Spectrum Sensing Methods for Cognitive Radio Networks: A Review

Abstract

The main spectrum sensing (SS) techniques suitable for cognitive radio networks (CRNs) such as energy, matched filter, covariance and Hadamard ratio-based detectors are analyzed. Principal methods and concepts associated with SS-CRNs are explored while numerical simulation experiments and comparison analysis are interpreted aiming to corroborate those concepts and demonstrate the effectiveness and drawbacks of those well-established SS-CRN techniques and methods.

Full text

Spectrum Sensing Methods for Cognitive Radio
Networks: A Review
Lucas Claudino
1
•Taufik Abra
˜o
1
Published online: 21 April 2017
ÓSpringer Science+Business Media New York 2017
Abstract The main spectrum sensing (SS) techniques suitable for cognitive radio net-
works (CRNs) such as energy, matched filter, covariance and Hadamard ratio-based
detectors are analyzed. Principal methods and concepts associated with SS-CRNs are
explored while numerical simulation experiments and comparison analysis are interpreted
aiming to corroborate those concepts and demonstrate the effectiveness and drawbacks of
those well-established SS-CRN techniques and methods.
Keywords Spectrum sensing Cognitive radio network Energy detector Matched
filter Covariance detector Hadamard ratio-based detector Underlay
CRN mode Overlay CRN mode
1 Introduction
In order to optimize the spectrum utilization, cognitive radio (CR) principles establish for a
secondary user (SU) a methodology of co-transmitting with primary users via either
spectrum hole access or low power transmission over used frequencies. Spectrum hole is
defined as an unused spectrum band that can be used by unlicensed user; spectrum holes
are basic resource for cognitive radio systems. Most of existing contributions detect
spectrum opportunities by sensing whether a primary signal is present or not and then try to
access them so that CRs and primary users use the spectrum band either at different time
&Taufik Abra
˜o
taufik@uel.br; abrao@ieee.org; taufik.abrao@gmail.com;
http://www.uel.br/pessoal/taufik
Lucas Claudino
lsclaudino@gmail.com
1
Electrical Engineering Department, State University of Londrina (DEEL-UEL), Rod. Celso Garcia
Cid - PR445, s/n, Campus Universita
´rio, Po. Box 10.011, Londrina, PR 86057-970, Brazil
123
Wireless Pers Commun (2017) 95:5003–5037
DOI 10.1007/s11277-017-4143-1

slots or in different geographic locations [43]. Specifically, a CR system has a high-level of
environmental awareness so that it is able to recognize available band and to adapt its
transmission (frequency, waveform and protocols) to achieve a better performance within a
certain quality of service (QoS) [5,42].
A CR has to constantly monitor the spectrum and look for opportunities either in bands
or channels and investigate interference levels. This monitoring stage is not only important
for CRs to detect white spaces in spectrum, but also to keep control of all interference
which may harm any primary transmission [31].
Based on the above characteristics, cognitive radio operation is basically divided in
three ways: underlay, overlay or hybrid modes. The underlay method for spectrum sharing
allows the secondary user to transmit over all primary frequencies, as long as all inter-
ferences caused by this transmission do not harm the primary system’s performance. In
overlay approach, secondary users must use spectrum sensing (SS) techniques to detect
unused frequencies; then, the unlicensed user access these frequencies to transmit its data
without interfering PU’s transmission. Additionally, hybrid CR mixes both underlay and
overlay approaches. Spectrum sensing is also performed in hybrid access; however, when a
PU is detected, underlay constraints for transmission power and interference levels are
taken into consideration [9,27,33].
Figure 1shows basic operation modes for a CR system. Basically, for every scenario,
there will be Navailable channels to be sensed and shared between PUs and SUs. When
transmitting with underlay access strategies, channel status is not required, but transmis-
sion power upper limits must be respected, so all interference levels are kept under a
certain threshold over all transmission time. A SU transmission without SS is depicted in
Fig. 1a, where unlicensed user is transmitting over all the time Twithout impinging
interference to PU’s signal. Differently, in overlay access mode, Fig. 1b, SU firstly divides
the available time-slot Tin a sensing part (s) and a transmission part (Ts). Then, every
channel is sensed; in case of absence of primary signals, SU is allowed to transmit with its
full power; however, in case of presence of a PU, this channel must be left free to all
Ch. 1
Ch. 2
Ch. N
Ch. 1
Ch. 2
Ch. N
Ch. 1
Ch. 2
Ch. N
Frequency
Frequency
Frequency
emiTemiT
Time
Underlay transmission strategies
Overlay transmission strategies
Sensing time
No transmission
TτT - τ
τT - τ
(a) Underlay access
(c) Hybrid access
(b) Overlay access
Fig. 1 Access strategies in cognitive radio networks
5004 L. Claudino, T. Abra
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current primary transmissions. Finally, a hybrid access strategy mixes both underlay and
overlay modes. The hybrid sensing is depicted in Fig. 1c, where SU also divides the
available time into two parts, i.e., sand (Ts); when a PU is not detected in that specific
channel, the secondary transmitter adapts its technique to transmit over the channel with a
maximum power Pmthat does not harm the licensed signal. In case of a free channel, full
power is used for secondary transmissions.
