ArticlePDF Available

Abstract and Figures

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.
Content may be subject to copyright.
Hindawi Publishing Corporation
EURASIP Journal on Advances in Signal Processing
Volume 2010, Article ID 381465, 15 pages
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, ASTAR, Singapore 138632
Correspondence should be addressed to Yonghong Zeng,
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
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 eciency 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 [912].
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) [1619],
and some newly emerging methods such as eigenvalue-based
sensing [6,2025], wavelet-based sensing [26], covariance-
based sensing [6,27,28], and blindly combined energy
detection [29]. These methods have dierent 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
When there are multiple secondary users/receivers dis-
tributed at dierent locations, it is possible for them to
cooperate to achieve higher sensing reliability. There are
various sensing cooperation schemes in the current literature
[3444]. 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 [4552].
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 M1 antennas at the receiver.
These antennas can be suciently 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
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 eects. In general, si(n) can be expressed as
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
coecient 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
coecients 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,whichdenes,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.
The hypothesis testing problem based on Nsignal samples is
then obtained as
H1:x(n)=s(n)+η(n),n=0, ...,N1.(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
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, ...,N1.Such a likelihood ratio
test decides H1when TLRT(x) exceeds a threshold γ,andH0
The major diculty 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 dicult to
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
If we further assume that noise and signal samples are both
Gaussian distributed, that is, η(n)N(0,σ2
N(0,Rs), the LRT becomes the estimator-correlator (EC)
[13] detector for which the test statistic is given by
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):
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
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
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)canbedened.
The main drawbacks of the Bayesian approach are listed as
(1) The marginalization operation in (10)isoftennot
tractable except for very simple cases.
(2) The choice of prior distributions aects 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
dierence 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
dierent hypothesis (H0or H1), the unknown parameters
are also dierent.
TheGLRTisoneecient 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
Θ1=arg max
where Θ0and Θ1are the set of unknown parameters under
H0and H1, respectively. Then, the GLRT statistic is formed
Finally, the GLRT decides H1if TGLRT(x),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 ecient
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 dierent 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 dicult 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 dierent 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 coecients 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, ...,N1.(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
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
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
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.
signal covariance matrix, which is usually unknown. To
overcome this diculty, 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
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
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
that is,
Then, the test statistics for the resulting blindly combined
energy detection (BCED) [29]becomes
It can be verified that
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) [2025].
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
(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(nΔ0)g(tnΔ0), (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
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
h(kΔs)s0((nk)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
(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
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(n1)··· xM(n1)
··· x1(nL+1
)··· xM(nL+1
sL(n)=[s1(n)··· sM(n)s1(n1)··· sM(n1)
··· s1(nL+1
)··· sM(nL+1
ηL(n)=η1(n)··· ηM(n)η1(n1)··· ηM(n1)
··· η1(nL+1
)··· ηM(nL+1
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 [2124] 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]brieydescribed
as follows. Defining the space-time statistical covariance
matrices for the signal and noise as
respectively, we can verify that
If the signal is not present, RL,s=0, and thus the o-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 o-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
Based on the sample covariance matrix, we could develop the
covariance absolute value (CAV) test [27,28]denedas
m=1|rnm(N)|, (33)
where rnm(N) denotes the (n,m)th element of the sample
covariance matrix
There are other ways to utilize the elements in the
sample covariance matrix, for example, the maximum value
of the nondiagonal elements, to form dierent 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 ecient test.
Another eective usage of the covariance matrix for
sensing is the eigenvalue based detection (EBD) [2025],
which uses the eigenvalues of the covariance matrix as test
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 [1618]. 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 dierent signals may have dierent 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
(4) Digital-modulated signals are as follows
(a) Amplitude-Shift Keying: x(t)=[
n=−∞ anp(t
nΔst0)] cos(2πf
ct+φ0). It has cyclic
frequencies at k/Δs,k/
0, ±1, ±2, ....
(b) Phase-Shift Keying: x(t)=cos[2πf
n=−∞ anp(tnΔst0)]. 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/
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
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 aected by the unknown channel; (4) the sampling time
error and frequency oset could aect the cyclic frequencies.
8. Cooperative Sensing
When there are multiple users/receivers distributed in dier-
ent locations, it is possible for them to cooperate to achieve
higher sensing reliability, thus resulting in various cooper-
ative sensing schemes [3444,53,62]. 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 )N1
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
giTED,i, (36)
where giis the combining coecient, with gi0and
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 coecients can
be found [38,43]. For the low-SNR case, it can be shown [43]
that the optimal combining coecients are given by
,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
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
i=1(1Pd,i)andPfa =1M
respectively, where Pd,iand Pfa,iare the probability
of detection and probability of false alarm for user i,
(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
(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
Pfa =
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
tradeobetween 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 dierent 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
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 [911]: (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 dicult to obtain the accurate noise power.
Let the estimated noise power be σ2
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
eective [911,64].
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 dierence M
K, the average of the MKsmallest 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
Probability of detection
Probability of false alarm
ED-0.5 dB
ED-1 dB
ED-1.5 dB
ED-2 dB
Figure 1: ROC curve: i.i.d source signal.
