 

s = e 

/[ e 】 

: =~P( )6p 。 一 (I8)^- 

。 

Then g1 )on logarithmic operations: 

g2 ) In )) 

nI P(Ho)+ m + ln 

: 

+ 

2一 2 、 

Thus equivalently converted to determine the rela‘ 

tionship between Zq.(9)and 0. 

Substituting 0, l, 0 and 6l in Eq.(9)and 

RESEARCH PAPER 

沦文 锦 

simplifying it into 

tween the detection probability and false alarm prob— 

+ 

2,v 1 

4 A + 2 

ability with various SNRs.The sign“+”refers to 

the simulated value of detection threshold and the 

curve refers to the theoret ̄al values.Furthermore, 

the simulated results match the theoret ̄al results 

g2( ) 一 

2A +2A+l 

N 

4A+2 

2A+1 1 

ln 

J 

(10) 

wel1. 

When the SNR is more ideal,i.e.A>1/2,g2( ) 

is an opening down quadratic function.Denoting the 

two roots ofg2 )=0 by 1 and 2,theng2 )>0 

within interval( 1, 2),g2( )<0 on(一。。, 2)and 

( 2,+∞).It is clear in the range( 1,s2)satisfying 

_厂 )>0.Therefore,the target function 占)at

3 

2 3 

 the 

2 

8 

2 will obtain the maximum value.Solving the e- 

quation g2(£)=0 yields 

一6 …) 

where 

(A)=1+(2a一1)2A +2A+1+ ± ・ 

In +— m— J+ ] 

IV.SIMULATlON 

In this section,computer simulation resuks are 

presented to evaluate the detection threshold choice 

for energy detection technique with various SNRs. 

The simulation scenar ̄assuming: 

1)PU adopted BPSK,and at any time the idle 

probability for PU is 50%. 

21 SU's received SNR and noise variance are 

known. 

31 Per sampling points JV=10. 

Figure 1 shows the comparison between simula— 

ted and theoretical detection threshold obtained ac— 

cording to Eq.(10)by maximizing the difference be- 

+Real ++/  

● . 

… 

l0 2I【-L 

2 2 , ● 

4 2 2 8 6 4 

/ 

+ 

/ 

/ . 

/ 山 

0 1 2 3 4 5 6 7 8 9 l0 

SNR/dB 

巧g.1 Acts!midlhe0re6c甜deleelionthresholdm跹.蛐 ng 

diference between Pd and Pf forvar ̄m SN凡 

For the CR.the most important issue is still to 

ensure a high detection probability.Therefore,we 

choose to observe the curves of detection probability 

and false alarlTl probabiliyt and difference between the 

wto probabilities VS.various detection trhesholds with 

SNR=3 dB.4.8 dB.Since it has been assumed that 

the prior probabiliyt of PUs’presence or absence is 

50%,we can directly observe the 一Pf curve.In 

Figures 2 and 3,comparing the actual maximum val- 

ue of Pd—Pf with the corresponding theoretical val- 

ue of 一尸f at the detection trheshold with SNR=3 

nad 4.8 dB respectively,the difference between them 

si less than l%.at the same time can achieve a high 

detection probability. 

2011_1 

17 

2 

6 

呻国逼{专 China Communications 

jIll蛊q0J^ 

\ 

\ 

_- 蚀

 ,

——

P t 

meet this need,just make a slight change ofthe two 

terms’coefficient in Zq.(6).呻西逼性 

Acknowledgements 

This workwas supportedin part bytheNationalNatural Science 

、 

、 舶 +

Real 

Th

eore6ca ̄ 

{ 

(1& 

、 { 

 

, 

√ 

\ 

Foundation of China(Grant Nos.60971082.60872O49.6O972073 

… 

、 

\ 

| 、 t \ 

} \ 、\ 

\ 

Threshold 

玛 , 柚dfile稠№喇 e be 咖themforvmious 

d曲ect‘Dn曲l嚣t-0 while SNIR=3皿 

——

rfPi 

f212 , rd 

Pt 

1 、 \ 一j—}  RThe

eoretical

al 

 

, \ 

\ 

\ 

, 、 

、 

, 

、 

、 

\ 

# 

\ 

\ 

、 

3 ,Pf舳dthe d 呲e betweenthemforv ̄iem 

d咖clI n th懈hoH w岫e SNR=4.8 dB 

V.CONCLUS}ONS 

In this Pa口er,we focus on the maximum of the 

difference between P and P and try to find out 

how to determine the threshold with this precondi- 

tion under various S for energy detection.Sim— 

ulation results show that the proposed method can 

effectively approach the ideal optimal result.Since 

sometimes we may have higher requirements for 

detection probability in the actual system,in order to 

1 8 z011.1 

and 60871042),theNatoinalKeyBasic ResearchProgram ofChi- 

na(Grant No.200903320400),the National Great Science Spe- 

ciifc Project(rGant Nos.2oo9z r03003-001.2009z 3oo3 l1 

nad 2010乃,030ol—003),and Cheese Universities Scientiifc Fund. 

China. 

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Biography 

J 

删l,Ph.D.,associate professor,graduated from neOing 

Universicy of Posts and Telecommunicatoins,now working at 

the School of Information and Engineering,BUPT.Iris recent 

research interests are wireless communication theory,networ— 

king technologies and embedded applications including Coopera- 

tire Communication,Cognitive Radio technologies,WAVE and 

Network codiog. 

2o11.1 

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