A chronological perspective for representative spectrum sensing methods applied to
CRNs is presented in Table 1. This is a sample for the state-of-art in SS-CRNs, covering
from spectrum sensing detectors to capacity aspects, single-band and multi-band power
spectral density (PSD) estimation scenarios, compressive sub-Nyquist sensing methods, as
well as cooperative SS applied to CRNs.
This paper is divided as follows: Sect. 2explains all basic access methods for CR, its
characteristics and operation. Basic processes of spectrum sensing and how each access
method uses them are shown in Sect. 3. Section 4studies the four main methods for
sensing primary signals. An important performance metric, namely SNR Wall, is explained
and applied to SS-CR methods in Sect. 5. Finally, representative numerical results are
analyzed in Sect. 6, whereas main conclusions and final remarks are offered in Sect. 7.
2 Access Methods for Cognitive Radio
As stated before, there are three basic ways a CR can operate: underlay, overlay and hybrid
modes. The next subsections are devoted to explain each of them.
2.1 Underlay CR Networks
In underlay mode, the whole available spectrum is shared by primary and secondary users.
From the primary user’s point of view, any secondary signal is seen as a kind of inter-
ference. Hence, when measuring the primary’s signal-to-interference plus noise ratio
(SINR), the interference level must be less than a pre-determined value. This interference
constraint means that total power of any secondary signal must respect a spectral mask
bounded by the power spectral density (PSD) interference over all frequencies under the
sensing band. Alternatively, for low variant interference constraints scenarios, the
threshold might be simply set according to an average value of the PSD interference taken
across all licensed frequencies [5].
Considering xias channel input for a secondary user instant i,yiis the correspondent
channel output at the primary user. Hence, the average interference power due to secondary
users at primary receiver under underlay mode is limited by a threshold c:
1
nX
n
i¼1
Ejyij2xi
hi
cð1Þ
where E½ is the expectation operator. Equation 1means that the interference’s average
power is given by the conditional expectation function of all received interference at PU
receiver in relation to transmitted secondary signal.
In order to quantize how harmful the interference is in a certain transmission, the
Federal Communications Community (FCC) established a metric to measure interference
caused by SUs in a primary transmission, named Interference Temperature (IT) [12], which
is defined as:
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Table 1 Contributions in spectrum sensing methods for CRNs
Year References Description
2004 [6] Matched filtering, energy detection and cyclostationary feature detectors in CR are
investigated; the goal is to evaluate the ability to sense the spectral environment and
the flexibility to adapt transmission parameters aiming to maximize system capacity
while coexisting with legacy wireless networks. Cyclostationary detection has
advantages due to its ability to differentiate modulated signals, interference and noise
in low SNRs
2006 [36] Wideband spectrum sensing via wavelet transform (WT) approach is studied. WT is
used to identify spectrum irregularities and characterize frequency bounds of each
subband, and also estimate the spectrum mask, which defines used subbands and
white spaces. The proposed PSD estimation scheme showed to be simple and
efficient while is able to detect white spaces in wideband scenarios. However, when
noise floor increases, multiscale product method is required to increase accuracy and
consequently, computational complexity is also increased
2007 [21] CR Capacity is defined when transmitter and receiver have different, but correlated,
spectrum hole estimations. An analysis on the distributed and dynamic nature of CR
channels is made aiming to evaluate all channel availability uncertainties. Using
derived capacity expressions and results about the effect of correlation of spectral
activity, the authors analyze how important is/isn’t to add overhead of periodic
feedforward and/or feedback about spectrum occupancy on secondary transmissions
2007 [37] Authors propose a sub-Nyquist sampled compressed sensing technique based on
wavelet edge detection. White space detection is performed by: (1) compressing
random sub-Nyquist sampling of the spectrum, (2) linear PSD reconstruction via
Basis Pursuit technique, (3) number and width of subbands and spectrum spaces; (4)
estimation of the amplitude of each subband and classification in black, gray or white
spaces. A technique to directly estimate each suband’s characteristics (location,
width and amplitude) directly from the compressed sampled data is proposed
2008 [28] Overview about existing challenges and possible solutions for collaborative wideband
SS in CR networks, including a SS techniques review and the main challenges, i.e.,
SS reliability and high-resolution requirement for wideband sensing. A methodology
of combining SS of distributed nodes operating over narrowbands is proposed and
two fusion schemes are analyzed: hard decision fusion and summary statistics
combination. Also, a multiband joint detection is studied, where the wideband SS
jointly optimizes a group of narrowband sensors. A few considerations on physical
layer issues that emerge while designing a wideband CR network are made
2008 [8] Security aspects os SS: this contribution investigates the effect of primary user
emulation (PUE) attack, which is when a certain secondary user tries to copy PU’s
transmissions in order to confuse other SUs. Numerical results demonstrate how
harmful this action is and quantizes its influence on SS. A solution called LocDef
(location-based defense) is formulated to estimate location and other characteristics
of the transmitted signal while identify whether it is a legitimate PU or not
2008 [14] A SS methodology based on filter banks is proposed. Authors formulate a PSD
estimation technique for multiband CR using filter banks and compare its
performance with other former SS known as Thomson’s multipaper method (MPM).