Probability of detection
Probability of false alarm
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 dicult 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
is a statistic related to the noise distribution under H0.For
example, for the energy detection with known noise power,
we have
For the matched-filtering detection with known noise power,
we have
For the EME/MME detection with no knowledge on the
noise power, we have
λmin(N) is the minimum eigenvalue of the sample
covariance matrix. For the CAV detection, we can set
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 dicult to find, while some known results
are given as follows.
For energy detection defined in (8), it can be shown that
for a suciently large values of N, its test statistic can be well
approximated by the Gaussian distribution, that is,
NMunder H0.(44)
Accordingly, for given Pfa and N, the corresponding γ1can
be found as
, (45)
teu2/2du. (46)
For the matched-filtering detection defined in (9), for a
suciently large N,wehave
n=0s(n)2TMF(x)N0, σ2
ηunder H0.(47)
Thereby, for given Pfa and N, it can be shown that
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,
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
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
ηfor any finite N.
With a finite N,
Rx(N)maybeverydierent from the actual
covariance matrix Rxdue to the noise. In fact, characterizing
the eigenvalue distributions for
Rx(N) is a very complicated
problem [6669], which also makes the choice of γ1dicult
in general.
When there is no signal,
Rη(N), which
is the sample covariance matrix of the noise only. It is known
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 1. Let A(N)=(N/σ2
and ν=(N1+M)(1/N1+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
tq(u)+(ut)q2(u)du, (50)
where q(u) is the solution of the nonlinear Painlev´
dierential equation given by
Accordingly, numerical solutions can be found for function
F1(t)atdierent 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
=Pλmax(A(N)) μ
which leads to
ν1Pfa (53)
or equivalently,
Probability of false alarm
0.91 0.915 0.92 0.925 0.93 0.935 0.94 0.945 0.95
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
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 dierences 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 suer 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
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
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
Ψsuch that
Ψ=arg min
Hubber [75] proved that the optimal test statistic is a
“censored” version of the LRT given by
r(x(n)), (58)
and c0,c1are nonnegative numbers related to 0,1,f0
1[75,78]. Note that if choosing c0=0andc1=+, the
test is the conventional LRT with respect to nominal PDFs,
0and f0
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
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
In practice, the signal vector smay not be known exactly. For
example, smay be only known to be around s0with some
errors modeled by
ss0Δ, (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
Itwasprovedin[76,77] that the optimal solution for the
above maxmin problem is
g=Rη+δI1s0, (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 dicult, 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
[8082]. Although there have been studies in wideband
sensing algorithms [26,8387], more researches are needed
especially when the center frequencies and bandwidths of the
primary signals are unknown within the frequency range of
(5) Complexity. This is of course one of the major factors
aecting the implementation of a sensing method. Simple
but eective 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 eectively 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 eective 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.
[1] FCC, “Spectrum policy task force report,” in Proceedings of the
Federal Communications Commission (FCC ’02), Washington,
DC, USA, November 2002.
in Singapore: occupancy measurements and analysis,” in
Proceedings of the 3rd International Conference on Cogni-
tive Radio Oriented Wireless Networks and Communications
(CROWNCOM ’08), Singapor, May 2008.
[3] J. Mitola and G. Q. Maguire, “Cognitive radio: making soft-
ware radios more personal,IEEE Personal Communications,
vol. 6, no. 4, pp. 13–18, 1999.
[4] S. Haykin, “Cognitive radio: brain-empowered wireless com-
munications,IEEE Transactions on Communications, vol. 23,
no. 2, pp. 201–220, 2005.
[5] N. Devroye, P. Mitran, and V. Tarokh, “Achieveable rates in
cognitive radio channels,IEEE Transactions on Information
Theory, vol. 52, no. 5, pp. 1813–1827, 2006.
[6] 802.22 Working Group, “IEEE 802.22 D1: draft stan-
dard for wireless regional area networks,” March 2008,
EURASIP Journal on Advances in Signal Processing 13
[7] C. Stevenson, G. Chouinard, Z. D. Lei, W. D. Hu, S.
Shellhammer, and W. Caldwell, “IEEE 802.22: the first cog-
nitive radio wireless regional area network standard,IEEE
Communications Magazine, vol. 47, no. 1, pp. 130–138, 2009.
[8] Wireless Innovation Alliance, 2008, http://www.wirelessin-
[9] A. Sonnenschein and P. M. Fishman, “Radiometric detection
of spreadspectrum signals in noise of uncertainty power,IEEE
Transactions on Aerospace and Electronic Systems,vol.28,no.3,
pp. 654–660, 1992.
[10] A. Sahai and D. Cabric, “Spectrum sensing: fundamental
limits and practical challenges,” in IEEE International Sympo-
sium on New Frontiers in Dynamic Spectrum Access Networks
(DySPAN ’05), Baltimore, Md, USA, November 2005.
[11] R. Tandra and A. Sahai, “Fundamental limits on detection
in low SNR under noise uncertainty,” in Proceedings of the
International Conference on Wireless Networks, Communica-
tions and Mobile Computing (WirelessCom ’05), vol. 1, pp. 464–
469, Maui, Hawaii, USA, June 2005.
