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Hindawi Publishing Corporation

EURASIP Journal on Advances in Signal Processing

Volume 2010, Article ID 381465, 15 pages

doi:10.1155/2010/381465

Review Article

A Review on Spectrum Sensing for Cognitive Radio:

Challenges and Solutions

Yonghong Zeng, Ying-Chang Liang, Anh Tuan Hoang, and Rui Zhang

Institute for Infocomm Research, A∗STAR, Singapore 138632

Correspondence should be addressed to Yonghong Zeng, yhzeng@i2r.a-star.edu.sg

Received 13 May 2009; Accepted 9 October 2009

Academic Editor: Jinho Choi

Copyright © 2010 Yonghong Zeng et al. This is an open access article distributed under the Creative Commons Attribution

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

cited.

Cognitive radio is widely expected to be the next Big Bang in wireless communications. Spectrum sensing, that is, detecting the

presence of the primary users in a licensed spectrum, is a fundamental problem for cognitive radio. As a result, spectrum sensing

has reborn as a very active research area in recent years despite its long history. In this paper, spectrum sensing techniques from the

optimal likelihood ratio test to energy detection, matched ﬁltering detection, cyclostationary detection, eigenvalue-based sensing,

joint space-time sensing, and robust sensing methods are reviewed. Cooperative spectrum sensing with multiple receivers is also

discussed. Special attention is paid to sensing methods that need little prior information on the source signal and the propagation

channel. Practical challenges such as noise power uncertainty are discussed and possible solutions are provided. Theoretical analysis

on the test statistic distribution and threshold setting is also investigated.

1. Introduction

It was shown in a recent report [1] by the USA Federal

Communications Commission (FCC) that the conventional

ﬁxed spectrum allocation rules have resulted in low spectrum

usage eﬃciency in almost all currently deployed frequency

bands. Measurements in other countries also have shown

similar results [2]. Cognitive radio, ﬁrst proposed in [3], is

a promising technology to fully exploit the under-utilized

spectrum, and consequently it is now widely expected to be

the next Big Bang in wireless communications. There have

been tremendous academic researches on cognitive radios,

for example, [4,5], as well as application initiatives, such as

the IEEE 802.22 standard on wireless regional area network

(WRAN) [6,7] and the Wireless Innovation Alliance [8]

including Google and Microsoft as members, which advocate

to unlock the potential in the so-called “White Spaces” in

the television (TV) spectrum. The basic idea of a cognitive

radio is spectral reusing or spectrum sharing, which allows

the secondary networks/users to communicate over the

spectrum allocated/licensed to the primary users when they

are not fully utilizing it. To do so, the secondary users

are required to frequently perform spectrum sensing, that

is, detecting the presence of the primary users. Whenever

the primary users become active, the secondary users have

to detect the presence of them with a high probability

and vacate the channel or reduce transmit power within

certain amount of time. For example, for the upcoming IEEE

802.22 standard, it is required for the secondary users to

detect the TV and wireless microphone signals and vacant

the channel within two seconds once they become active.

Furthermore, for TV signal detection, it is required to achieve

90% probability of detection and 10% probability of false

alarm at signal-to-noise ratio (SNR) level as low as −20 dB.

There are several factors that make spectrum sensing

practically challenging. First, the required SNR for detection

may be very low. For example, even if a primary transmitter

is near a secondary user (the detection node), the transmitted

signal of the primary user can be deep faded such that

the primary signal’s SNR at the secondary receiver is well

below −20 dB. However, the secondary user still needs

to detect the primary user and avoid using the channel

because it may strongly interfere with the primary receiver

if it transmits. A practical scenario of this is a wireless

microphone operating in TV bands, which only transmits

with a power less than 50 mW and a bandwidth less than

2 EURASIP Journal on Advances in Signal Processing

200 KHz. If a secondary user is several hundred meters

away from the microphone device, the received SNR may

be well below −20 dB. Secondly, multipath fading and time

dispersion of the wireless channels complicate the sensing

problem. Multipath fading may cause the signal power to

ﬂuctuate as much as 30 dB. On the other hand, unknown

time dispersion in wireless channels may turn the coherent

detection unreliable. Thirdly, the noise/interference level

may change with time and location, which yields the noise

power uncertainty issue for detection [9–12].

Facing these challenges, spectrum sensing has reborn as

a very active research area over recent years despite its long

history. Quite a few sensing methods have been proposed,

including the classic likelihood ratio test (LRT) [13], energy

detection (ED) [9,10,13,14], matched ﬁltering (MF) detec-

tion [10,13,15], cyclostationary detection (CSD) [16–19],

and some newly emerging methods such as eigenvalue-based

sensing [6,20–25], wavelet-based sensing [26], covariance-

based sensing [6,27,28], and blindly combined energy

detection [29]. These methods have diﬀerent requirements

for implementation and accordingly can be classiﬁed into

three general categories: (a) methods requiring both source

signal and noise power information, (b) methods requiring

only noise power information (semiblind detection), and

(c) methods requiring no information on source signal or

noise power (totally blind detection). For example, LRT,

MF, and CSD belong to category A; ED and wavelet-based

sensing methods belong to category B; eigenvalue-based

sensing, covariance-based sensing, and blindly combined

energy detection belong to category C. In this paper, we

focus on methods in categories B and C, although some

other methods in category A are also discussed for the sake

of completeness. Multiantenna/receiver systems have been

widely deployed to increase the channel capacity or improve

the transmission reliability in wireless communications. In

addition, multiple antennas/receivers are commonly used

to form an array radar [30,31] or a multiple-input

multiple-output (MIMO) radar [32,33] to enhance the

performance of range, direction, and/or velocity estimations.

Consequently, MIMO techniques can also be applied to

improve the performance of spectrum sensing. Therefore,

in this paper we assume a multi-antenna system model in

general, while the single-antenna system is treated as a special

case.

When there are multiple secondary users/receivers dis-

tributed at diﬀerent locations, it is possible for them to

cooperate to achieve higher sensing reliability. There are

various sensing cooperation schemes in the current literature

[34–44]. In general, these schemes can be classiﬁed into two

categories: (A) data fusion: each user sends its raw data or

processed data to a speciﬁc user, which processes the data

collected and then makes the ﬁnal decision; (B) decision

fusion: multiple users process their data independently and

send their decisions to a speciﬁc user, which then makes the

ﬁnal decision.

In this paper, we will review various spectrum sensing

methods from the optimal LRT to practical joint space-time

sensing, robust sensing, and cooperative sensing and discuss

their advantages and disadvantages. We will pay special

attention to sensing methods with practical application

potentials. The focus of this paper is on practical sensing

algorithm designs; for other aspects of spectrum sensing in

cognitive radio, the interested readers may refer to other

resources like [45–52].

The rest of this paper is organized as follows. The

system model for the general setup with multiple receivers

for sensing is given in Section 2. The optimal LRT-based

sensing due to the Neyman-Pearson theorem is reviewed

in Section 3. Under some special conditions, it is shown

that the LRT becomes equivalent to the estimator-correlator

detection, energy detection, or matched ﬁltering detection.