Even though MTM has shown better performance and less signal’s samples are
needed, it has a very high computational burden. On the other hand, filter bank has
presented very accurate results for higher number of samples and presents much
lower computational complexity
2009 [29] A technique to jointly detect PUs over multiple bands is proposed. Differently from
other methods, authors formulate the SS problem as aggregate opportunistic
throughput maximization problem and use the interference limit to PUs as a
constraint of the main problem. Additionally, exploitation of spatial diversity is used
to propose a cooperative wideband SS to enhance detection rates when single SUs
are not able to reliably detect white spaces due to channel uncertainties (fading/
shadowing).
5006 L. Claudino, T. Abra
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Table 1 continued
Year References Description
2009 [18] Multipaper method and cyclostationarity are investigated as strategies to enhance
spectrum sensing. MPM is theoretically studied and proved, via numerical results, to
be real-time computationally feasible, able to process multiband cases and present
cyclostationarity features that provide effective white space detection. Additionally,
it was proved that MPM may be formulated based on filter banks, which is a possible
solution to reduce complexity while preserve high detection rates
2010 [3] A joint cooperative multiband SS method to estimate the PSD at different locations is
proposed. This joint estimation allows SUs to have an overview about white spaces
at arbitrary locations, what may ease the spectrum management in CRNs. Indeed,
CRs cooperatively estimate the PSD and locate positions of different transmitters.
This architecture is useful in large CR areas, where an arbitrary PU signal does not
reaches all SUs. Results showed that implementation of an online D-Lasso
cooperation scheme stabilizes the PSD estimative over the entire network; as a
consequece, each SU is able to obtain a reliable PSD estimation. The overhead for
implementation of the D-Lasso procedure and its effect over the SU’s capacity have
not been considerered
2011 [40] Challenges in wideband cooperative SS-CRNs are discussed. Given the wideband
structure, compressive sensing is applied to reduce the necessary sampling rate.
Collaborative SS among spatially distributed CRs is exploited in order to make use
of spatial diversity principles. A decentralized decision algorithm is proposed to
manage all individual CR’s and obtain high performance with low computational
complexity or power overhead. Simulations are proceeded for cases with and without
channel knowledge
2012 [2] Overview on CRN structure and principles is carried out. Basic theory of energy
detection, feature detection, second order statistics-based, cyclostationarity-based,
covariance-based, filter bank-based and blind detectors is explained and a few
comparison points are enumerated. Authors also study wideband SS, compressive
and cooperative sensing
2013 [32] Analyses on various wideband SS methods, including Standard ADC (Analog-to-
Digital Conversion), Sweep-tune/filter bank sampling, Compressive sensing and
Multichannel sub-Nyquist sampling. Further discussion on the sub-Nyquist methods
as a solution to attend all necessary sampling rates of wideband CR networks. Also,
challenges of implementing feasible wideband SS for CR networks are addressed.