[12] R. Tandra and A. Sahai, “SNR walls for signal detection,IEEE
Journal on Selected Topics in Signal Processing, vol. 2, no. 1, pp.
4–17, 2008.
[13] S. M. Kay, Fundamentals of Statistical Signal Processing:
Detection Theory, vol. 2, Prentice Hall, Upper Saddle River, NJ,
USA, 1998.
[14] H. Urkowitz, “Energy detection of unkown deterministic
signals,Proceedings of the IEEE, vol. 55, no. 4, pp. 523–531,
[15] H. S. Chen, W. Gao, and D. G. Daut, “Signature based
spectrum sensing algorithms for IEEE 802.22 WRAN,” in
Proceedings of the IEEE International Conference on Commu-
nications (ICC ’07), pp. 6487–6492, Glasgow, Scotland, June
[16] W. A. Gardner, “Exploitation of spectral redundancy in
cyclostationary signals,IEEE Signal Processing Magazine, vol.
8, no. 2, pp. 14–36, 1991.
[17] W. A. Gardner, “Spectral correlation of modulated signals—
part I: analog modulation,IEEE Transactions on Communica-
tions, vol. 35, no. 6, pp. 584–595, 1987.
[18] W. A. Gardner, W. A. Brown III, and C.-K. Chen, “Spectral
correlation of modulated signals—part II: digital modula-
tion,IEEE Transactions on Communications,vol.35,no.6,pp.
595–601, 1987.
[19] N. Han, S. H. Shon, J. O. Joo, and J. M. Kim, “Spectral
correlation based signal detection method for spectrum
sensing in IEEE 802.22 WRAN systems,” in Proceedings of
the 8th International Conference on Advanced Communication
Technology, Phoenix Park, South Korea, Febraury 2006.
[20] Y. H. Zeng and Y.-C. Liang, “Eigenvalue based sensing
algorithms,” IEEE 802.22-06/0118r0, July 2006.
[21] Y. H. Zeng and Y.-C. Liang, “Maximum-minimum eigenvalue
detection for cognitive radio,” in Proceedings of the 18th
International Symposium on Personal, Indoor and Mobile Radio
Communications (PIMRC ’07), Athens, Greece, September
[22] Y. H. Zeng and Y.-C. Liang, “Eigenvalue-based spectrum
sensing algorithms for cognitive radio,IEEE Transactions on
Communications, vol. 57, no. 6, pp. 1784–1793, 2009.
[23] P. Bianchi, J. N. G. Alfano, and M. Debbah, “Asymptotics of
eigenbased collaborative sensing,” in Proceedings of the IEEE
Information Theory Workshop (ITW ’09), Taormina, Sicily,
Italy, October 2009.
[24] M. Maida, J. Najim, P. Bianchi, and M. Debbah, “Performance
analysis of some eigen-based hypothesis tests for collaborative
sensing,” in Proceedings of the IEEE Workshop on Statistical
Signal Processing,Cardi, Wales, UK, September 2009.
[25] F. Penna, R. Garello, and M. A. Spirito, “Cooperative spectrum
sensing based on the limiting eigenvalue ratio distribution in
wishart matrices,” IEEE Communications Letters, vol. 13, no. 7,
pp. 507–509, 2009.
[26] Z. Tian and G. B. Giannakis, “A wavelet approach to wideband
spectrum sensing for cognitive radios,” in Proceedings of the 1st
International Conference on Cognitive Radio Oriented Wireless
Networks and Communications (CROWNCOM ’07),Mykonos,
Greece, June 2007.
[27] Y. H. Zeng and Y.-C. Liang, “Covariance based signal
detections for cognitive radio,” in Proceedings of the 2nd
IEEE International Symposium on New Frontiers in Dynamic
Spectrum Access Networks (DySPAN ’07), pp. 202–207, Dublin,
Ireland, April 2007.
[28] Y. H. Zeng and Y.-C. Liang, “Spectrum-sensing algorithms
for cognitive radio based on statistical covariances,IEEE
Transactions on Vehicular Technology, vol. 58, no. 4, pp. 1804–
1815, 2009.
[29] Y. H. Zeng, Y.-C. Liang, and R. Zhang, “Blindly combined
energy detection for spectrum sensing in cognitive radio,
IEEE Signal Processing Letters, vol. 15, pp. 649–652, 2008.
[30] S. Pasupathy and A. N. Venetsanopoulos, “Optimum active
array processing structure and space-time factorability,IEEE
Transactions on Aerospace and Electronic Systems, vol. 10, no. 6,
pp. 770–778, 1974.
[31] A. Dogandzic and A. Nehorai, “Cramer-rao bounds for
estimating range, velocity, and direction with an active array,”
IEEE Transactions on Signal Processing, vol. 49, no. 6, pp. 1122–
1137, 2001.
[32] E. Fishler, A. Haimovich, R. Blum, D. Chizhik, L. Cimini, and
R. Valenzuela, “MIMO radar: an idea whose time has come,
in Proceedings of the IEEE National Radar Conference, pp. 71–
78, Philadelphia, Pa, USA, April 2004.