The Bayesian method and the generalized LRT for sensing

are discussed in Section 4. Detection methods based on

the spatial correlations among multiple received signals are

discussed in Section 5, where optimally combined energy

detection and blindly combined energy detection are shown

to be optimal under certain conditions. Detection methods

combining both spatial and time correlations are reviewed in

Section 6, where the eigenvalue-based and covariance-based

detections are discussed in particular. The cyclostationary

detection, which exploits the statistical features of the pri-

mary signals, is reviewed in Section 7. Cooperative sensing

is discussed in Section 8. The impacts of noise uncertainty

and noise power estimation to the sensing performance

are analyzed in Section 9. The test statistic distribution and

threshold setting for sensing are reviewed in Section 10,

where it is shown that the random matrix theory is very

useful for the related study. The robust spectrum sensing

to deal with uncertainties in source signal and/or noise

power knowledge is reviewed in Section 11,withspecial

emphasis on the robust versions of LRT and matched ﬁltering

detection methods. Practical challenges and future research

directions for spectrum sensing are discussed in Section 12.

Finally, Section 13 concludes the paper.

2. System Model

We assume that there are M≥1 antennas at the receiver.

These antennas can be suﬃciently close to each other to

form an antenna array or well separated from each other.

We assume that a centralized unit is available to process the

signals from all the antennas. The model under consideration

is also applicable to the multinode cooperative sensing [34–

44,53], if all nodes are able to send their observed signals to

a central node for processing. There are two hypotheses: H0,

signal absent, and H1, signal present. The received signal at

antenna/receiver iis given by

H0:xi(n)=ηi(n),

H1:xi(n)=si(n)+ηi(n),i=1, ...,M. (1)

In hypothesis H1,si(n) is the received source signal at

antenna/receiver i, which may include the channel multipath

and fading eﬀects. In general, si(n) can be expressed as

si(n)=

K

k=1

qik

l=0

hik(l)sk(n−l),(2)

EURASIP Journal on Advances in Signal Processing 3

where Kdenotes the number of primary user/antenna

signals, sk(n) denotes the transmitted signal from primary

user/antenna k,hik(l) denotes the propagation channel

coeﬃcient from the kth primary user/antenna to the ith

receiver antenna, and qik denotes the channel order for hik.

It is assumed that the noise samples ηi(n)’s are independent

and identically distributed (i.i.d) over both nand i.For

simplicity, we assume that the signal, noise, and channel

coeﬃcients are all real numbers.

The objective of spectrum sensing is to make a decision

on the binary hypothesis testing (choose H0or H1)basedon

the received signal. If the decision is H1, further information

such as signal waveform and modulation schemes may be

classiﬁed for some applications. However, in this paper, we

focus on the basic binary hypothesis testing problem. The

performance of a sensing algorithm is generally indicated by

two metrics: probability of detection, Pd,whichdeﬁnes,at

the hypothesis H1, the probability of the algorithm correctly

detecting the presence of the primary signal; and probability

of false alarm, Pfa

, which deﬁnes, at the hypothesis H0,

the probability of the algorithm mistakenly declaring the

presence of the primary signal. A sensing algorithm is called

“optimal” if it achieves the highest Pdfor a given Pfa with a

ﬁxed number of samples, though there could be other criteria

to evaluate the performance of a sensing algorithm.

Stacking the signals from the Mantennas/receivers yields

the following M×1vectors:

x(n)=x1(n)··· xM(n)T,

s(n)=s1(n)··· sM(n)T,

η(n)=η1(n)··· ηM(n)T.

(3)

The hypothesis testing problem based on Nsignal samples is

then obtained as

H0:x(n)=η(n),

H1:x(n)=s(n)+η(n),n=0, ...,N−1.(4)

3. Neyman-Pearson Theorem

The Neyman-Pearson (NP) theorem [13,54,55] states that,

for a given probability of false alarm, the test statistic that

maximizes the probability of detection is the likelihood ratio

test (LRT) deﬁned as

TLRT(x)=p(x|H1)

p(x|H0),(5)

where p(·) denotes the probability density function (PDF),

and xdenotes the received signal vector that is the aggre-

gation of x(n), n=0, 1, ...,N−1.Such a likelihood ratio

test decides H1when TLRT(x) exceeds a threshold γ,andH0

otherwise.

The major diﬃculty in using the LRT is its requirements

on the exact distributions given in (5). Obviously, the

distribution of random vector xunder H1is related to the

source signal distribution, the wireless channels, and the

noise distribution, while the distribution of xunder H0is

related to the noise distribution. In order to use the LRT, we

need to obtain the knowledge of the channels as well as the

signal and noise distributions, which is practically diﬃcult to

realize.

If we assume that the channels are ﬂat-fading, and the

received source signal sample si(n)’s are independent over n,

the PDFs in LRT are decoupled as

p(x|H1)=

N−1

n=0

p(x(n)|H1),

p(x|H0)=

N−1

n=0

p(x(n)|H0).

(6)

If we further assume that noise and signal samples are both

Gaussian distributed, that is, η(n)∼N(0,σ2

ηI)ands(n)∼

N(0,Rs), the LRT becomes the estimator-correlator (EC)

[13] detector for which the test statistic is given by

TEC(x)=

N−1

n=0

xT(n)RsRs+σ2

ηI−1x(n).(7)

From (4), we see that Rs(Rs+2σ2

ηI)−1x(n) is actually the

minimum-mean-squared-error (MMSE) estimation of the

source signal s(n). Thus, TEC(x)in(7) can be seen as the

correlation of the observed signal x(n) with the MMSE

estimation of s(n).

The EC detector needs to know the source signal

covariance matrix Rsand noise power σ2

η. When the signal

presence is unknown yet, it is unrealistic to require the source

signal covariance matrix (related to unknown channels) for

detection. Thus, if we further assume that Rs=σ2

sI, the EC

detector in (7) reduces to the well-known energy detector

(ED) [9,14] for which the test statistic is given as follows (by

discarding irrelevant constant terms):

TED(x)=

N−1

n=0

xT(n)x(n).(8)

Note that for the multi-antenna/receiver case, TED is actually

the summation of signals from all antennas, which is a

straightforward cooperative sensing scheme [41,56,57]. In

general, the ED is not optimal if Rsis non-diagonal.

If we assume that noise is Gaussian distributed and

source signal s(n) is deterministic and known to the receiver,

which is the case for radar signal processing [32,33,58], it is

easy to show that the LRT in this case becomes the matched

ﬁltering-based detector, for which the test statistic is

TMF(x)=

N−1

n=0

sT(n)x(n).(9)

4. Bayesian Method and the Generalized

Likelihood Ratio Test

In most practical scenarios, it is impossible to know the

likelihood functions exactly, because of the existence of

4 EURASIP Journal on Advances in Signal Processing

uncertainty about one or more parameters in these func-

tions. For instance, we may not know the noise power σ2

η

and/or source signal covariance Rs. Hypothesis testing in the

presence of uncertain parameters is known as “composite”

hypothesis testing. In classic detection theory, there are two

main approaches to tackle this problem: the Bayesian method

and the generalized likelihood ratio test (GLRT).