All analysis aim to explain, categorize and compare wideband SS methods. No
simulation or test results are provided to illustrate and quantify the comparisons
2014 [11] A detection scheme based on reconstruction of power spectrum of sub-Nyquist
sampled signals is proposed. Both sparse and non-sparse signals are considered as
well as, for the case of sparse signal, blind and non-blind detection schemes. For
each case, a minimal sampling rate and PSD reconstruction technique are proposed
(for noise-free environments). Numerical results, in therms of reliable (or not) PSD
reconstruction and ROC for each case are presented. Also, influence of SNR, number
of samples and number of frames is analyzed for different cases. Results demonstrate
that all sub-Nyquist PSD reconstruction proposed schemes are reliable solutions and
have similar performance, under a certain limit of SNR, if compared to detectors
implemented with Nyquist sampled signals
2015 [13] Wideband multichannel SS methods via FFT or filter-bank-based methods for
spectrum analysis are investigated under fine-grained spectrum analysis facilitating
the optimal energy detection in practical scenarios (non-flat spectrum). Such sensing
schemes can be tuned to the spectral characteristics of the target primary user signals,
allowing simultaneous sensing of multiple target primary signals with low additional
complexity. Model extension includes: specific scenario of detecting a reappearing
PU during secondary transmission, as well as in SS scenarios where the frequency
range of a primary user is unknown. The concept of area under the receiver
operating characteristics (RoC) curve is introduced for evaluating the overall
performance of the SS algorithms and scenarios
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5007
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TI¼PI
jWð2Þ
where PIis the average interfering power, Wis the bandwidth and j¼1:38 1023 J/K is
the Boltzmann’s constant. Specially, if a system allows a certain interference limit TL,SU
is allowed to generate a maximum interference power of jWTL.
Section 3discusses more specifically about how a CR system senses the interference
temperature level and decides whether the transmission is within the acceptable limit or
not.
2.2 Overlay CR Networks
The overlay CRN is a method where secondary users are known as opportunistic users.
Unlicensed users are constantly monitoring the spectrum in order to detect any PU
occupancy in frequency, space or time dimensions. Once a temporary white space is
detected, SUs opportunistically communicate over it via orthogonal dimensions with
minimum interference [5].
The main constraint of overlay CR protocols is that all unlicensed users must accurately
detect a white space, otherwise its transmission power will harm the PU’s signal. It means
that the SU’s spectrum sensing phase has to be able to always keep a very low miss-
detection rate. These factors are well discussed in spectrum sensing techniques, once the
user has to develop a reasonable method to correctly identify spectrum holes.
Another important factor is to identify the maximum capacity for an overlay trans-
mission. Considering a network with one primary Tx–Rx pair and one secondary Tx–Rx
pair; the capacity for each channel is dictated by the Shannon capacity equation. Thus, Cp
is the primary user’s Shannon capacity (for a transmission where SUs are in silent) and Cs
is the associated SU’s capacity, considering a transmission with silent primary user.
Now, supposing both primary and secondary users sharing the same spectrum band-
width; each one has its own fraction of time for transmitting. Hence, ais the PU’s
transmission time. Indeed, primary channel’s capacity is given by aCp, whereas SU’s
capacity is given by ð1aÞCs. Then, the rate region for this time sharing strategy is
defined by the 2-tuple:
½Rp;Rs¼½aCp;ð1aÞCs
Expanding the system for Kpprimary users and Kssecondary users (KpþKs¼K),
Shannon capacity for the i-th PU is Ci, while Cjis the j-th SU’s capacity with associated
Table 1 continued
Year References Description
2016 [23] Smart grids (SGs) require reliable, intelligent and energy/spectrum efficient
communications network; indeed, SGs are a very promising scenario for CR
technologies. CR should be able to provide reliable communication over all
frequency bands available for SG. This paper provides an extensive discussion about
SG architecture, communication network requirements and possible solutions/
implementations of CR for this scenario. Additionally, a study of SS methods
(energy detection, feature detection) and management architectures for SS is done.
Authors also explain possible solutions to integrate CR and SG, summarize
IEEE.802.22 standard and relate it to SG architectures. Also, a study on interference
mitigation for CR-based SG is showed and possible solutions are proposed
5008 L. Claudino, T. Abra
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time slots ap
iand as
jrespectively. Furthermore, the capacity region is the union over all ap
i
and as
j:
[R1¼a1Cp1;...;RKp¼aKpCKp;RKpþ1
¼as1Cs1;RK¼asKsCsKsgð3Þ
where PKp
i¼1apiþPKs
j¼1asj1 guarantees the spectrum sharing between secondary and
primary users.
3 Spectrum Sensing in CRNs: Basic Principles
Spectrum sensing is one of the necessary steps of cognitive radio networking. SS is
responsible for analyzing the medium and giving an overview about the spectrum scenario,
so the CR will be able to deploy these informations and adapt its techniques to co-transmit
with a primary user. Hence, understanding how SS works will be very useful for a more
accurate analysis of CR networks. Next, general spectrum sensing formulation in CRNs is
explored [7].