[33] A. Sheikhi and A. Zamani, “Coherent detection for MIMO
radars,” in Proceedings of the IEEE National Radar Conference,
pp. 302–307, April 2007.
[34] P. K. Varshney, Distributed Detection and Data Fusion,
Springer, New York, NY, USA, 1996.
[35] J. Unnikrishnan and V. V. Veeravalli, “Cooperative sensing for
primary detection in cognitive radio, IEEE Journal on Selected
Topics in Signal Processing, vol. 2, no. 1, pp. 18–27, 2008.
[36] G. Ganesan and Y. Li, “Cooperative spectrum sensing in
cognitive radio—part I: two user networks,IEEE Transactions
on Wireless Communications, vol. 6, pp. 2204–2213, 2007.
[37] G. Ganesan and Y. Li, “Cooperative spectrum sensing in cog-
nitive radio—part II: multiuser networks, IEEE Transactions
on Wireless Communications, vol. 6, pp. 2214–2222, 2007.
[38] Z. Quan, S. Cui, and A. H. Sayed, “Optimal linear cooperation
for spectrum sensing in cognitive radio networks,IEEE
Journal on Selected Topics in Signal Processing,vol.2,no.1,pp.
28–40, 2007.
[39] S. M. Mishra, A. Sahai, and R. W. Brodersen, “Cooperative
sensing among cognitive radios,” in Proceedings of the IEEE
International Conference on Communications (ICC ’06), vol. 4,
pp. 1658–1663, Istanbul, Turkey, June 2006.
14 EURASIP Journal on Advances in Signal Processing
[40] C. Sun, W. Zhang, and K. B. Letaief, “Cluster-based coop-
erative spectrum sensing in cognitive radio systems,” in
Proceedings of the 18th International Symposium on Personal,
Indoor and Mobile Radio Communications (PIMRC ’07),pp.
2511–2515, Athens, Greece, September 2007.
[41] J. Ma and Y. Li, “Soft combination and detection for
cooperative spectrum sensing in cognitive radio networks,
in Proceedings of the IEEE Global Communications Conference
(GlobeCom ’07), Washington, DC, USA, November 2007.
[42] E. Peh and Y.-C. Liang, “Optimization for cooperative sensing
in cognitive radio networks,” in Proceedings of the IEEE
Wireless Communications and Networking Conference (WCNC
’07), pp. 27–32, Hong Kong, March 2007.
[43] Y.-C. Liang, Y. H. Zeng, E. Peh, and A. T. Hoang, “Sensing-
throughput tradeofor cognitive radio networks,IEEE
Transactions on Wireless Communications,vol.7,no.4,pp.
1326–1337, 2008.
[44] R. Tandra, S. M. Mishra, and A. Sahai, “What is a spectrum
hole and what does it take to recognize one,IEEE Proceedings,
vol. 97, no. 5, pp. 824–848, 2009.
[45] I. F. Akyildiz, W. Y. Lee, M. C. Vuran, and S. Mohanty, “Next
generation/dynamic spectrum access/cognitive radio wireless
networks: a survey,Computer Networks Journal, vol. 50, no.
13, pp. 2127–2159, 2006.
[46] Q. Zhao and B. M. Sadler, “A survey of dynamic spectrum
access: signal processing, networking, and regulatory policy,
IEEE Signal Processing Magazine, vol. 24, pp. 79–89, 2007.
[47] T. Ycek and H. Arslan, “A survey of spectrum sensing
algorithms for cognitive radio applications,IEEE Communi-
cations Surveys & Tutorials, vol. 11, no. 1, pp. 116–160, 2009.
[48] A. Sahai, S. M. Mishra, R. Tandra, and K. A. Woyach, “Cog-
nitive radios for spectrum sharing,IEEE Signal Processing
Magazine, vol. 26, no. 1, pp. 140–145, 2009.
[49] A. Ghasemi and E. S. Sousa, “Spectrum sensing in cognitive
radio networks: requirements, challenges and design trade-
os,IEEE Communications Magazine,vol.46,no.4,pp.32
39, 2008.
[50] D. Cabric, “Addressing the feasibility of cognitive radios,IEEE
Signal Processing Magazine, vol. 25, no. 6, pp. 85–93, 2008.
sensing device for detecting vacant channels in TV bands,
in Proceedings of the 3rd International Conference on Cogni-
tive Radio Oriented Wireless Networks and Communications,
(CrownCom ’08), Singapore, March 2008.
[52] S. W. Oh, T. P. C. Le, W. Q. Zhang, S. A. A. Naveen, Y. H.
Zeng, and K. J. M. Kua, “TV white-space sensing prototype,”
Wireless Communications and Mobile Computing, vol. 9, pp.
1543–1551, 2008.
[53] Y. H. Zeng, Y.-C. Liang, E. Peh, and A. T. Hoang, “Cooperative
covariance and eigenvalue based detections for robust sens-
ing,” in Proceedings of the IEEE Global Communications Con-
ference (GlobeCom ’09), Honolulu, Hawaii, USA, December
[54] H. V. Poor, An Introduction to Signal Detection and Estimation,
Springer, Berlin, Germany, 1988.