In the Bayesian method [13], the objective is to eval-

uate the likelihood functions needed in the LRT through

marginalization, that is,

p(x|H0)=p(x|H0,Θ0)p(Θ0|H0)dΘ0, (10)

where Θ0represents all the unknowns when H0is true. Note

that the integration operation in (10) should be replaced

with a summation if the elements in Θ0are drawn from a

discrete sample space. Critically, we have to assign a prior

distribution p(Θ0|H0) to the unknown parameters. In

other words, we need to treat these unknowns as random

variables and use their known distributions to express our

belief in their values. Similarly, p(x|H1)canbedeﬁned.

The main drawbacks of the Bayesian approach are listed as

follows.

(1) The marginalization operation in (10)isoftennot

tractable except for very simple cases.

(2) The choice of prior distributions aﬀects the detection

performance dramatically and thus it is not a trivial

task to choose them.

To make the LRT applicable, we may estimate the

unknown parameters ﬁrst and then use the estimated

parameters in the LRT. Known estimation techniques could

be used for this purpose [59]. However, there is one major

diﬀerence from the conventional estimation problem where

we know that signal is present, while in the case of spectrum

sensing we are not sure whether there is source signal or not

(the ﬁrst priority here is the detection of signal presence). At

diﬀerent hypothesis (H0or H1), the unknown parameters

are also diﬀerent.

TheGLRTisoneeﬃcient method [13,55] to resolve the

above problem, which has been used in many applications,

for example, radar and sonar signal processing. For this

method, the maximum likelihood (ML) estimation of the

unknown parameters under H0and H1is ﬁrst obtained as

Θ0=arg max

Θ0

p(x|H0,Θ0),

Θ1=arg max

Θ1

p(x|H1,Θ1),

(11)

where Θ0and Θ1are the set of unknown parameters under

H0and H1, respectively. Then, the GLRT statistic is formed

as

TGLRT(x)=px|

Θ1,H1

px|

Θ0,H0.(12)

Finally, the GLRT decides H1if TGLRT(x)>γ,whereγis a

threshold, and H0otherwise.

It is not guaranteed that the GLRT is optimal or

approaches to be optimal when the sample size goes to

inﬁnity. Since the unknown parameters in Θ0and Θ1are

highly dependent on the noise and signal statistical models,

the estimations of them could be vulnerable to the modeling

errors. Under the assumption of Gaussian distributed source

signals and noises, and ﬂat-fading channels, some eﬃcient

spectrum sensing methods based on the GLRT can be found

in [60].

5. Exploiting Spatial Correlation of

Multiple Received Signals

The received signal samples at diﬀerent antennas/receivers

are usually correlated, because all si(n)’s are generated from

the same source signal sk(n)’s. As mentioned previously, the

energy detection deﬁned in (8) is not optimal for this case.

Furthermore, it is diﬃcult to realize the LRT in practice.

Hence, we consider suboptimal sensing methods as follows.

If M>1, K=1, and assuming that the propagation

channels are ﬂat-fading (qik =0, ∀i,k) and known to the

receiver, the energy at diﬀerent antennas can be coherently

combined to obtain a nearly optimal detection [41,43,

57]. This is also called maximum ratio combining (MRC).

However, in practice, the channel coeﬃcients are unknown

at the receiver. As a result, the coherent combining may not

be applicable and the equal gain combining (EGC) is used in

practice [41,57], which is the same as the energy detection

deﬁned in (8).

In general, we can choose a matrix Bwith Mrows to

combine the signals from all antennas as

z(n)=BTx(n),n=0, 1, ...,N−1.(13)

The combining matrix should be chosen such that the

resultant signal has the largest SNR. It is obvious that the

SNR after combining is

Γ(B)=E

BTs(n)

2

E

BTη(n)

2, (14)

where E(·) denotes the mathematical expectation. Hence,

the optimal combining matrix should maximize the value

of function Γ(B). Let Rs=E[s(n)sT(n)] be the statistical

covariance matrix of the primary signals. It can be veriﬁed

that

Γ(B)=TrBTRsB

σ2

ηTr(BTB),(15)

where Tr(·) denotes the trace of a matrix. Let λmax be the

maximum eigenvalue of Rsand let β1be the corresponding

eigenvector. It can be proved that the optimal combining

matrix degrades to the vector β1[29].

Upon substituting β1into (13), the test statistic for the

energy detection becomes

TOCED(x)=1

N

N−1

n=0z(n)2.(16)

EURASIP Journal on Advances in Signal Processing 5

The resulting detection method is called optimally combined

energy detection (OCED) [29]. It is easy to show that this test

statistic is better than TED(x)intermsofSNR.

TheOCEDneedsaneigenvectorofthereceivedsource

signal covariance matrix, which is usually unknown. To

overcome this diﬃculty, we provide a method to estimate

the eigenvector using the received signal samples only.

Considering the statistical covariance matrix of the signal

deﬁned as

Rx=Ex(n)xT(n), (17)

we can verify that

Rx=Rs+σ2

ηIM.(18)

Since Rxand Rshave the same eigenvectors, the vector β1

is also the eigenvector of Rxcorresponding to its maximum

eigenvalue. However, in practice, we do not know the

statistical covariance matrix Rxeither, and therefore we

cannotobtaintheexactvectorβ1. An approximation of the

statistical covariance matrix is the sample covariance matrix

deﬁned as

Rx(N)=1

N

N−1

n=0

x(n)xT(n).(19)

Let

β1(normalized to

β12=1) be the eigenvector of the

sample covariance matrix corresponding to its maximum

eigenvalue. We can replace the combining vector β1by

β1,

that is,

z(n)=

βT

1x(n).(20)

Then, the test statistics for the resulting blindly combined

energy detection (BCED) [29]becomes

TBCED(x)=1

N

N−1

n=0

z(n)

2.(21)

It can be veriﬁed that

TBCED(x)=1

N

N−1

n=0

βT

1x(n)xT(n)

β1

=

βT

1

Rx(N)

β1

=

λmax(N),

(22)

where

λmax(N) is the maximum eigenvalue of

Rx(N). Thus,

TBCED(x) can be taken as the maximum eigenvalue of the

sample covariance matrix. Note that this test is a special case

of the eigenvalue-based detection (EBD) [20–25].

6. Combining Space and Time Correlation

In addition to being spatially correlated, the received signal

samples are usually correlated in time due to the following

reasons.

(1) The received signal is oversampled. Let Δ0be the

Nyquist sampling period of continuous-time signal sc(t)and

let sc(nΔ0) be the sampled signal based on the Nyquist

sampling rate. Thanks to the Nyquist theorem, the signal

sc(t) can be expressed as

sc(t)=∞

n=−∞

sc(nΔ0)g(t−nΔ0), (23)

where g(t) is an interpolation function. Hence, the signal

samples s(n)=sc(nΔs) are only related to sc(nΔ0), where

Δsis the actual sampling period. If the sampling rate at

the receiver is Rs=1/Δs>1/Δ0, that is, Δs<Δ0, then

s(n)=sc(nΔs) must be correlated over n. An example of

this is the wireless microphone signal speciﬁed in the IEEE

802.22 standard [6,7], which occupies about 200 KHz in a

6-MHz TV band. In this example, if we sample the received

signal with sampling rate no lower than 6 MHz, the wireless

microphone signal is actually oversampled and the resulting

signal samples are highly correlated in time.