The spectrum sensing is based on signal detection techniques, which can be simply
stated by the following hypothesis test:
yðkÞ¼ gðkÞ:H0
sðkÞþgðkÞ:H1
ð4Þ
where y(k) is the sample to be analyzed at each instant k;gðkÞis additive noise and s(k)is
the transmitted signal. H0and H1are the two possible hypothesis: noise-only and signal-
plus-noise. In a more developed and realistic form, it can be re-written considering fading
and shadowing wireless channel effects, given by the complex random variable h:
yðkÞ¼ gðkÞ:H0
hsðkÞþgðkÞ:H1
ð5Þ
Figure 2depicts all four possible cases of signal detection:
1. Declaring H0when H0is true ðH0jH0Þ
2. Declaring H1when H1is true ðH1jH1Þ
3. Declaring H0when H1is true ðH0jH1Þ
4. Declaring H1when H0is true ðH1jH0Þ
H1
H0
H0
H1
P(H0|H0)
P(H
1
|H
0
)
P(H0|H1)
P(H1|H1)
Fig. 2 Hypothesis tests and
possible solutions for detection
problems
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Case 3 is known as the missed detection, while case 4 is the false alarm, and cases 1 and
2 are correct detection. Basically, a detector targets a high number of correct detections
while keeping false alarm and the missed detection rates as low as possible.
3.1 SS in Underlay CR
A method of measuring the spectrum for cognitive underlaying mode is related to
Sect. 2.1. In this technique, the CR device has to be able to select a bandwidth and a power
level for transmitting its data without violating the interference temperature constraints.
Hence, the goal is to monitor transmission power levels in order to keep them under a pre-
defined limit and hence follow all interference temperature constraints [10]. Furthermore,
the work in [10] explores spectrum sensing models for underlay CR networks leading with
interference temperature.
3.2 SS in Overlay CR
According to Sect. 2.2, for overlay CR networks, the cognitive radio has to sense a white-
space in the spectrum and then use it for a secondary transmission. Hence, the sensing
systems must be able to do it without any help of the primary user, since in this work
relying on cooperative networks has not been considered. Many different techniques for
signal detection have been studies in CR context, i.e. energy detection (ED) sensing (EnS),
coherent sensing, cyclostationary-based sensing, matched filter sensing (MfS) [5][7],
Hadamard ratio-based spectrum sensing (HrS) [20,38], among others.
3.3 SS in Hybrid CR
Hybrid networks are a mix of underlay and overlay networks. Once SS is also necessary for
hybrid networks, all SS techniques studied for overlay CR will also be applied to hybrid
CR. The only difference is that, if no white space are detected, the CR transceiver may
adapt its transmission strategies to remain within a certain interference limit (underlay CR
mode).
4 Spectrum Sensing Methods
Correct detection of (un)occupied spectrum bands is extremely important in CR, once all
secondary transmission strategies are based on outcomes of this stage. Indeed, SS must
overcome all challenges and uncertainties like noise, channel effects and multipath fading
[15]. Several methods can be used for sensing those white-spaces, such as energy detection
(ED) sensing (EnS), coherent sensing (CS), cyclostationary-based sensing (CsS), matched
filter sensing (MfS) [5,7,19], Hadamard ratio-based spectrum sensing (HrS) [20,38],
combined sensors like energy-based maximum likelihood [24] among others. Each one has
its own characteristics, complexity and accuracy of detection. A brief comparison of basic
sensors in terms of accuracy and complexity is depicted in Fig. 3.
In this section, the main methods commonly deployed to sensing CRNs are explained
and analyzed in order to give theoretical base for results obtained in Sect. 6.
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4.1 Energy Detection Method
An Energy Detector has to basically measure the energy of all signals present on the
medium and than compare it with a suitable threshold. The decision metric nED for this
sensor is formulated as:
nED ¼1
NX
N1
k¼0jyðkÞj2ð6Þ
Or, using the definition of signal energy:
nED ¼ZjyðtÞj2dt;ð7Þ
where Nis the total number of samples and y(n) is the sampled received signal, as
formulated in (5). Thus, the calculated signal energy is compared to a threshold cED and
finally hypothesis are chosen as H0if nED\cED and H1when nED cED ð.
Energy detector method is a very simple and easy to implement, if compared to other
sensors; however, it may be very susceptible to noise floor, presence of interferences in the
band, presence of frequency-selective fading and also its performance is very dependent on
the sample rate.