[55] H. L. Van-Trees, Detection, Estimation and Modulation Theory,
John Wiley & Sons, New York, NY, USA, 2001.
[56] H. Uchiyama, K. Umebayashi, Y. Kamiya, et al., “Study on
cooperative sensing in cognitive radio based ad-hoc network,
in Proceedings of the 18th International Symposium on Personal,
Indoor and Mobile Radio Communications (PIMRC ’07),
Athens, Greece, September 2007.
[57] A. Pandharipande and J. P. M. G. Linnartz, “Perfromcane anal-
ysis of primary user detection in multiple antenna cognitive
radio,” in Proceedings of the IEEE International Conference on
Communications (ICC ’07), Glasgow, Scotland, June 2007.
[58] P. Stoica, J. Li, and Y. Xie, “On probing signal design for MIMO
radar,IEEE Transactions on Signal Processing,vol.55,no.8,
pp. 4151–4161, 2007.
[59] G. B. Giannakis, Y. Hua, P. Stoica, and L. Tong, “Signal
Processing Advances in Wireless & Mobile Communications,
Prentice Hall PTR, vol. 1, 2001.
[60] T. J. Lim, R. Zhang, Y. C. Liang, and Y. H. Zeng, “GLRT-
based spectrum sensing for cognitive radio,” in Proceedings of
the IEEE Global Telecommunications Conference (GLOBECOM
’08), pp. 4391–4395, New Orleans, La, USA, December 2008.
[61] Y. H. Zeng and Y.-C. Liang, “Simulations for wireless
microphone detection by eigenvalue and covariance based
methods,” IEEE 802.22-07/0325r0, July 2007.
[62] E. Peh, Y.-C. Liang, Y. L. Guan, and Y. H. Zeng, “Optimization
of cooperative sensing in cognitive radio networks: a sensing-
throughput trade oview,IEEE Transactions on Vehicular
Technology, vol. 58, pp. 5294–5299, 2009.
[63] Z. Chair and P. K. Varshney, “Optimal data fusion in multple
sensor detection systems,IEEE Transactions on Aerospace and
Electronic Systems, vol. 22, no. 1, pp. 98–101, 1986.
[64] S. Shellhammer and R. Tandra, “Performance of the power
detector with noise uncertainty,” doc. IEEE 802.22-06/0134r0,
July 2006.
[65] C. Clanton, M. Kenkel, and Y. Tang, “Wireless microphone
signal simulation method,” IEEE 802.22-07/0124r0, March
[66] A. M. Tulino and S. Verd ´
u, Random Matrix Theory and
Wireless Communications, Now Publishers, Hanover, Mass,
USA, 2004.
[67] I. M. Johnstone, “On the distribution of the largest eigenvalue
in principle components analysis,The Annals of Statistics, vol.
29, no. 2, pp. 295–327, 2001.
[68] K. Johansson, “Shape fluctuations and random matrices,
Communications in Mathematical Physics, vol. 209, no. 2, pp.
437–476, 2000.
[69] Z. D. Bai, “Methodologies in spectral analysis of large
dimensional random matrices, a review,Statistica Sinica, vol.
9, no. 3, pp. 611–677, 1999.
[70] A. Zanella, M. Chiani, and M. Z. Win, “On the marginal
distribution of the eigenvalues of wishart matrices,” IEEE
Transactions on Communications, vol. 57, no. 4, pp. 1050–
1060, 2009.
[71] C. A. Tracy and H. Widom, “On orthogonal and symplectic
matrix ensembles,Communications in Mathematical Physics,
vol. 177, no. 3, pp. 727–754, 1996.
[72] C. A. Tracy and H. Widom, “The distribution of the largest
eigenvalue in the Gaussian ensembles,” in Calogero-Moser-
Sutherland Models, J. van Diejen and L. Vinet, Eds., pp. 461–
472, Springer, New York, NY, USA, 2000.
[73] M. Dieng, RMLab Version 0.02, 2006, http://math.arizona
[74] P. J. Huber, “Robust estimation of a location parameter,The
Annals of Mathematical Statistics, vol. 35, pp. 73–104, 1964.
[75] P. J. Huber, “A robust version of the probability ratio test,” The
Annals of Mathematical Statistics, vol. 36, pp. 1753–1758, 1965.
[76] L.-H. Zetterberg, “Signal detection under noise interference in
agamesituation,IRE Transactions on Information Theory, vol.
8, pp. 47–57, 1962.
EURASIP Journal on Advances in Signal Processing 15
[77] H. V. Poor, “Robust matched filters,IEEE Transactions on
Information Theory, vol. 29, no. 5, pp. 677–687, 1983.
[78] S. A. Kassam and H. V. Poor, “Robust techniques for signal
processing: a survey,Proceedings of the IEEE,vol.73,no.3,
pp. 433–482, 1985.
[79] D. J. Rabideau and L. C. Howard, “Mitigation of digital array
nonlinearities,” in Proceedings of the IEEE National Radar
Conference, pp. 175–180, Atlanta, Ga, USA, May 2001.