(2) The propagation channel is time-dispersive. In this

case, the received signal can be expressed as

sc(t)=∞

−∞h(τ)s0(t−τ)dτ,(24)

where s0(t) is the transmitted signal and h(t) is the response

of the time-dispersive channel. Since the sampling period Δs

is usually very small, the integration (24) can be approxi-

mated as

sc(t)≈Δs

∞

k=−∞

h(kΔs)s0(t−kΔs).(25)

Hence,

sc(nΔs)≈Δs

J1

k=J0

h(kΔs)s0((n−k)Δs), (26)

where [J0Δs,J1Δs] is the support of the channel response

h(t), with h(t)=0fort/

∈[J0Δs,J1Δs]. For time-dispersive

channels, J1>J

0and thus even if the original signal samples

s0(nΔs)’s are i.i.d., the received signal samples sc(nΔs)’s are

correlated.

(3) The transmitted signal is correlated in time. In this

case, even if the channel is ﬂat-fading and there is no

oversampling at the receiver, the received signal samples are

correlated.

The above discussions suggest that the assumption of

independent (in time) received signal samples may be invalid

in practice, such that the detection methods relying on this

assumption may not perform optimally. However, additional

correlation in time may not be harmful for signal detection,

while the problem is how we can exploit this property. For

the multi-antenna/receiver case, the received signal samples

are also correlated in space. Thus, to use both the space

and time correlations, we may stack the signals from the M

6 EURASIP Journal on Advances in Signal Processing

antennas and over Lsampling periods all together and deﬁne

the corresponding ML ×1 signal/noise vectors:

xL(n)=[x1(n)··· xM(n)x1(n−1)··· xM(n−1)

··· x1(n−L+1

)··· xM(n−L+1

)]T

(27)

sL(n)=[s1(n)··· sM(n)s1(n−1)··· sM(n−1)

··· s1(n−L+1

)··· sM(n−L+1

)]T

(28)

ηL(n)=η1(n)··· ηM(n)η1(n−1)··· ηM(n−1)

··· η1(n−L+1

)··· ηM(n−L+1

)T.

(29)

Then, by replacing x(n)byxL(n), we can directly extend the

previously introduced OCED and BCED methods to incor-

porate joint space-time processing. Similarly, the eigenvalue-

based detection methods [21–24] can also be modiﬁed to

work for correlated signals in both time and space. Another

approach to make use of space-time signal correlation is

the covariance based detection [27,28,61]brieﬂydescribed

as follows. Deﬁning the space-time statistical covariance

matrices for the signal and noise as

RL,x=ExL(n)xT

L(n),

RL,s=EsL(n)sT

L(n),

(30)

respectively, we can verify that

RL,x=RL,s+σ2

ηIL.(31)

If the signal is not present, RL,s=0, and thus the oﬀ-diagonal

elements in RL,xare all zeros. If there is a signal and the signal

samples are correlated, RL,sis not a diagonal matrix. Hence,

the nonzero oﬀ-diagonal elements of RL,xcan be used for

signal detection.

In practice, the statistical covariance matrix can only be

computed using a limited number of signal samples, where

RL,xcan be approximated by the sample covariance matrix

deﬁned as

RL,x(N)=1

N

N−1

n=0

xL(n)xT

L(n).(32)

Based on the sample covariance matrix, we could develop the

covariance absolute value (CAV) test [27,28]deﬁnedas

TCAV(x)=1

ML

ML

n=1

ML

m=1|rnm(N)|, (33)

where rnm(N) denotes the (n,m)th element of the sample

covariance matrix

RL,x(N).

There are other ways to utilize the elements in the

sample covariance matrix, for example, the maximum value

of the nondiagonal elements, to form diﬀerent test statistics.

Especially, when we have some prior information on the

source signal correlation, we may choose a corresponding

subset of the elements in the sample covariance matrix to

form a more eﬃcient test.

Another eﬀective usage of the covariance matrix for

sensing is the eigenvalue based detection (EBD) [20–25],

which uses the eigenvalues of the covariance matrix as test

statistics.

7. Cyclostationary Detection

Practical communication signals may have special statisti-

cal features. For example, digital modulated signals have

nonrandom components such as double sidedness due to

sinewave carrier and keying rate due to symbol period. Such

signals have a special statistical feature called cyclostation-

arity, that is, their statistical parameters vary periodically

in time. This cyclostationarity can be extracted by the

spectral-correlation density (SCD) function [16–18]. For a

cyclostationary signal, its SCD function takes nonzero values

at some nonzero cyclic frequencies. On the other hand, noise

does not have any cyclostationarity at all; that is, its SCD

function has zero values at all non-zero cyclic frequencies.

Hence, we can distinguish signal from noise by analyzing the

SCD function. Furthermore, it is possible to distinguish the

signal type because diﬀerent signals may have diﬀerent non-

zero cyclic frequencies.

In the following, we list cyclic frequencies for some

signals of practical interest [17,18].

(1) Analog TV signal: it has cyclic frequencies at mul-

tiples of the TV-signal horizontal line-scan rate

(15.75 KHz in USA, 15.625 KHz in Europe).

(2) AM signal: x(t)=a(t)cos(2πf

ct+φ0). It has cyclic

frequencies at ±2fc.

(3) PM and FM signal: x(t)=cos(2πf

ct+φ(t)). It usually

has cyclic frequencies at ±2fc. The characteristics of

the SCD function at cyclic frequency ±2fcdepend on

φ(t).

(4) Digital-modulated signals are as follows

(a) Amplitude-Shift Keying: x(t)=[∞

n=−∞ anp(t

−nΔs−t0)] cos(2πf

ct+φ0). It has cyclic

frequencies at k/Δs,k/

=0and±2fc+k/Δs,k=

0, ±1, ±2, ....

(b) Phase-Shift Keying: x(t)=cos[2πf

ct+

∞

n=−∞ anp(t−nΔs−t0)]. For BPSK, it has cyclic

frequencies at k/Δs,k/

=0, and ±2fc+k/Δs,k=

0, ±1, ±2, ....For QPSK, it has cycle frequencies

at k/Δs,k/

=0.

When source signal x(t) passes through a wireless

channel, the received signal is impaired by the unknown

propagation channel. In general, the received signal can be

written as

y(t)=x(t)⊗h(t), (34)

EURASIP Journal on Advances in Signal Processing 7

where ⊗denotes the convolution, and h(t) denotes the

channel response. It can be shown that the SCD function of

y(t)is

Syf=Hf+α

2H∗f−α

2Sxf, (35)

where ∗denotes the conjugate, αdenotes the cyclic fre-

quency for x(t), H(f) is the Fourier transform of the

channel h(t), and Sx(f) is the SCD function of x(t). Thus,

the unknown channel could have major impacts on the

strength of SCD at certain cyclic frequencies.

