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A Credibility-Based Cooperative Spectrum Sensing

Technique for Cognitive Radio Systems

Chin-Liang WangDeapertment of Electrical Engineering and

Institute of Communications Engineering

National Tsing Hua University

Hsinchu, Taiwan 30013, R.O.C

clwang@ee.nthu.edu.tw

Han-Wei Chen and Yu-Ren Chou

Institute of Communications Engineering

National Tsing Hua University

Hsinchu, Taiwan 30013, R.O.Cd9564820@oz.nthu.edu.twg9764528@oz.nthu.edu.tw

AbstractSpectrum sensing is one of the major elements ofcognitive radio applications. A single secondary user (SU) usuallycannot provide robust sensing capability due to channel effects.In order to overcome this problem, cooperative spectrum sensingtechniques have been proposed. Because conventional cooperativespectrum sensing schemes assumed that all sensing nodes have

the same sensing reliability, the SUs were assigned identical false-alarm probability even though some of them suffer deep fading,which may degrade their detection performance. In this study,we propose an adaptive credibility-based cooperative spectrumsensing technique, which evaluates the sensing reliability ofSUs based on previous sensing performance, and adjusts theprobability of false alarm of each SU individually. Assigning ahigher false alarm probability for a more reliable SU can resultin better detection performance. To verify the effectiveness of theproposed cooperative spectrum sensing technique, both the falsealarm probability and the detection probability are simulatedunder Rayleigh fading channels, and the results show thatthe proposed approach outperforms any conventional detectionmethod in terms of detection performance.

I. INTRODUCTION

As the development for broadband wireless communication

technologies advances, the frequency spectrum is becoming

more crowded than ever. In fact, recent investigations done by

the Federal Communications Commissions Spectrum Policy

Task Force have indicated inefficiency in the utilization of

licensed spectrum resources [1]. Therefore, it has become an

issue to efficiently utilize the available spectrum.

A special type of software defined radio, namely cognitive

radio (CR) [2] has been proposed to solve the problem of

spectrum scarcity by sharing licensed spectrum with other

unlicensed users in a non-interference opportunistic manner;

it is believed this method enhances the efficiency of wireless

spectrum utilization. In CR applications, SUs are required toperform spectrum sensing periodically to sense and monitor

the utilization of licensed radio spectrum holes. Many effective

spectrum sensing algorithms have been proposed for CR ap-

plications; however, a single SU cannot provide robust sensing

because of hidden nodes, shadowing, and fading channels.

Cooperative spectrum sensing has been getting considerable

attention, for it not only combats channel effects but also

achieves high sensing agility. In this manner, the SUs in the

CR network can perform local spectrum sensing individually

and report their local decisions to the cognitive radio base

station (CRBS), the CRBS then combines the local decisions

to make a global decision.

While the number of studies dedicated to cooperative spec-

trum sensing has increased noticeably in the past few years,

various approaches to decision combination such as AND ruleand OR rule were discussed [3], with weighted combining

being a more recent approach. Various weighting schemes

have been proposed [4]-[7], such as weighting based on the

quality of channel condition or geometrical location, and

considering the weighting factor with the local decision in

the combining process. However, the reliability of each SU

is assumed identical at the CRBS, where their false-alarm

probability is equal among all SUs in the CR network, even

though some of the SUs are in deep fade and tend to induce

errors.

In this study, we have proposed a cooperative spectrum

sensing technique where the false-alarm probability of each

SU is dynamically adjusted according to their performancesin previous sensing trials. We have employed the credibility

principle to design an adaptive algorithm in which the CRBS

records the local decision of each SU and compares the result

with the global decision. Therefore, the false-alarm probability

of the SUs at each trial can fluctuate in line with their

credibility. With this method, no distance information and

instantaneous channel state information is required a priori.

Furthermore, it does not conflict with the decision combining

process for cooperative spectrum sensing. The organization of

this paper is as follows; Section II starts with a cooperative

spectrum sensing system model. Section III and IV detail the

target problem and the proposed algorithm. Section V shows

the simulation results of the proposed cooperative spectrum

sensing technique. Conclusion is provided in Section VI.

I I . SYSTEM MODEL

The detection of a spectrum hole can be reduced to a binary

hypothesis-testing problem,

H0 : y(t) = n(t),H1 : y(t) = h(t) x(t) + n(t). (1)

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Clearly, hypothesis H0 refers to the presence of ambient

noise, and hypothesis H1 refers to the presence of a primary

user (PU)s signal. The parameter y(t) denotes the signalreceived by the spectrum sensors, x(t) is the signal transmittedby the PU, n(t) is the additive white Gaussian noise (AWGN),and h(t) is the channel gain between the PU and the SUs.

