optimization of parameter

7/21/2019 Optimization of Parameter

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Optimization of Parameters for Spectrum Sensing in

Cognitive Radios

Yue Wang, Chunyan Feng, Caili Guo, Fangfang Liu

School of Information and Communication EngineeringBeijing University of Posts and Telecommunications, Beijing, China

Email: [email protected]

Abstract — In cognitive radios, the first and crucial task is to

detect the spectrum holes or the presence of primary user by

employing spectrum sensing. However, there exist two kinds of

detection errors (i.e., miss-detection error and false-alarm error),

which degrade the sensing performance severely. Aiming at

minimizing the probability of total detection errors, based on the

law of total probability we propose a novel target function (which

also denotes the so-called comprehensive sensing performance

metric) for optimization of sensing parameters. According to

such established target function, we then apply the method of

extremum seeking to develop the optimization of time-bandwidth

product and sensing threshold jointly for local spectrum sensing

with energy detection. Moreover, we further derive the closed-

form expression of the optimal fusion rule for cooperative

spectrum sensing by performing the discrete difference operation

on the target function. Finally, the optimal area of joint

parameters selection for local spectrum sensing and the effect of

different detecting channel conditions on the optimization for

cooperative spectrum sensing are evaluated numerically.

Keywords— cognitive radio; spectrum sensing; target function;

optimization; parameter

I.

I NTRODUCTION

In the scenario of cognitive radio (CR), to discover the potential spectrum holes defined as the licensed spectrum butunused by primary user (PU) and to be aware of the PUreappearance, spectrum sensing is the first and crucial task inCR technology. In particular, local spectrum sensingtechniques employed by a secondary user (SU) include energydetection, matched filter detection, cyclostationary featuredetection, etc [1]. Furthermore, in order to efficiently overcomethe fading of the detecting channel between PU and SU as wellas the problem of hidden terminal which happens when a SU isshadowed, cooperative spectrum sensing participated by agroup of spatially distributed SUs is usually conducted basedupon their local spectrum sensing results [2].

However, during both local and cooperative spectrumsensing processes, there inevitably exist two kinds of detectionerrors, i.e., miss-detection and false-alarm errors, whichrespectively reflect the interference level to PU and the wastelevel of available spectrum holes. Thus, for achieving bettersensing performance, such two kinds of detection errors should be avoided as much as possible in terms of lower probabilitiesof miss-detection and false-alarm. In [3], given the assumptionof known received signal to noise ratio (SNR) of PU signal andvariance of such received SNR at every SU, the optimal

number of SUs participating in cooperative spectrum sensing isevaluated for unilaterally pursuing either a targeted probabilityof miss-detection or that of false-alarm. In [4], the half votingrule is declared as the optimal fusion rule for cooperativespectrum sensing. However, the optimization in [4] is performed based on an oversimple target function which is lackof taking the spectrum occupancy statistics of PU into account.Moreover, such declaration indeed disregards the impact ofdifferent detecting channel conditions on optimization results.

In other words, the half voting rule may not always be optimal, but dependent on specific detecting channel conditions.

In this paper, to thoroughly minimize the probability oftotal miss-detection and false-alarm errors, we investigate theoptimization of parameters for both local spectrum sensing andcooperative spectrum sensing. Specifically, according to thelaw of total probability in probability theory, we firstly proposea novel target function for optimization of a variety of sensing parameters. In local spectrum sensing with energy detection, based on our established target function, the joint optimizationof time-bandwidth product and sensing threshold is developedthrough the method of extremum seeking. After the analysis oflocal spectrum sensing, we further derive the closed-formexpression of the optimal fusion rule for cooperative spectrumsensing with a given number of total collaborative SUs andcertain spectrum occupancy statistics of PU. Finally, we alsoevaluate the optimal area of joint parameters selection for localspectrum sensing and the effect of detecting channel conditionson the optimization for cooperative spectrum sensing.