[80] E. J. Cand`
es, J. Romberg, and T. Tao, “Robust uncertainty
principles: exact signal reconstruction from highly imcom-
plete frequency information,IEEE Transactions on Informa-
tion Theory, vol. 52, no. 2, pp. 489–509, 2006.
[81] E. J. Cand`
es and M. B. Wakin, “An introduction to compressive
sampling,IEEE Signal Processing Magazine,vol.21,no.3,pp.
21–30, 2008.
[82] D. L. Donoho, “Compressed sensing,IEEE Transactions on
Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006.
[83] Y. L. Polo, Y. Wang, A. Pandharipande, and G. Leus, “Com-
presive wideband spectrum sensing,” in Proceedings of the
IEEE International Conference on Acoustics, Speech, and Signal
Processing (ICASSP ’09), Taipei, Taiwan, April 2009.
[84] Y. H. Zeng, S. W. Oh, and R. H. Mo, “Subcarrier sensing
for distributed OFDMA in powerline communication,” in
Proceedings of the IEEE International Conference on Commu-
nications (ICC ’09), Dresden, Germany, June 2009.
[85] Z. Quan, S. Cui, H. V. Poor, and A. H. Sayed, “Collaborative
wideband sensing for cognitive radios,IEEE Signal Processing
Magazine, vol. 25, no. 6, pp. 60–73, 2008.
multiband joint detection for spectrum sensing in dynamic
spectrum access networks, IEEE Transactions on Signal Pro-
cessing, vol. 57, no. 3, pp. 1128–1140, 2009.
[87] Y. Pei, Y.-C. Liang, K. C. Teh, and K. H. Li, “How much time
is needed for wideband spectrum sensing?” to appear in IEEE
Transactions on Wireless Communications.
[88] R. Zhang and Y.-C. Liang, “Exploiting hidden power-feedback
loops for cognitive radio,” in Proceedings of the IEEE Sympo-
sium on New Frontiers in Dynamic Spectrum Access Networks
(DySPAN ’08), pp. 730–734, October 2008.
[89] G. Zhao, Y. G. Li, and C. Yang, “Proactive detection of
spectrum holes in cognitive radio,” in Proceedings of the
IEEE International Conference on Communications (ICC ’09),
Dresden, Germany, June 2009.
... Furthermore, SUs have two sets of bands: a set of sensedfree bands ( ) and a set of sensed-busy bands ( ). It is well known that ED is the simplest detection scheme; however, it is necessary to estimate the noise power level accurately [1], [3], [5], [6]. In [6], a two-step detection scheme was implemented, and the noise power level was estimated. ...
... For a given desired probability of a false alarm, denoted as , threshold was set based on the Neyman-Pearson criterion. This is only possible if the noise power is known [1], [3], [4]. If the SU estimates the noise power, the presence of an intelligent adversary can contaminate the estimate. ...
... This is the author's version which has not been fully edited and content may change prior to final publication. [1], [3], [6], assumes that the PU signal is a Gaussian signal, with a PDF of ~(0, 2 ), where 2 is the power of the PU signal on the band and the signal-to-noise-ratio (SNR) is denoted by ≜ / , of the PU in the band. ...
Full-text available
Spectrum sensing vulnerabilities in cognitive radio networks can significantly degrade performance. Most disruption attacks in the current literature involve spoofing of the free bands used for sensing by making them appear busy. In this study, we proposed a different approach for sensing disruptions. We examined the optimal strategy for an intelligent adversary with a given power to flip busy bands and make them appear free. The mechanism of sensing disruption was established by contaminating the noise power measurements. This is illustrated by a two-step sensing scheme in which energy detection, in conjunction with noise power estimation, is used by secondary users. We show that to flip busy bands, the optimal strategy for sensing link disruptions is equal-power, and partial-band flipping. We demonstrated that the maximum average number of missed detections can be derived under a constraint on power of the adversary. Through analytical and numerical results, we demonstrated the effectiveness of our approach in terms of the impact of disruption attacks on spectrum sensing.
... According to the amount of prior information required, spectrum sensing methods can be divided into un-blind detection, semi-blind detection, and full-blind detection. The likelihood ratio test (LRT) based on the Neyman-Pearson criterion is currently known as the optimal detection method, which requests a known distribution of the received signal that is generally related to the PU information, the Sensors 2023, 23, 7428 3 of 20 fusion criteria [28]. Hard fusion criteria represent the local decision results as 0 or 1 and upload them to the FC. ...
... Sensors 2023, 23, x FOR PEER REVIEW 3 of 21 using spatial diversity among SUs is a good solution to achieve highly reliable spectrum sensing [27]. In CSS, there are two types of fusion criteria based on the different forms of data that local SUs upload to the fusion center (FC), which are hard fusion criteria and soft fusion criteria [28]. Hard fusion criteria represent the local decision results as 0 or 1 and upload them to the FC. ...