Two important metric parameters, the detection probability

Pd

and the false-alarm probability Pf

, are introduced to

evaluate the detection performance,

Pd = Pr {H1 |H1 } , (2)and

Pf = Pr {H1 |H0 } . (3)Consider using an energy detector, the sensing outcomes under

hypotheses H0 and H1 with instantaneous signal-to-noise ratio

(SNR) can be modeled as [8]

Y

22u, H0;

22u(2), H1;

(4)

where u is the time-bandwidth product, 2

2u and 2

2u(2)each denotes the central chi-square distribution and the non-

central chi-square distribution, respectively, with 2u degreesof freedom and the non-centrality parameter of 2. Therefore,with a given decision threshold , the Pd can be expressed as

[9]

Pd = Pr {Y > |, H1 } =

Qu(

2,

)f()dx, (5)

Qu(, ) is the generalized Marcum Q-function and

f() =1

exp

, 0, (6)

is the probability density function (PDF) of the channel effectwith the average SNR . The Pf will be

Pf = Pr {Y > |H0 } = (u, /2)(u)

; (7)

where () and (, ) are the complete and the incompletegamma function, respectively. A high detection probability has

a small chance of interfering in the PU system. A false-alarm

does not cause interference to PUs transmission but wastes

additional power and sensing time to SU device. Thus, the

design of a sensing algorithm aims to meet a high Pd with a

low Pf. Unfortunately a high Pd always accompanies a high

Pf [10].

Moreover, the detection performance for single SU wouldbe severely degraded due to the hidden node problem, fading,

and shadowing in real communication environments. In order

to overcome those effects, the cooperative spectrum sensing

has been proposed to exploit multiuser diversity in sensing

processing, and it can reduce the sensing time and the sensi-

tivity requirement of the SUs [10].

The CR system model adopted in this paper is illustrated in

Fig. 1. Consider a centralized CR network of N SUs, denoted

by S= {1, , N}, randomly deployed in a two-dimensional

Primaryuser

: Sensingchannel: Reportingchannel

Secondaryuser2

SecondaryuserN

Secondaryuser1

SecondaryuserBSSecondaryuseri

Fig. 1. System model of cooperative spectrum sensing for cognitive radiosystems.

area. Besides, one CRBS and one PU are also in this scenario.

The channel between the PU and the SU is referred as sensing

channel, and the channel between the SU and the CRBS

is referred to as reporting channel. In cooperative spectrum

sensing, SUs play a role of spectrum sensors and perform local

sensing individually using an energy detector and afterwards

report their local decision to the CRBS through the control

channel. The CRBS fuses the decisions from the SUs and

makes a global decision which indicates the absence or the

presence of the PU network.

In general, the global detection probability Qd and the

global false-alarm probability Qf for cooperative spectrum

sensing can be written as follows [3],

Qd = 1 Ni=1

(1 Pd,i), i S, (8)

and

Qf = 1 Ni=1

(1 Pf,i), i S. (9)

III. PROBLEM FORMULATIONIn view of opportunistic transmission, the global false-alarm

probability Qf was preset to restrain the tolerable false-alarm

rate of the CR network. Thus, the Qf can be regarded as finite

resource in the CR system, and the SUs in the CR network

share the responsibility of achieving a global false-alarm prob-

ability. Most cooperative sensing schemes assumed that the

SUs in the CR network would experience an independent and

identically distributed fading channel with the same average

SNR. Hence, for a given global false-alarm probability Qf

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defined in (9), each SU was assigned the same false-alarm

probability for detection because the CRBS assumed that all

the SUs have the same sensing reliability. Thus, the false-alarm

probability of the ith SU can be represented as

Pf,i = 1 (1 Qf)1/N, i S. (10)In such case, the performance of cooperative spectrum sensing

would increase along with the number of cooperative SUs.However, when some of the SUs suffer a lower level of average

SNR, the reliability of those SUs would degrade and the

performance of cooperative spectrum sensing would no longer

be proportional to the number of cooperative SUs. Therefore,

it is not sensible to assume the same reliability or false-alarm

probability to all SUs.

Suppose two SUs suffer different degrees of channel fading;

SU-1 is in a good channel condition, while SU-2 is in a bad

one. Fig.2 shows the probability density function under H0and H1 of these two SUs. The goal of spectrum detection

is to distinguish hypothesis H1 from hypothesis H0. The

decision threshold is set according to the given false-alarm

probability. Clearly, the detection probability Pd,i is closelyrelated to the false-alarm probability Pf,i, and is a tradeoff

between them.