Once the sensor has already estimated the decision metric nED, it has to compare it with
an optimized threshold and evaluate if the transmission is within the interference levels or
not.
The performance of a detector can be analyzed via probabilities of false alarm and
missed detection. A simple model for ED without high noise effects is formulated in [5].
Indeed, the probability of false alarm (Pf) is given by:
PED
f¼E½nEDP1
NX
N1
n¼0jynj2[cED H0
!
¼E½nEDP2
r2
yX
N1
n¼0jynj2[2NcED
r2
yH0
!
ð8Þ
EnS
MfS
HrSCAV
CsS
Complexity
Accuracy
Fig. 3 Comparison of SS
methods in therms of complexity
accuracy
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where the random variable (r.v.) nED Ncð0;r2
nÞand PðjÞ is the conditional probability;
consequently, the total sum in the conditional probability’s argument results in a chi-
squared distribution with 2Ndegrees of freedom.
Additionally, Eq. (8) can be re-written using a few notations:
PED
f¼QðN;NcED=r2
yÞð9Þ
where Qð;Þ denotes the generalized Marcumm Q-function.
Similarly, the probability of detection is given by:
PED
d¼Qffiffiffi
k
p;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2NcED=r2
y
q

;ð10Þ
where
k,2
r2
xX
N1
n¼0jxnj2ð11Þ
4.1.1 Energy Detection in AWGN Channels
There are three important measurements for a EnS model: probability of false alarm PED
f,
probability of detection PED
dand threshold of detection cED, defined as:
cED ¼Q1PED
f

r2
0þr2
gð12Þ
PED
f¼QcED r2
g
r2
0
! ð13Þ
PED
d¼QcED l1
r2
1
 ð14Þ
where r2
0¼r2
g
ffiffiffiffi
N
p,l1¼r2
nð1þSNRÞand r2
1¼r2
0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2SNR þ1
p.
Majority of researches on energy detection in CR apply uniform sampling; however,
random sampling was proved to be a good alternative to channel uncertainties and for-
bidden band restriction [30]. Herein, even though random sampling has been proven to
enhance performance, it will be focused on using uniform sampling of signals due to ease
on implementation and mathematical analysis.
4.2 Matched Filter Detection
In scenarios where there is a previous knowledge about some information of the primary
users transmission, MfS can enhance the sensing process. Basically, a prior knowledge
regarding some PU’s information is needed, usually a pilot sequence. This received signal
is then correlated with a pilot sequence at SU’s receiver device and a channel status
response is generated based on a certain preset threshold. An important point, which is
considered in this work, is the formulation of a threshold level that maximizes probabilities
of detection. Hence, the MfS uses this threshold value to decide between hypothesis H0and
H1.
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In a continuous form, the statistical test comes from the correlation between received
signal y(t) and a replica of pilot sequence x(t); hence, the signal to be compared with a
threshold [26] is given by:
b
sðtÞ¼ZT
0
xðtsÞyðsÞdsð15Þ
Or, in discrete time [7]:
b
s½n¼X
N
k¼1
x½nky½kð16Þ
where N¼T
Ts, with Tsbeing the sampling period and Tthe total sensing time.
Figure 4shows an example of MF-based spectrum sensing signals to be compared with
a threshold. In Fig. 4a PU’s transmitted pilot pulse can be identified, while in Fig. 4ban
usual replica of pilot pulse in the MF filter, which is a mirrored version of the transmitted
pilot pulse. Graphic in Fig. 4c is a delayed version of this signal, while Fig. 4d is the
received signal (pilot pulse plus the additive noise), typically at low SNR. After a con-
volution operation step, the MF output signal identified by plot in Fig. 4e shows a peak of
energy, which is supposed to be at least the pilot signal replica’s energy.
Indeed, MF’s decision region is given by:
Decidefor ¼H0;if b
s\cMF;
H1;if b
scMF:
ð17Þ
where cMF is the threshold energy of detection in for MfS devices.
Furthermore, the probabilities of detection and false alarm for a MF spectrum sensing
detector are given by [4,26]:
(a)
(b)
(c)
(d)
(e) kEx
A
A
A
A
T
T
T
T
t
0
Peak SNR
Fig. 4 Example of a MF
detection signals
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Pmf
f¼Pb
s[cMFjH0
fg
¼QcMF
ffiffiffiffiffiffiffi
er2
g
q
0
B
@1
C
Að18Þ
PMF
d¼Pb
s[cMFjH1
fg
¼QcMF e
ffiffiffiffiffiffiffi
er2
g
q
0
B
@1
C
Að19Þ
where e¼PN
k¼1x2½kand r2
gis the additive noise’s variance.