The rest of this paper is organized as follows. In Section II,we describe the system model and establish the target function.The time-bandwidth product and sensing threshold for localspectrum sensing are analyzed and optimized in Section III.The optimization of fusion rule for cooperative spectrumsensing is developed in Section IV. In Section V, thesimulation results of optimization and performance evaluationsare provided. Finally, we draw the conclusions in Section VI.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In a centralized CR spectrum sensing manner, there aremainly three elements: PU, SU, and fusion center. PU has theexclusive priority to the licensed spectrum bands and shouldnot be harmfully interfered by the operations of any other SUs.SU senses spectrum bands and performs local observations ofPU signal according to a certain local spectrum sensingalgorithm. Since the energy detection is widely adopted with

This research was supported in part by China National “973” Project underGrant No.2009CB320400 and National Science Foundation of China under

Grant No.60772110.

978-1-4244-3693-4/09/$25.00 ©2009 IEEE



low computational complexity and no requirement of priorknowledge, we conduct our work with energy detection as thelocal spectrum sensing algorithm. At the fusion center, toexploit the multi-user cooperation gain, local spectrum sensingresults obtained by spatially distributed SUs are combined anda global decision is then made according to a certain fusion rule.

The goal of CR spectrum sensing is to detect between twohypotheses: H

B1B

or H B0B

, which means PU signal present or absent

( ) ( ) ( )

( )

1

0

, ,

, ,

g s t n t H r t

n t H

+⎧⎪= ⎨

⎪⎩ (1)

where r (t ) is the signal received by a SU, s(t ) represents thetransmitted PU signal, n(t ) is the zero-mean additive whiteGaussian noise (AWGN), and g indicates the amplitude gain ofdetecting channel between PU and SU.

Under these two hypotheses, the traditional sensing performance metric for CR spectrum sensing optimization isusually pursued by either minimizing the probability of miss-detection P BmB for a given probability of false-alarm P B f B orminimizing P B f B for a given P BmB. In this paper, however,

considering both of these two kinds of detection errors shouldassociatedly be decreased as largely as possible for bettercomprehensive sensing performance, we hence focus on theminimization of the probability of total detection errors. First ofall, a target function based on the law of total probability isestablished for following optimization of various sensing

parameters, and meanwhile it denotes the comprehensivesensing performance metric of CR spectrum sensing in this

paper. In particular, since the miss-detection and false-alarmerrors take place corresponding to H B1B and H B0 cases respectively,our target function is thus formulated in terms of a linearcombination of such two kinds of detection errors probabilitieswith the spectrum occupancy statistics of PU as weights

( ) ( )1 0 ,e m f P P H P P H P +

(2)

where P ( H 1) and P ( H 0) represent the probabilities of PU presence and absence respectively, and in the meantime theyalso satisfy the constraint equation of P ( H 1)+ P ( H 0)=1.

III. OPTIMIZATION FOR LOCAL SPECTRUM SENSING

As mentioned above, energy detection is usually executedas the local spectrum sensing algorithm in CR technology. At aSU, after squaring and integrating the received signal, thedecision statistic of energy detection, Y , has the distribution [5]

( )2

2 1

2

2 0

2 , ,

, ,

u

u

H Y

H

χ γ

χ

⎧ ⎪= ⎨

⎪⎩

(3)

where u is the time-bandwidth product, γ is the SNR of

detecting channel, and ( )2

2 2u χ γ and 2

2u χ represent non-central

and central chi-square distributions each with 2u degrees offreedom and a non-centrality parameter 2γ for the former one.

When the detecting channel is assumed to be the AWGNchannel, the probabilities of miss-detection and false-alarm oflocal spectrum sensing at a SU with energy detection are as [6]

( ) ( )1 2 ,Pr | 1 ,m u P Y H Q γ λ λ = < = − (4)

( ) ( )

( )0

, 2Pr | , f

u P Y H

u

λ λ

Γ = > =

Γ (5)

where λ is the sensing threshold, QBuB

(.,.) is generalized MarcumQ-function, Г(.,.) and Г(.) are incomplete and complete Gammafunctions respectively. It is also worth noting that in the case of

a certain fading detecting channel condition Q BuB(.,.) in P m of (4)should be further averaged over the particular statistics of SNRof corresponding fading detecting channel while P f of (5)remains the same since P f is independent of the SNR ofdetecting channel.