Consider a good channel condition, such as SU-1, the PDFs

of H0 and H1 can be easily separated. However, in a deep

fading scenario as SU-2, the PDFs of H0 and H1 are very

close. To assign SU-1 and SU-2 with the same false-alarm

probability, that is, setting the same threshold for them is

not efficient, because a high false-alarm probability for SU-1

can significantly improve the detection probability, it does so

only a little for SU-2. Thus, we suggest that to allocate the

finite resource, the false-alarm probability, to the SUs which

are in good channel condition may considerably increase the

global detection probability in the same global false-alarmprobability.

To adjust the false-alarm probability of each SU according

to its channel conditions may improve the performance of

cooperative spectrum sensing. However, the instantaneous

channel state information or geometrical location information

cannot be easily obtained. Thus, we proposed a cooperative

spectrum sensing technique where the false-alarm probability

of each SU is dynamically adjusted according to their per-

formances in previous sensing trials, which is based on the

credibility principle and will be described in Section IV.

IV. PROPOSED METHOD

Consider a slow fading environment, where the sensingcredibility of the ith SU can be obtained by comparing its

local decision to the global decision. In other words, if the

local decision of ith SU is different from the global decision,

the CRBS will knock down the credibility of ith SU. In this

manner, as the detection performance is continuously traced,

the credibility of each SU could be updated adaptively. The

credibility would provide a basis for the CRBS to assign

the fitting false-alarm probability for each SU; an SU with a

higher credibility would be assigned with a higher false-alarm

1H

0H

fP

,1d fP P

,2d fP P

0H

1H

SU-1:

SU-2:

fP

Fig. 2. SUs suffer different degrees of channel fading. SU-1 is in a goodchannel condition, while SU-2 is in a bad one. Assigning the same decisionthreshold or false-alarm probability Pf is not sensible.

probability. We have separated the algorithm into two parts,

credibility evaluation and false-alarm probability adjustment.

A. Credibility Evaluation Algorithm

The design of the credibility evaluation algorithm is based

on the credibility principle. The credibility of ith SU at time

n is denoted as Credi[n]. Let di[n] be the local decisionmade by the ith SU at time n, and D[n] be the globaldecision made by the CRBS at time n. Initially, we set the

initial credibility of all the SUs to be 1, and the iteration

process begins. The credibility of the ith SU at time (n + 1)will be updated according to their sensing results of time n,

the details are described in the following:

Credibility Evaluation Algorithm

1) Initialization: assign initial credibility

Credi[0] = 1, i S2) Iteration: for n 1

a) if di[n] = D[n]Credi[n] = Credi[n 1] i[n]

b) if di[n] = D[n]

Credi[n] = Credi[n 1] + i[n]c) Normalization:

iS

Credi[n] = N

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d) Mean Credibility:

Credi[n] =1

n + 1

nk=0

Credi[k], i S

The equations above are the proposed algorithm which

manages the credibility of the SUs individually. The reason

for choosing addition over multiplication to grow credibility

is that, considering the credibility principle, a good credibil-ity must accumulate continuously; however, one breach of

promise can cause severe damage to it. For this reason, the

design of the credibility evaluation algorithm follows this rule.

In step 2, i[n] and i[n] refer to the reduction factor andthe growth factor, respectively. The value of i[n] lies between0 and 1. Instead of a constant value over time, the reduction

factor i[n] is designed to be credibility-dependent, which ideais illustrated in Fig. 3. Two thresholds are set to divide the

degree of mean credibility; if the current mean credibility is

higher than L1 or lower than L2, the reduction factor will

be a fixed value. Once the mean credibility has fallen into

the ambiguous area between L1 and L2, the reduction factor

would change over time. The procedures described abovewould improve the convergence of the mean credibility and

can be represented as the following equation,

i[n] =

i[n 1] 0.01 U{L1 Credi[n 1]}

U{Credi[n 1] L2}+ U{L2 Credi[n 1]},

(11)

where is a constant value less than one. U() is the unit stepfunction defined as

U(x) =

1, x 0;0, x < 0.

(12)

The value of the growth factor i[n] is directly related to

the total amount of the credibility reduced from other SUs.Defined W is the set included the SUs whose local decisionis different from the global decision at time n, and i[n] is

i[n] =1

Nc[n]

kW

|Credk[n] Credk[n 1]|, (13)

where Nc[n] is the number of the SUs whose local decisionis the same as the global decision at time n.