4.3 Covariance Absolute Value
The covariance absolute value (CAV) spectrum sensing detector is based on second order
statistics of received signal samples. Considering Lconsecutive samples, the received
signal, data and noise vectors can be defined, respectively, as:
yðkÞ¼ yðkÞyðk1Þ  yðkLþ1Þ½
Tð20Þ
sðkÞ¼ sðkÞsðk1Þ  sðkLþ1Þ½
Tð21Þ
gðkÞ¼ gðkÞgðk1Þ  gðkLþ1Þ½
Tð22Þ
where Lis known as smoothing factor length. Additionally, received and transmitted
signals covariance matrices are obtained as the expected values:
Ry¼EyðkÞyTðkÞ
 ð23Þ
Rs¼EsðkÞsTðkÞ
 ð24Þ
while the following equality holds:
Ry¼Rsþr2
gILð25Þ
If there is a signal, and its samples are sort of correlated, some of the off-diagonal elements
of Ryare non-zero. In contrast, if the signal is absent, then Rs¼0; hence, Ryhas all the
off-diagonal elements equals to zero. With this understanding, it is possible to create two
tests aiming to define presence or absence of signal. Denoting rij as the ith row and jth
column element of Ry, the following test metric can be deployed:
T1¼1
LX
L
i¼1X
L
j¼1jrijjð26Þ
T2¼1
LX
L
‘¼1jr‘‘j¼tr½Ry
Lð27Þ
where tr½ is the trace matrix operator; indeed, T1metric has all the elements of Ry, while
T2presents only the diagonal ones. Thus, if there is no signal, the ratio T1
T2¼1. However, if
the signal is present, T1
T2
[1.
5014 L. Claudino, T. Abra
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In practice, Nsamples are received, but the system is usually limited to work with L
samples. The covariance matrix Rycan be estimated via the sample covariance matrix:
b
Ry¼
bð0Þbð1Þ  bðL1Þ
bð1Þbð0Þ  bðL2Þ
.
.
..
.
...
..
.
.
bðL1ÞbðL2Þ  bð0Þ
2
6
6
6
6
4
3
7
7
7
7
5ð28Þ
where bð‘Þ¼1
NX
N1
n¼0
yðnÞyðn‘Þ;‘¼0;1;...;L1ð29Þ
Also, the statistics T1and T2can be adjusted according to b
RyðNÞ[16]:
b
T1¼1
LX
L
i¼1X
L
j¼1jb
rijjð30Þ
b
T2¼1
LX
L
i¼1jb
riijð31Þ
where b
rij is the ijth element of the sample covariance matrix, b
Ry.
In order to analyze the efficiency of a CAV detector, probabilities of detection and false
alarm have to be calculated [17,41]:
PCAV
f¼Pb
T1
b
T2
[cCAVH0
!
¼1Q
L1
cCAV ffiffiffiffiffiffiffi
2
Np
r1
ffiffiffiffiffiffiffiffiffi
2=N
p
0
B
B
B
@1
C
C
C
A
ð32Þ
PCAV
d¼Pb
T1
b
T2
[cCAVH1
!
¼1Q
1
cCAV þLSNR
cCAVðSNR þ1Þ1
ffiffiffiffiffiffiffiffiffi
2=N
p
0
B
B
@1
C
C
A
ð33Þ
where Lis the overall correlation strength:
L,2
LX
L1
‘¼1ðL‘Þja‘jð34Þ
and the normalized form of (34), namely normalized correlation coefficient, is given by
b
L¼L
r2
sr2
gð35Þ
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and
a‘¼E½sðnÞsðn‘Þ
r2
s¼Rsð‘Þ
r2
sð36Þ
Applying the inverse Q function, the value of the threshold cCAV is found based on an
estimation of PCAV
f:
cCAV ¼
1þðL1Þffiffiffiffiffiffiffi
2
Np
r
1Q1ðPCAV
fÞffiffiffiffiffiffiffiffiffi
2=N
pð37Þ
4.4 Hadamard Ratio-Based Robust Spectrum Sensing
Hadamard ratio (HR) test is a robust method to provide signal detection in multivariate
analysis which is able to deal with non-independent and identically distributed (IID) noise
[20]. Recently, the HR test has been exploited for robust spectrum sensing in CR [38]. This
subsection is devoted to analyze Hadamard ratio method for robust spectrum sensing
purpose. By computing the first and second exact negative moments for the signal-presence
hypothesis along with employing Beta distribution approximation, authors of [20] derived
accurate analytical expression for detection probability, enabling to theoretically evaluate
the detection behavior of the Hadamard ratio test. The analytic formula for the detection
probability of the Hadamard ratio test derived in [20] allows us to theoretically evaluate the
HrS performance.