Then, based on our established target function as proposedin Section II, the probability of total detection errors in localspectrum sensing with adopting energy detection can beobtained by substituting (4) and (5) into (2)

( ) ( )( ) ( ) ( )

( ), 1 02 ,

, 21 .

e l u

u P P H Q P H

uγ λ

λ

Γ = − +

Γ (6)

According to (6), for the given SNR of detecting channel aswell as the known spectrum occupancy statistics of PU whichare both assumed to be accessible by certain measurements, the probability of total detection errors P e,l in local spectrumsensing thus become a binary function with two variables of parameters, i.e., time-bandwidth product u and sensingthreshold λ. Therefore, we can develop the optimization of suchtwo sensing parameters jointly for local spectrum sensingthrough the method of extremum seeking, searching theextreme minimum value of P e,l to be exact as below

2

, ,

2

2, ,

2

0, 0,

0, 0,

e l e l

e l e l

u u u u

P P

u u

P P

λ λ λ λ λ λ

= =

= =

⎧ ∂ ∂= >⎪

∂ ∂⎪⎪⎨

∂ ∂⎪ = >⎪∂ ∂⎪⎩

(7)

where ( , )u λ are the jointly optimal sensing parameters gotten

over the two dimensional space of both the time-bandwidth product and the sensing threshold for local spectrum sensing.

IV. OPTIMIZATION FOR COOPERATIVE SPECTRUM SENSING

During CR spectrum sensing, due to the practical problemof hidden terminal and the serious impact of fading detectingchannel, purely depending upon the implementation andoptimization of local spectrum sensing may not be reliable

enough to ensure achieving the sensing performancerequirement. In reality, by taking advantage of the multi-userspatial diversity gain, several spatially distributed SUs areusually incorporated to execute cooperative spectrum sensing.Through cooperative spectrum sensing, the sensing

performance can therefore be improved efficiently. In the process of cooperative spectrum sensing, every SU firstly performs local spectrum sensing and reports the observationresult to a fusion center independently, and then the fusioncenter makes a global decision.



At the fusion center, according to the difference of how tomake the global decision, there are logically three kinds offusion rules, i.e., OR-rule, AND-rule, and K-out-of-N-rule. Inthe OR-rule, the global decision declares a PU exists as long asone SU detects the PU. In the AND-rule, PU is viewed to beappeared only when all SUs report PU presence. In the K-out-of-N rule, the global decision announces an appearance of PUwhen at least K SUs discover a PU exists. For the sake ofsimplicity in our analysis, we assume that every SU has thesame sensing ability. Hence, the probabilities of miss-detectionand false-alarm of the three kinds of fusion rules duringcooperative spectrum sensing are respectively given as

( ),

,

,:

1 1 ,

N

m m i

N

f f i

P P OR rule

P P

⎧ =⎪

− ⎨= − −⎪⎩

(8)

( ),

,

1 1 ,:

,

N

m m i

N

f f i

P P AND rule

P P

⎧ = − −⎪

− ⎨=⎪⎩

(9)

( )( )

( ) ( )

, ,

, ,

1 1 ,

: 1 ,

N j N j

m m i m i

j K

N N j j

f f i f i

j K

N P P P

j K out of

N rule N P P P j

−

=

−

=

⎧= − −⎪

⎪− − ⎨

− − ⎪ = −⎪⎩

∑

∑ (10)

where P Bm,iB and P B f,iB are the probabilities of miss-detection andfalse-alarm at the ith distributed SU (SUBiB) derived from (4) and(5), and N is the total number of SUs participating incooperative spectrum sensing.

Consequently, an optimization problem in cooperativespectrum sensing naturally arises, i.e., which is the optimalfusion rule with the given total number of collaborative SUs.Specifically, by comparing (8) and (9) with (10), it is worthemphasizing that both OR-rule and AND-rule are two specialcases of K-out-of-N-rule, respectively corresponding to K =1

and K = N cases. Therefore, the optimization of fusion rule forcooperative spectrum sensing can be transformed into the problem of deriving the optimal parameter K for the purpose ofmaximally decreasing the probability of total detection errors.After substituting (10) into (2), we can then obtain the targetfunction for optimization of the parameter K as

( ) ( ) ( )

( ) ( ) ( )

, 1 , ,

0 , ,

1 1

1 .