Although cyclostationary detection has certain advan-

tages (e.g., robustness to uncertainty in noise power and

propagation channel), it also has some disadvantages: (1) it

needs a very high sampling rate; (2) the computation of SCD

function requires large number of samples and thus high

computational complexity; (3) the strength of SCD could

be aﬀected by the unknown channel; (4) the sampling time

error and frequency oﬀset could aﬀect the cyclic frequencies.

8. Cooperative Sensing

When there are multiple users/receivers distributed in diﬀer-

ent locations, it is possible for them to cooperate to achieve

higher sensing reliability, thus resulting in various cooper-

ative sensing schemes [34–44,53,62]. Generally speaking,

if each user sends its observed data or processed data to a

speciﬁc user, which jointly processes the collected data and

makes a ﬁnal decision, this cooperative sensing scheme is

called data fusion. Alternatively, if multiple receivers process

their observed data independently and send their decisions to

a speciﬁc user, which then makes a ﬁnal decision, it is called

decision fusion.

8.1. Data Fusion. If the raw data from all receivers are sent

to a central processor, the previously discussed methods

for multi-antenna sensing can be directly applied. However,

communication of raw data may be very expensive for

practical applications. Hence, in many cases, users only send

processed/compressed data to the central processor.

A simple cooperative sensing scheme based on the energy

detection is the combined energy detection. For this scheme,

each user computes its received source signal (including the

noise) energy as TED,i=(1/N )N−1

n=0|xi(n)|2and sends it to

the central processor, which sums the collected energy values

using a linear combination (LC) to obtain the following test

statistic:

TLC(x)=

M

i=1

giTED,i, (36)

where giis the combining coeﬃcient, with gi≥0and

M

i=1gi=1. If there is no information on the source signal

power received by each user, the EGC can be used, that is,

gi=1/M for all i. If the source signal power received by

each user is known, the optimal combining coeﬃcients can

be found [38,43]. For the low-SNR case, it can be shown [43]

that the optimal combining coeﬃcients are given by

gi=σ2

i

M

k=1σ2

k

,i=1, ...,M, (37)

where σ2

iis the received source signal (excluding the noise)

power of user i.

A fusion scheme based on the CAV is given in [53],

which has the capability to mitigate interference and noise

uncertainty.

8.2. Decision Fusion. In decision fusion, each user sends its

one-bit or multiple-bit decision to a central processor, which

deploys a fusion rule to make the ﬁnal decision. Speciﬁcally, if

each user only sends one-bit decision (“1” for signal present

and “0” for signal absent) and no other information is

available at the central processor, some commonly adopted

decision fusion rules are described as follows [42].

(1) “Logical-OR (LO)” Rule: If one of the decisions is “1,”

the ﬁnal decision is “1.” Assuming that all decisions

are independent, then the probability of detection

and probability of false alarm of the ﬁnal decision are

Pd=1−M

i=1(1−Pd,i)andPfa =1−M

i=1(1−Pfa,i),

respectively, where Pd,iand Pfa,iare the probability

of detection and probability of false alarm for user i,

respectively.

(2) “Logical-AND (LA)” Rule: If and only if all decisions

are “1,” the ﬁnal decision is “1.” The probability of

detection and probability of false alarm of the ﬁnal

decision are Pd=M

i=1Pd,iand Pfa =M

i=1Pfa,i,

respectively.

(3) “Kout of M”Rule:IfandonlyifKdecisions

or more are “1”s, the ﬁnal decision is “1.” This

includes “Logical-OR (LO)” (K=1), “Logical-AND

(LA)” (K=M), and “Majority” (K=M/2)as

special cases [34]. The probability of detection and

probability of false alarm of the ﬁnal decision are

Pd=

M−K

i=0⎛

⎝M

K+i⎞

⎠1−Pd,iM−K−i

×1−Pd,iK+i,

Pfa =

M−K

i=0⎛

⎝M

K+i⎞

⎠1−Pfa,iM−K−i

×1−Pfa,iK+i,

(38)

respectively.

Alternatively, each user can send multiple-bit decision

such that the central processor gets more information to

make a more reliable decision. A fusion scheme based on

multiple-bit decisions is shown in [41]. In general, there is a

tradeoﬀbetween the number of decision bits and the fusion

8 EURASIP Journal on Advances in Signal Processing

reliability. There are also other fusion rules that may require

additional information [34,63].

Although cooperative sensing can achieve better perfor-

mance, there are some issues associated with it. First, reliable

information exchanges among the cooperating users must

be guaranteed. In an ad hoc network, this is by no means

a simple task. Second, most data fusion methods in literature

are based on the simple energy detection and ﬂat-fading

channel model, while more advanced data fusion algorithms

such as cyclostationary detection, space-time combining,

and eigenvalue-based detection, over more practical prop-

agation channels need to be further investigated. Third,

existing decision fusions have mostly assumed that decisions

of diﬀerent users are independent, which may not be true

because all users actually receive signals from some common

sources. At last, practical fusion algorithms should be robust

to data errors due to channel impairment, interference, and

noise.

9. Noise Power Uncertainty and Estimation

For many detection methods, the receiver noise power is

assumed to be known a priori, in order to form the test

statistic and/or set the test threshold. However, the noise

power level may change over time, thus yielding the so-

called noise uncertainty problem. There are two types of

noise uncertainty: receiver device noise uncertainty and

environment noise uncertainty. The receiver device noise

uncertainty comes from [9–11]: (a) nonlinearity of receiver

components and (b) time-varying thermal noise in these

components. The environment noise uncertainty is caused

by transmissions of other users, either unintentionally or

intentionally. Because of the noise uncertainty, in practice,

it is very diﬃcult to obtain the accurate noise power.

Let the estimated noise power be σ2

η=ασ2

η,whereαis

called the noise uncertainty factor. The upper bound on α

(in dB scale) is then deﬁned as

B=sup10 log10α, (39)

where Bis called the noise uncertainty bound. It is usually

assumed that αin dB scale, that is, 10 log10α, is uniformly

distributed in the interval [−B,B][10]. In practice, the

noise uncertainty bound of a receiving device is normally

below 2 dB [10,64], while the environment/interference

noise uncertainty can be much larger [10]. When there is

noise uncertainty, it is known that the energy detection is not

eﬀective [9–11,64].

To resolve the noise uncertainty problem, we need to

estimate the noise power in real time. For the multi-antenna

case, if we know that the number of active primary signals,

K, is smaller than M, the minimum eigenvalue of the sample

covariance matrix can be a reasonable estimate of the noise

power. If we further assume to know the diﬀerence M−

K, the average of the M−Ksmallest eigenvalues can be

used as a better estimate of the noise power. Accordingly,

instead of comparing the test statistics with an assumed noise

power, we can compare them with the estimated noise power

from the sample covariance matrix. For example, we can

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of detection

10−210−1100

Probability of false alarm

BCED

MME

EME

ED

ED-0.5 dB

ED-1 dB

ED-1.5 dB

ED-2 dB

Figure 1: ROC curve: i.i.d source signal.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of detection

10−210−1100

Probability of false alarm

BCED

MME

EME

ED

ED-0.5 dB

ED-1 dB

ED-1.5 dB

ED-2 dB

Figure 2: ROC curve: wireless microphone source signal.

compare TBCED and TED with the minimum eigenvalue of

the sample covariance matrix, resulting in the maximum

to minimum eigenvalue (MME) detection and energy to

minimum eigenvalue (EME) detection, respectively [21,22].

