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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
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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- )
一
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
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
、
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Real
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eore6ca ̄
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Foundation of China(Grant Nos.60971082.60872O49.6O972073
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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
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eoretical
al
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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
1 9
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