N j N j

e c m i m i

j K

N N j

j

f i f i

j K

N P P H P P

j

N P H P P

j

−

=

−

=

⎛ ⎞= − −⎜ ⎟

⎝ ⎠

+ −

∑

∑ (11)

Since K is a discrete variable, the optimization process for parameter K can thus be developed by performing the discretedifference operation on (11)

( ) ( ) ( )

( )( ) ( )

( )( ) ( )

, , ,

1 1

1 , ,

11

0 , ,

1

11

1 .1

e c e c e c

K N K

m i m i

N K K

f i f i

P K P K P K

N P H P P

K

N P H P P

K

−− +

− +−

∇ = − −

= −−

− −−

(12)

Then, the optimal parameter value of fusion rule K forcooperative spectrum sensing can be obtained by letting (12) be

equal to zero and meanwhile should always be kept no greaterthan the amount of collaborative SUs

( )( )

, 1

, 0

, ,

, ,

1ln ln

min 1 , ,1 1

ln ln

f i

m i

f i m i

m i f i

P P H N

P P H K N

P P

P P

−⎛ ⎞⎢ ⎥

−⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥= +

− −⎜ ⎟⎢ ⎥+⎜ ⎟⎢ ⎥

⎣ ⎦⎝ ⎠

(13)

where ⋅⎢ ⎥⎣ ⎦ means the floor function for keeping K being an

integer. From (13), we can note that the optimal fusion rule isdependent on the spectrum occupancy statistics of PU and thedetecting channel condition since it directly affects P Bm,iB.

V. SIMULATIONS AND R ESULTS

In this section, the optimization of parameters for both localand cooperative spectrum sensing is evaluated numerically.According to our established target function, the followingsimulations mainly focus on analyzing the comprehensivesensing performance and seeking the optimal selections ofvarious parameters, in order to minimize the probability of totaldetection errors occurring during CR spectrum sensing.

Fig.1 illustrates the comprehensive sensing performancemetric quantified by the probability of total detection errorsover the two dimensional space of time-bandwidth product u and sensing threshold λ in local spectrum sensing. From thefigure, it can be clearly observed that the total detection errorsoccur less frequently when the options of u and λ are selectedaround the diagonal area of the two dimensional space of u and λ compared with other areas. Intuitively speaking, in CRspectrum sensing applications, the selections of u and λ fromsuch optimal area can produce better comprehensive sensing

performance. Moreover, the difference of achieved performance and the slender shift of optimal selection area between Fig.1 (a) and (b) reveals that the optimization and

selection of parameter values of u and λ can be slightly variedaccording to the particular spectrum occupancy statistics of PUrepresented by P ( H 0) and P ( H 1).

Then, we analyze the optimal solution for the parameter K of fusion rule. Here, we present a paradigm that totally N =8SUs participate in the cooperative spectrum sensing. Fig.2 andFig.3 depict the probability of total detection errors with all

possible values of K conducted in AWGN and Rayleigh fadingenvironment cases respectively. From these two groups offigures, it is obvious that the optimal K through the examinedrange of sensing threshold is located at either the half voting as

K =4 or the minority voting as K =2 for either AWGN orRayleigh fading detecting channels. Noticeably, such meaning-ful difference demonstrates that the selection of optimal fusionrule should depend on the exact probability distribution andcondition of detecting channels. In addition, by comparing (a)with (b) of both Fig.2 and Fig.3, it reveals that the parallel shiftof sensing threshold corresponding to the optimal K is also dueto the variance of spectrum occupancy statistics of PU.

VI. CONCLUSIONS

In this paper, in order to associatedly decrease the probability of total detection errors, we propose a novel target



function for optimization of a series of sensing parameters,which characterizes the comprehensive sensing performancemetric. Then, pursuing the minimization of such establishedtarget function, we develop the joint optimization of time-

bandwidth product and sensing threshold for local spectrumsensing. Furthermore, we derive the closed-form expression ofthe optimal fusion rule for cooperative spectrum sensing. By

performing simulations and discussing results with variantspectrum occupancy statistics of PU, we find the diagonal areaover the two dimensional space of time-bandwidth product andsensing threshold is the optimal area of joint parametersselection for local spectrum sensing, and we also numericallyevaluate the effect of different detecting channel conditions onthe optimization of fusion rule which implies the half voting isoptimal for the AWGN detecting channel case whereas theminority voting is optimal for the Rayleigh fading case incooperative spectrum sensing.