These methods can also be used for the single-antenna case

if signal samples are time-correlated [22].

Figures 1and 2show the Receiver Operating Charac-

teristics (ROC) curves (Pdversus Pfa

)atSNR =−15 dB,

N=5000, M=4, and K=1. In Figure 1, the source

signal is i.i.d and the ﬂat-fading channel is assumed, while

in Figure 2, the source signal is the wireless microphone

signal [61,65] and the multipath fading channel (with eight

EURASIP Journal on Advances in Signal Processing 9

independent taps of equal power) is assumed. For Figure 2,

in order to exploit the correlation of signal samples in both

space and time, the received signal samples are stacked as in

(27). In both ﬁgures, “ED-x dB” means the energy detection

with x-dB noise uncertainty. Note that both BCED and ED

use the true noise power to set the test threshold, while

MME and EME only use the estimated noise power as the

minimum eigenvalue of the sample covariance matrix. It is

observed that for both cases of i.i.d source (Figure 1)and

correlated source (Figure 2), BCED performs better than ED,

and so does MME than EME. Comparing Figures 1and 2,we

see that BCED and MME work better for correlated source

signals, while the reverse is true for ED and EME. It is also

observed that the performance of ED degrades dramatically

when there is noise power uncertainty.

10. Detection Threshold and Test

Statistic Distribution

To make a decision on whether signal is present, we need to

set a threshold γfor each proposed test statistic, such that

certain Pdand/or Pfa can be achieved. For a ﬁxed sample

size N, we cannot set the threshold to meet the targets for

arbitrarily high Pdand low Pfa at the same time, as they

are conﬂicting to each other. Since we have little or no prior

information on the signal (actually we even do not know

whether there is a signal or not), it is diﬃcult to set the

threshold based on Pd. Hence, a common practice is to

choose the threshold based on Pfa under hypothesis H0.

Without loss of generality, the test threshold can be

decomposed into the following form: γ=γ1T0(x), where γ1

is related to the sample size Nand the target Pfa

,andT0(x)

is a statistic related to the noise distribution under H0.For

example, for the energy detection with known noise power,

we have

T0(x)=σ2

η.(40)

For the matched-ﬁltering detection with known noise power,

we have

T0(x)=ση.(41)

For the EME/MME detection with no knowledge on the

noise power, we have

T0(x)=

λmin(N),(42)

where

λmin(N) is the minimum eigenvalue of the sample

covariance matrix. For the CAV detection, we can set

T0(x)=1

ML

ML

n=1|rnn(N)|.(43)

In practice, the parameter γ1can be set either empirically

based on the observations over a period of time when the

signal is known to be absent, or analytically based on the

distribution of the test statistic under H0. In general, such

distributions are diﬃcult to ﬁnd, while some known results

are given as follows.

For energy detection deﬁned in (8), it can be shown that

for a suﬃciently large values of N, its test statistic can be well

approximated by the Gaussian distribution, that is,

1

NMTED(x)∼Nσ2

η,2σ4

η

NMunder H0.(44)

Accordingly, for given Pfa and N, the corresponding γ1can

be found as

γ1=NM⎛

⎝2

NMQ−1Pfa

+1

⎞

⎠, (45)

where

Q(t)=1

√2π+∞

te−u2/2du. (46)

For the matched-ﬁltering detection deﬁned in (9), for a

suﬃciently large N,wehave

1

N−1

n=0s(n)2TMF(x)∼N0, σ2

ηunder H0.(47)

Thereby, for given Pfa and N, it can be shown that

γ1=Q−1Pfa

!

N−1

n=0s(n)2.(48)

For the GLRT-based detection, it can be shown that the

asymptotic (as N→∞) log-likelihood ratio is central chi-

square distributed [13]. More precisely,

2lnTGLRT(x)∼χ2

runder H0, (49)

where ris the number of independent scalar unknowns

under H0and H1. For instance, if σ2

ηis known while Rsis

not, rwill be equal to the number of independent real-valued

scalar variables in Rs. However, there is no explicit expression

for γ1in this case.

Random matrix theory (RMT) is useful for determining

the test statistic distribution and the parameter γ1for

the class of eigenvalue-based detection methods. In the

following, we provide an example for the BCED detection

method with known noise power, that is, T0(x)=σ2

η.For

this method, we actually compare the ratio of the maximum

eigenvalue of the sample covariance matrix

Rx(N) to the

noise power σ2

ηwith a threshold γ1. To set the value for γ1,we

need to know the distribution of

λmax(N)/σ2

ηfor any ﬁnite N.

With a ﬁnite N,

Rx(N)maybeverydiﬀerent from the actual

covariance matrix Rxdue to the noise. In fact, characterizing

the eigenvalue distributions for

Rx(N) is a very complicated

problem [66–69], which also makes the choice of γ1diﬃcult

in general.

When there is no signal,

Rx(N)reducesto

Rη(N), which

is the sample covariance matrix of the noise only. It is known

that

Rη(N) is a Wishart random matrix [66]. The study

of the eigenvalue distributions for random matrices is a

10 EURASIP Journal on Advances in Signal Processing

very hot research topic over recent years in mathematics,

communications engineering, and physics. The joint PDF of

the ordered eigenvalues of a Wishart random matrix has been

known for many years [66]. However, since the expression

of the joint PDF is very complicated, no simple closed-form

expressions have been found for the marginal PDFs of the

ordered eigenvalues, although some computable expressions

have been found in [70]. Recently, Johnstone and Johansson

have found the distribution of the largest eigenvalue [67,68]

of a Wishart random matrix as described in the following

theorem.

Theorem 1. Let A(N)=(N/σ2

η)

Rη(N),μ=(√N−1+√M)2,

and ν=(√N−1+√M)(1/√N−1+1/√M)1/3. Assume that

limN→∞(M/N)=y(0 <y<1).Then,(λmax(A(N)) −

μ)/νconverges (with probability one) to the Tracy-Widom

distribution of order 1 [71,72].

The Tracy-Widom distribution provides the limiting law

for the largest eigenvalue of certain random matrices [71,

72]. Let F1be the cumulative distribution function (CDF)

of the Tracy-Widom distribution of order 1. We have

F1(t)=exp−1

2∞

tq(u)+(u−t)q2(u)du, (50)

where q(u) is the solution of the nonlinear Painlev´

eII

diﬀerential equation given by

q(u)=uq(u)+2q3(u).(51)

Accordingly, numerical solutions can be found for function

F1(t)atdiﬀerent values of t. Also, there have been tables for

values of F1(t)[67] and Matlab codes to compute them [73].