Full-text available
Spectrum sensing in Cognitive radio (CR) is a way to improve spectrum utilization by detecting spectral holes to achieve a dynamic allocation of spectrum resources. As it is often difficult to obtain accurate wireless environment information in real-world scenarios, the detection performance is limited. Signal-to-noise ratio (SNR), noise variance, and channel prior occupancy rate are critical parameters in wireless spectrum sensing. However, obtaining these parameter values in advance is challenging in practical scenarios. A lifting wavelet-assisted Expectation-Maximization (EM) joint estimation and detection method is proposed to estimate multiple parameters and achieve full-blind detection, which uses lifting wavelet in noise variance estimation to improve detection probability and convergence speed. Moreover, a stream learning strategy is used in estimating SNR and channel prior occupancy rate to fit the scenario where the SU has mobility. The simulation results demonstrate that the proposed method can achieve comparable detection performance to the semi-blind EM method.
... The work further discusses the challenges involved in sensing the PU spectrum and the concept of CSS and its types. The survey [34] reviews SS techniques by categorizing them into three classes based on whether they need both source signal and noise power information, only noise power information (semiblind detection) or no prior information (totally blind detection), with a particular focus on semi-blind and blind techniques. An analysis on detection threshold and test statistics distribution is provided and the challenges in developing a practical SS device are discussed. ...
Full-text available
As we advance towards 6G communication systems, the number of network devices continues to increase resulting in spectrum scarcity. With the help of Spectrum Sensing (SS), Cognitive Radio (CR) exploits the frequency spectrum dynamically by detecting and transmitting in underutilized bands. The performance of 6G networks can be enhanced by utilizing Deep Neural Networks (DNNs) to perform SS. This paper provides a detailed survey of several Deep Learning (DL) algorithms used for SS by classifying them as Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, combined CNN-LSTM architectures and Autoencoders (AEs). The works are discussed in terms of the input provided to the DL algorithm, data acquisition technique used, data pre-processing technique used, architecture of each algorithm, evaluation metrics used, results obtained, and comparison with standard SS detectors. This survey further provides an overview of traditional ML algorithms and simple Artificial Neural Networks (ANNs) while highlighting the drawbacks of conventional SS approaches for completeness. A description of some publicly available Radio Frequency (RF) datasets is included and the need for comprehensive RF datasets and Transfer Learning (TL) is discussed. Furthermore, the research challenges related to the use of DL for SS are highlighted along with potential solutions.
... The technique used by the secondary network to utilize vacant bands is called spectrum sensing. This technique is extensively covered in the literature; see for example [3,4,[6][7][8] and references therein. ...
Full-text available
Recently, the Gini index detector (GID) has been proposed as an alternative for data-fusion cooperative spectrum sensing, being mostly suitable for channels with line-of-sight or dominant multi-path components. The GID is quite robust against time-varying noise and signal powers, has the constant false-alarm rate property, can outperform many the state-of-the-art robust detectors, and is one of the simplest detectors developed so far. The modified GID (mGID) is devised in this article. It inherits the attractive attributes of the GID, yet with a computational cost far below the GID. Specifically, the time complexity of the mGID obeys approximately the same run-time growth rate of the GID, but has a constant factor approximately 23.4 times smaller. Equivalently, the mGID takes approximately 4% of the computation time spent to calculate the GID test statistic, which brings a huge reduction in the latency of the spectrum sensing process. Moreover, this latency reduction comes with no performance loss with respect to the GID.
... An unlicensed user, secondary user (SU), in spectrum sensing periodically monitors the licensed user's, primary user (PU), spectrum so as to gain its spectrum information. Using the learned radio environment of PUs spectrum, a SU can then determine whether to use that frequency band or not [7]. ...
Full-text available
The internet of things (IoT) may be considered as an emerging paradigm that has led to the transformation of the physical world into an advanced system comprising interconnected devices on an unparalleled scale. To accommodate the spectrum, need of these numerous IoT devices concept of cognitive radio technology may be considered a boon. The cognitive radio (CR) aims to alleviate the spectrum crunch problem through detection of the available spectrum holes and their efficient utilization. This paper incorporates the spectrum sensing concept in the LoRaWAN network for better utilization of the spectrum. A non-relay and relay-based type of communication has been investigated to analyze the enhancement in the detection probability of the sensing technique for a LoRaWAN network in terms of minimal sensing time, maximum coverage, and low signal-to-noise (SNR). The effect of sensing time, distance and SNR on detection probability for 915 MHz and 866.4 MHz LoRa bands has been analyzed and critically evaluated at uplink bandwidth of 125 kHz and 250 kHz respectively using MATLAB. The simulated results validate the performance improvement through multiple relays in a LoRaWAN communication model in context to a higher probability of detection for energy detection-based spectrum sensing.
... In the research of spectrum sensing, studies considering both spatial-temporal correlations [31]- [33] and space-frequency correlation [34] have been reported, and these works have obtained an improvement in sensing performance. However, it is still an innovative work to use the information of timefrequency correlation modeling as the prior input for deep learning-based wideband spectrum sensing models. ...