R EFERENCES

[1]

Ian F. Akyildiz, Won-yeol Lee, et al., “Next generation/dynamicspectrum access/cognitive radio wireless networks: a survey,” Computer

Networks, vol. 50, no. 13, pp. 2127-2159, Sep. 2006.

[2]

Yue Wang, Chunyan Feng, et al., “A robust and energy efficientcooperative spectrum sensing scheme in cognitive radio networks,” 11P

thP

International Conference on Advanced Communication Technology,Gangwon-Do, South Korea, Feb. 2009, pp. 640-645.

[3]

Peh E. and Ying-Chang Liang, “Optimization for Cooperative Sensing

in Cognitive Radio Networks," IEEE Wireless Communications and Networking Conference 2007, Hong Kong, China, Mar. 2007, pp. 27-32.

[4]

W. Zhang, R. Mallik, et al., “Cooperative Spectrum SensingOptimization in Cognitive Radio Networks,” IEEE InternationalConference on Communications 2008, Beijing, China, May 2008, pp.3411-3415.

[5]

H. Urkowitz, “Energy detection of unknown deterministic signals," Proc.IEEE, vol. 55, pp. 523-531, Apr. 1967.

[6] F. F. Digham, M. S. Alouini, et al., “On the energy detection ofunknown signals over fading channels,” IEEE Transactions onCommunications, vol. 55, no. 1, pp. 21-24, Jan. 2007.

510

1520

2530

2

4

6

8

10

10-1

100

Sensing Threshold, λ

(a) P(H0)=0.8, P(H

1)=0.2

Time-Bandwidth Product, u

P r o b a b i l i t y o f T o t a l D e t e c t i o n

E r r o r s ,

P e , l

510

1520

2530

2

4

6

8

10

10-1

100


(b) P(H0)=0.5, P(H

1)=0.5

Time-Bandwidth Product, u

P r o b a b i l i t y o f T o t a l D e t e c t i o n

E r r o r s ,

P e , l

Figure 1. Probability of total detection errors vs. time-bandwidth product and sensing threshold of local spectrum sensing (SNR=10dB)

10 15 20 25 30 35 40 45 50

10-2

10-1

100

(a) P(H0)=0.8, P(H

1)=0.2


P r o b a b i l i t y o f T o t a l D e t e c t i o n E

r r o r s ,

P e , c

K=1

K=2

K=3

K=4

K=5

K=6

K=7

K=8

10 15 20 25 30 35 40 45 50

10-2

10-1

100

(b) P(H0)=0.5, P(H

1)=0.5


P r o b a b i l i t y o f T o t a l D e t e c t i o n E

r r o r s ,

P e , c

K=1

K=2

K=3

K=4

K=5

K=6

K=7

K=8

Figure 2. Probability of total detection errors vs. sensing threshold when 8 SUs cooperate with different fusion rules in AWGN environment (SNR=10dB)

10 15 20 25 30 35 40 45 50

10-2

10-1

100

(a) P(H0)=0.8, P(H

1)=0.2


P r o b a b i l i t y o f T o t a l D e t e c t i o n E r r o r s ,

P e , c

K=1

K=2

K=3

K=4

K=5

K=6

K=7

K=8

10 15 20 25 30 35 40 45 5010

-2

10-1

100

(b) P(H0)=0.5, P(H

1)=0.5


P r o b a b i l i t y o f T o t a l D e t e c t i o n E r r o r s ,

P e , c

K=1

K=2

K=3

K=4

K=5

K=6

K=7

K=8

Figure 3. Probability of total detection errors vs. sensing threshold when 8 SUs cooperate with different fusion rules in Rayleigh fading environment (SNR=10dB)

optimization of parameter

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