Based on the above results, the probability of false alarm

for the BCED detection can be obtained as

Pfa =P

λmax(N)>γ

1σ2

η

=Pσ2

η

Nλmax(A(N)) >γ

1σ2

η

=Pλmax(A(N)) >γ

1N

=Pλmax(A(N)) −μ

ν>γ1N−μ

ν

≈1−F1γ1N−μ

ν,

(52)

which leads to

F1γ1N−μ

ν≈1−Pfa (53)

or equivalently,

γ1N−μ

ν≈F−1

11−Pfa

.(54)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Probability of false alarm

0.91 0.915 0.92 0.925 0.93 0.935 0.94 0.945 0.95

1/threshold

Theoretical Pfa

Actual Pfa

Figure 3: Comparison of theoretical and actual Pfa.

From the deﬁnitions of μand νin Theorem 1,weﬁnally

obtain the value for γ1as

γ1≈√N+√M2

N

×⎛

⎜

⎝1+√N+√M−2/3

(NM)1/6F−1

11−Pfa

⎞

⎟

⎠.

(55)

Note that γ1depends only on Nand Pfa

. A similar approach

like the above can be used for the case of MME detection, as

shown in [21,22].

Figure 3 shows the expected (theoretical) and actual (by

simulation) probability of false alarm values based on the

theoretical threshold in (55)forN=5000, M=8, and

K=1. It is observed that the diﬀerences between these two

sets of values are reasonably small, suggesting that the choice

of the theoretical threshold is quite accurate.

11. Robust Spectrum Sensing

In many detection applications, the knowledge of signal

and/or noise is limited, incomplete, or imprecise. This is

especially true in cognitive radio systems, where the primary

users usually do not cooperate with the secondary users

and as a result the wireless propagation channels between

the primary and secondary users are hard to be predicted

or estimated. Moreover, intentional or unintentional inter-

ference is very common in wireless communications such

that the resulting noise distribution becomes unpredictable.

Suppose that a detector is designed for speciﬁc signal and

noise distributions. A pertinent question is then as follows:

how sensitive is the performance of the detector to the errors

in signal and/or noise distributions? In many situations,

the designed detector based on the nominal assumptions

may suﬀer a drastic degradation in performance even with

EURASIP Journal on Advances in Signal Processing 11

small deviations from the assumptions. Consequently, the

searching for robust detection methods has been of great

interest in the ﬁeld of signal processing and many others [74–

77]. A very useful paradigm to design robust detectors is the

maxmin approach, which maximizes the worst case detection

performance. Among others, two techniques are very useful

for robust cognitive radio spectrum sensing: the robust

hypothesis testing [75] and the robust matched ﬁltering

[76,77]. In the following, we will give a brief overview

on them, while for other robust detection techniques, the

interested readers may refer to the excellent survey paper [78]

and references therein.

11.1. Robust Hypothesis Testing. Let the PDF of a received

signal sample be f1at hypothesis H1and f0at hypothesis

H0. If we know these two functions, the LRT-based detection

described in Section 2 is optimal. However, in practice, due

to channel impairment, noise uncertainty, and interference,

it is very hard, if possible, to obtain these two functions

exactly. One possible situation is when we only know that f1

and f0belong to certain classes. One such class is called the

ε-contamination class given by

H0:f0∈F0,F0=$(1−0)f0

0+0g0%,

H1:f1∈F1,F1=$(1−1)f0

1+1g1%,(56)

where f0

j(j=0, 1) is the nominal PDF under hypothesis Hj,

jin [0, 1] is the maximum degree of contamination, and gj

is an arbitrary density function. Assume that we only know

f0

jand j(an upper bound for contamination), j=1, 2. The

problem is then to design a detection scheme to minimize

the worst-case probability of error (e.g., probability of false

alarm plus probability of mis-detection), that is, ﬁnding a

detector

Ψsuch that

Ψ=arg min

Ψmax

(f0,f1)∈F0×F1Pfa

f0,f1,Ψ+1−Pdf0,f1,Ψ.

(57)

Hubber [75] proved that the optimal test statistic is a

“censored” version of the LRT given by

Ψ=TCLRT(x)=

N−1

n=0

r(x(n)), (58)

where

r(t)=

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

c1,c1≤f0

1(t)

f0

0(t),

f0

1(t)

f0

0(t),c0<f0

1(t)

f0

0(t),<c

1

c0,f0

1(t)

f0

0(t)≤c0,

(59)

and c0,c1are nonnegative numbers related to 0,1,f0

0,and

f0

1[75,78]. Note that if choosing c0=0andc1=+∞, the

test is the conventional LRT with respect to nominal PDFs,

f0

0and f0

1.

After this seminal work, there have been quite a few

researches in this area [78]. For example, similar minmax

solutions are found for some other uncertainty models [78].

11.2. Robust Matched Filtering. We turn the model (4) into a

vector form as

H0:x=η,

H1:x=s+η,(60)

where sis the signal vector and ηis the noise vector. Suppose

that sis known. In general, a matched-ﬁltering detection

is TMF =gTx. Let the covariance matrix of the noise be

Rη=E(ηηT). If Rη=σ2

ηI, it is known that choosing g=s

is optimal. In general, it is easy to verify that the optimal gto

maximize the SNR is

g=R−1

ηs.(61)

In practice, the signal vector smay not be known exactly. For

example, smay be only known to be around s0with some

errors modeled by

s−s0≤Δ, (62)

where Δis an upper bound on the Euclidean-norm of the

error. In this case, we are interested in ﬁnding a proper value

for gsuch that the worst-case SNR is maximized, that is,

g=arg max

gmin

s:||s−s0||≤ΔSNRs,g.(63)

Itwasprovedin[76,77] that the optimal solution for the

above maxmin problem is

g=Rη+δI−1s0, (64)

where δis a nonnegative number such that δ2g2=Δ.

It is noted that there are also researches on the robust

matched ﬁltering detection when the signal has other types

of uncertainty [78]. Moreover, if the noise has uncertainties,

that is, Rηis not known exactly, or both noise and signal have

uncertainties, the optimal robust matched-ﬁltering detector

was also found for some speciﬁc uncertainty models in [78].

12. Practical Considerations and

Future Developments

Although there have been quite a few methods proposed

for spectrum sensing, their realization and performance in

practical cognitive radio applications need to be tested [50–

52]. To build a practical sensing device, many factors should

be considered. Some of them are discussed as follows.

(1) Narrowband noise. One or more narrowband ﬁlters

may be used to extract the signal from a speciﬁc band. These

ﬁlters can be analog or digital. Only if the ﬁlter is ideally

designed and the signal is critically sampled (sampling rate

is the same as the bandwidth of the ﬁlter), the discrete noise

samples could be i.i.d. In a practical device, however, the

12 EURASIP Journal on Advances in Signal Processing

noise samples are usually correlated. This will cause many

sensing methods unworkable, because they usually assume

that the noise samples are i.i.d. For some methods, a noise

prewhitening process can be used to make the noise samples

i.i.d. prior to the signal detection. For example, this method

has been deployed in [22] to enable the eigenvalue-based

detection methods. The similar method can be used for

covariance-based detection methods, for example, the CAV.