B. Fluctuating False-Alarm Probability

The CRBS evaluates the mean credibility of each SU and

assigns the false-alarm probability to each SU according to

Credi[n

1] for the (n) time spectrum sensing. A weight-

ing parameter i[n] is defined for adjusting the false-alarmprobability,

i[n] =Credi[n]

jS

Credj [n]. (14)

Finally, the false-alarm probability for the ith SU, Pf,i[n],will be

Pf,i[n] = i[n]

1 (1 Qf)1/N, i S

. (15)

1L

2L

Fixed

[ ]iCred n

Fixed

Variable

1

0 n

Fig. 3. The region definition for the credibility-dependent reduction factori[n].

Unlike most of the cooperative spectrum sensing schemes,

no prior information is needed for this algorithm, such as

the instantaneous channel state information and geometrical

location.

V. SIMULATION

The proposed cooperative spectrum sensing technique in

this study is based on the idea of fluctuating false-alarm

probability. The proposed scheme does not conflict with any

existing decision combining methods of cooperative spectrum

sensing. In this section we will explain how we have applied

our algorithm to other combining methods, and examined the

changes in the global detection probability.

Two cooperative sensing combining methods, hard combin-

ing and soft combining, are compared with our algorithm.

Cooperative spectrum sensing with hard-combining method

under Rayleigh fading channel with log-normal shadowing isstudied in [3]. With this approach, the CRBS assigns equal

false-alarm probability to all SUs as (10), and uses an OR-

rule to fuse the binary decision of the SUs. The simulation

parameters are set as follows: the number of SUs N = 15,average SNR = 6dB, and the SUs perform spectrum sens-ing by energy detector with time-bandwidth product u = 10.The performance of cooperative spectrum sensing in terms

of receiver operating characteristic (ROC) using the hard

combining approach is shown in Fig. 4. The solid line refers to

the hard combining method, while the dotted line refers to the

hard combining method with the proposed algorithm. Fig. 4

shows that when high false-alarm probability is assigned to the

SUs which have a high credibility with the propose scheme,the detection performance of cooperative spectrum sensing has

seen great improvement.

Cooperative spectrum sensing with soft combining approach

under Rayleigh fading channel has also been studied [4],[5],

where the SUs perform spectrum sensing and feedback soft

information to the CRBS. The CRBS uses simple weighting

combining (SWC) method to fuse the soft information. The

detection performance in terms of ROC is illustrated in Fig.

5. The solid line refers to soft combining using SWC method,

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103

102

101

100

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

hard combining with proposed scheme

hard combining

Fig. 4. Illustration of the hard-combining case with or without the proposed

technique. Y-axis represents the global detection probability Qd and X-axisrepresents the global false-alarm probability Qf (N= 15 , = 6dB).

103

102

101

100

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

soft combining with proposed scheme

soft combining

Fig. 5. Illustration of the soft-combining case with or without the proposedtechnique. Y-axis represents the global detection probability Qd and X-axisrepresents the global false-alarm probability Qf (N= 15 , = 6dB).

and the dotted line refers to soft combining method with the

proposed scheme. Similarly, the parameters were set as N =15, = 6dB, and u = 10. It has shown that detectionperformance of soft combining method is much better than

hard combining method. Applying the proposed technique to

the soft combining approach, we can find that the detection

performance can be improved significantly.

V I . CONCLUSION

In this study, a new cooperative spectrum sensing approach

in view of the false-alarm probability is proposed. In terms

of the reliability of spectrum sensing, it is not sensible for

the CRBS to treat all SUs equally. The principle findings

in this paper have suggested that the fluctuating false-alarm

probability method for cooperative spectrum sensing can result

in better detection performance through a proper allocationof false-alarm probability to each of the SUs. An adaptive

credibility evaluation algorithm is further proposed for the

assignment of false-alarm probability of each SU. The major

advantage of the proposed credibility evaluation algorithm

is that it does not need any instantaneous channel state

information or geometrical location knowledge of the PU

and the SUs. Furthermore, the proposed approach does not

conflict with the decision combining process for cooperative

spectrum sensing, i.e., the cooperative sensing performance

can be further enhanced by adding our approach to any

existing combining method. Simulation results provided in

Section V have also indicated that the proposed scheme has

a significantly positive effect on the detection probability forcooperative spectrum sensing of CR systems.

ACKNOWLEDGMENT

This work was supported by the National Science Council

of the Republic of China under Grants NSC 97-2221-E-007-

005-MY3 and NSC 99-2221-E-007-016-MY3.

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