In the beyond 5 G (B5G)/6 G era, to achieve ultra-dense and ultra-large-capacity intelligent connection of all things, an intelligent wideband spectrum sensing technology is particularly important. However, in an extremely wide frequency range, it is still a challenge to achieve high-precision and high-reconstruction-capability wideband spectrum sensing (WSS) under a very low SNR. We propose a Time-Frequency-Fused adjustable Deep Convolutional Neural Network (TFF_aDCNN). Meanwhile, a novel TFF_aDCNN-based sensing framework is also proposed. In this framework, we can obtain a pre-trained base model with a single distribution by training TFF_aDCNN. Then, for the sensing task in the actual environment, we use the base model for transfer learning, so that a newly trained sensing model can be obtained very quickly (i.e. fine-tuned model). In the TFF_aDCNN, we design a main network and an adjustable auxiliary network, where the former learns complex and abstract signal features, while the latter assists the main network in learning different data distribution patterns during the training process and regulates the focus direction of the main network during the perception process. Simulation results show that TFF_aDCNN can significantly reduce hardware cost and improve reconstruction accuracy and reconstruction capability, when compared with SOMP and SwSOMP-based WSS algorithms, single-dimensional deep learning spectrum sensing method, and deep learning-based WSS (DLWSS), especially at very low SNRs.
Cognitive radio (Cr) is one of among the most promising developments, which combines optical non-orthogonal multiple access (O-NOMA) methods to increase the fifth generation (5G) spectrum’s usage efficiency. In this work, we provide a hybrid approach based on cyclic stationary feature detection (CFD) and energy detection (ED). The probability of false alarm (PFA), on which it is based, is used to choose which spectrum sensing (SS) approach to use. When PFA is less than 0.5, the ED is chosen; otherwise, the MF is. The suggested detection method in O-NOMA is investigated using Matlab-2016 simulation with reference to several metrics, such as bit error rate (BER), signal-to-noise ratio (SNR), probability of detection (PD), and PFA.
Next-generation communication networks (NextG or 5G and beyond) have become more essential to be able to realize cutting-edge applications, such as autonomous cars, mobile healthcare and education, metaverse, digital twins, virtual reality, and many more. All those applications need high-speed, low latency, and secure data transmission. Artificial intelligence (AI) technologies are the main drivers and play a critical role because of their significant contribution to all layers in NextG, i.e., from the physical to the application layer. On the other hand, the security and privacy concerns for applications using AI-based methods in next-generation networks have not been fully investigated in terms of cyber vulnerabilities. This book chapter focuses on the AI-enabled applications on the physical layer of NextG networks, including multiple input multiple output (MIMO) beamforming, channel estimation, spectrum sensing, and intelligent reflecting surfaces (IRS), as well as provides a comprehensive analysis of the potential use case, i.e., channel estimation, along with its vulnerability under adversarial machine learning attacks with and without the defensive distillation mitigation method. According to simulations outcomes, AI-enabled Next-G applications are vulnerable to adversarial attacks, and the proposed mitigation methods are able to improve the robustness and performance of AI-enabled models under adversarial attacks.KeywordsNext-generation networks5G and beyondCybersecurityAdversarial machine learning
Cognitive radio network provides an efficient solution for spectrum utilization. The cooperative spectrum sensing is one of the sensing techniques with which the secondary users of cognitive radio network (CRN) could learn about the availability of the spectrum. In this article, authors had designed and developed their own CRN simulation model in which the RF spectrum range of 54 MHz to 648 MHz is divided into various channels. Secondary users are kept moving in these various channels along with the primary user. The presence of primary user is detected by applying weights on the energy received by local secondary users. The information about the energy of primary user is collected locally by SU and provided to the fusion center for PU detection. This article discusses how the secondary user detects the energy of primary user using weights.
Full-text available
Spectrum sensing is an essential functionality that enables cognitive radios to detect spectral holes and to opportunistically use under-utilized frequency bands without causing harmful interference to legacy (primary) networks. In this paper, a novel wideband spectrum sensing technique referred to as multiband joint detection is introduced, which jointly detects the primary signals over multiple frequency bands rather than over one band at a time. Specifically, the spectrum sensing problem is formulated as a class of optimization problems, which maximize the aggregated opportunistic throughput of a cognitive radio system under some constraints on the interference to the primary users. By exploiting the hidden convexity in the seemingly nonconvex problems, optimal solutions can be obtained for multiband joint detection under practical conditions. The situation in which individual cognitive radios might not be able to reliably detect weak primary signals due to channel fading/shadowing is also considered. To address this issue by exploiting the spatial diversity, a cooperative wideband spectrum sensing scheme refereed to as spatial-spectral joint detection is proposed, which is based on a linear combination of the local statistics from multiple spatially distributed cognitive radios. The cooperative sensing problem is also mapped into an optimization problem, for which suboptimal solutions can be obtained through mathematical transformation under conditions of practical interest. Simulation results show that the proposed spectrum sensing schemes can considerably improve system performance. This paper establishes useful principles for the design of distributed wideband spectrum sensing algorithms in cognitive radio networks.
Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. Random Matrix Theory and Wireless Communications is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth. The authors have created a uniquely comprehensive work that provides the reader with a full understanding of the foundations of random matrix theory and demonstrates the trends of their applications, particularly in wireless communications. Random Matrix Theory and Wireless Communications is a valuable resource for all students and researchers working on the cutting edge of wireless communications.