(2) Spurious signal and interference. The received signal

may contain not only the desired signal and white noise but

also some spurious signal and interference. The spurious

signal may be generated by Analog-to-Digital Convert-

ers (ADC) due to its nonlinearity [79] or other inten-

tional/unintentional transmitters. If the sensing antenna is

near some electronic devices, the spurious signal generated

by the devices can be strong in the received signal. For some

sensing methods, such unwanted signals will be detected as

signals rather than noise. This will increase the probability

of false alarm. There are methods to mitigate the spurious

signal at the device level [79]. Alternatively, signal processing

techniques can be used to eliminate the impact of spurious

signal/interference [53]. It is very diﬃcult, if possible, to

estimate the interference waveform or distribution because

of its variation with time and location. Depending on

situations, the interference power could be lower or higher

than the noise power. If the interference power is much

higher than the noise power, it is possible to estimate the

interference ﬁrst and subtract it from the received signal.

However, since we usually intend to detect signal at very

low SNR, the error of the interference estimation could be

large enough (say, larger than the primary signal) such that

the detection with the residue signal after the interference

subtraction is still unreliable. If the interference power is

low, it is hard to estimate it anyway. Hence, in general we

cannot rely on the interference estimation and subtraction,

especially for very low-power signal detection.

(3) Fixed point realization. Many hardware realizations

use ﬁxed point rather than ﬂoating point computation. This

will limit the accuracy of detection methods due to the signal

truncation when it is saturated. A detection method should

be robust to such unpredictable errors.

(4) Wideband sensing. A cognitive radio device may

need to monitor a very large contiguous or noncontiguous

frequency range to ﬁnd the best available band(s) for

transmission. The aggregate bandwidth could be as large

as several GHz. Such wideband sensing requires ultra-

wide band RF frontend and very fast signal processing

devices. To sense a very large frequency range, typically

a corresponding large sampling rate is required, which is

very challenging for practical implementation. Fortunately,

if a large part of the frequency range is vacant, that is, the

signal is frequency-domain sparse, we can use the recently

developed compressed sampling (also called compressed

sensing) to reduce the sampling rate by a large margin

[80–82]. Although there have been studies in wideband

sensing algorithms [26,83–87], more researches are needed

especially when the center frequencies and bandwidths of the

primary signals are unknown within the frequency range of

interest.

(5) Complexity. This is of course one of the major factors

aﬀecting the implementation of a sensing method. Simple

but eﬀective methods are always preferable.

To detect a desired signal at very low SNR and in a harsh

environment is by no means a simple task. In this paper,

major attention is paid to the statistical detection methods.

The major advantage of such methods is their little depen-

dency on signal/channel knowledge as well as relative ease for

realization. However, their disadvantage is also obvious: they

are in general vulnerable to undesired interferences. How we

can eﬀectively combine the statistical detection with known

signal features is not yet well understood. This might be

a promising research direction. Furthermore, most exiting

spectrum sensing methods are passive in the sense that they

have neglected the interactions between the primary and

secondary networks via their mutual interferences. If the

reaction of the primary user (e.g., power control) upon

receiving the secondary interference is exploited, some active

spectrum sensing methods can be designed, which could

signiﬁcantly outperform the conventional passive sensing

methods [88,89]. At last, detecting the presence of signal is

only the basic task of sensing. For a radio with high level

of cognition, further information such as signal waveform

and modulation schemes may be exploited. Therefore, signal

identiﬁcation turns to be an advanced task of sensing. If we

could ﬁnd an eﬀective method for this advanced task, it in

turn can help the basic sensing task.

13. Conclusion

In this paper, various spectrum sensing techniques have been

reviewed. Special attention has been paid to blind sensing

methods that do not need information of the source signals

and the propagation channels. It has been shown that space-

time joint signal processing not only improves the sensing

performance but also solves the noise uncertainty problem to

some extent. Theoretical analysis on test statistic distribution

and threshold setting has also been investigated.

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Photographȱ©ȱTurismeȱdeȱBarcelonaȱ/ȱJ.ȱTrullàs

Preliminaryȱcallȱforȱpapers

The 2011 European Signal Processing Conference (EUSIPCOȬ2011) is the

nineteenth in a series of conferences promoted by the European Association for

Signal Processing (EURASIP, www.eurasip.org). This year edition will take place

in Barcelona, capital city of Catalonia (Spain), and will be jointly organized by the

Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) and the

Universitat Politècnica de Catalunya (UPC).

EUSIPCOȬ2011 will focus on key aspects of signal processing theory and

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MiguelȱA.ȱLagunasȱ(CTTC)

GeneralȱChair

AnaȱI.ȱPérezȬNeiraȱ(UPC)

GeneralȱViceȬChair

CarlesȱAntónȬHaroȱ(CTTC)

TechnicalȱProgramȱChair

XavierȱMestreȱ(CTTC)

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relevance and originality. Accepted papers will be published in the EUSIPCO

proceedings and presented during the conference. Paper submissions, proposals

for tutorials and proposals for special sessions are invited in, but not limited to,

the following areas of interest.

Areas of Interest

• Audio and electroȬacoustics.

• Design, implementation, and applications of signal processing systems.

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JavierȱHernandoȱ(UPC)

MontserratȱPardàsȱ(UPC)

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FerranȱMarquésȱ(UPC)

YoninaȱEldarȱ(Technion)

SpecialȱSessions

IgnacioȱSantamaríaȱ(Unversidadȱ

deȱCantabria)

MatsȱBengtssonȱ(KTH)

Finances

Montserrat Nájar (UPC)

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• Image and multidimensional signal processing.

• Signal detection and estimation.

• Sensor array and multiȬchannel signal processing.

• Sensor fusion in networked systems.

• Signal processing for communications.

• Medical imaging and image analysis.

• NonȬstationary, nonȬlinear and nonȬGaussian signal processing.

Submissions

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(UPC)

Tutorials

DanielȱP.ȱPalomarȱ

(HongȱKongȱUST)

BeatriceȱPesquetȬPopescuȱ(ENST)

Publicityȱ

StephanȱPfletschingerȱ(CTTC)

MònicaȱNavarroȱ(CTTC)

Publications

AntonioȱPascualȱ(UPC)

CarlesȱFernándezȱ(CTTC)

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Submissions

Procedures to submit a paper and proposals for special sessions and tutorials will

be detailed at www.eusipco2011.org. Submitted papers must be cameraȬready, no

more than 5 pages long, and conforming to the standard specified on the

EUSIPCO 2011 web site. First authors who are registered students can participate

in the best student paper competition.

ImportantȱDeadlines:

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AngelikiȱAlexiouȱȱ

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AlbertȱSitjàȱ(CTTC)

InternationalȱLiaison

JuȱLiuȱ(ShandongȱUniversityȬChina)

JinhongȱYuanȱ(UNSWȬAustralia)

TamasȱSziranyiȱ(SZTAKIȱȬHungary)

RichȱSternȱ(CMUȬUSA)

RicardoȱL.ȱdeȱQueirozȱȱ(UNBȬBrazil)

Webpage:ȱwww.eusipco2011.org

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Proposalsȱforȱtutorials 18ȱFeb 2011

Electronicȱsubmissionȱofȱfullȱpapers 21ȱFeb 2011

Notificationȱofȱacceptance 23ȱMay 2011

SubmissionȱofȱcameraȬreadyȱpapers 6ȱJun 2011