Remembering that, according to (5), a received signal at instant kis y(k),s(k) is the
transmitted symbol and gðkÞis a zero mean complex Gaussian noise. Aiming to decide
between the two main hypothesis H0and H1the HrS detection method starts with a general
likelihood ratio test (GLRT) derivation.
For this purpose, a MIMO (Multiple Input Multiple Output) CR network where the SU
is equipped with nRantennas has been considering sensing the data from nTPUs; hence, a
hypothesis test has to be adjusted in (5), where now the observation vectors are given by:
sðkÞ¼ s1ðkÞs2ðkÞ  snTðkÞ½
Tð38Þ
gðnÞ¼ g1ðkÞg2ðkÞgnRðkÞ

Tð39Þ
yðkÞ¼ y1ðkÞy2ðkÞ  ynRðkÞ½
Tð40Þ
while the channel matrix established between SU and PUs is denoted by H2CnRnT.
Besides, we have assumed that elements of vector sðkÞare Gaussian-distributed values
with siðkÞNð0;r2
siÞ;i¼1;...;nTand giðkÞNð0;r2
giÞfor i¼1;...;nR. Indeed, the
binary hypothesis can be re-written as:
yðkÞ¼ gðkÞ:H0
HsðkÞþgðkÞ:H1
ð41Þ
Assuming that the observation vector follows a Gaussian distribution yjHiN 0;RðiÞ

,
i¼0;1, where RðiÞis the covariance matrix. The covariance matrix under H0becomes
Rð0Þ¼diagðrv1; ::; rvmÞ, while under H1is given by Rð1Þ,ðrijÞnRnR. According to these
5016 L. Claudino, T. Abra
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assumptions, the likelihood function under a general hypothesis Hiis expressed by
[20,25]:
LYjRðiÞ

¼1
jRðiÞjNexp Ntr RðiÞ
hi
1b
R
 ð42Þ
Or even the log-likelihood function (LLF) of Y:
LYjRðiÞ

¼Nlog RðiÞ
þNtr RðiÞ
hi
b
R
 ð43Þ
where b
R¼1
NYYHis the sample covariance matrix and Y¼½y1;...;yNwith Nbeing the
number of samples. Note that, under hypothesis H0,b
Rð0Þ¼diagðb
RÞ, and under H1
becomes b
Rð1Þ¼b
R. Moreover, the GLRT, which takes into account the relationship
between probabilities of the two hypothesis, is computed and compared it with a preset
threshold in order to determine presence or absence of a PU, which is expressed by:
LYjRð0Þ

LYjRð1Þ
 ð44Þ
The Hadamard Ratio is now obtained substituting (43) into (44):
nHR ¼b
Rð1Þ

b
Rð0Þ

?
H0
H1
cHR ð45Þ
The exact distribution for this GLRT may assume complex values; however, its moments
can be easily expressed. Also, values for GLRT are always between 0 and 1, what allows
us to adopt a Beta distribution to approximate the test probabilities [25]. For this solution, a
moment determination for nHR is needed. Indeed, first and second exact negative moments
are computed and detection probability is obtained by matching these moments with the
Beta distribution ones. Hence, let’s firstly define the PDF of a Beta distribution with
parameters aand b[39]:
fZðhÞ’
ha1ð1hÞb1
Bða;bÞ;0h1
0;otherwise
8
<
:ð46Þ
where Bða;bÞ¼CðaÞCðbÞ
CðaþbÞis the Beta Function.
Given the k-th negative moment of a random variable Zdefined as Mk,E½Zk, the
first two negative moments of a Beta-distributed r.v. are defined as [22]:
M1¼aþb1
a1ð47Þ
M2¼ðaþb1Þðaþb2Þ
ða1Þða2Þð48Þ
Now, solving (47) and (48) for aand b:
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a¼M12M2
M1þ1
M1M2
M1
ð49Þ
b¼ð1M
1Þð1aÞð50Þ
FðxÞ¼ 1
Bða;bÞZx
0
ha1ð1hÞb1dh¼Bxða;bÞ
Bða;bÞð51Þ
where Bxða;bÞ¼Rx
0ha1ð1hÞb1dhis the incomplete Beta function.
Hence, whenever the moments of the test statistic in (45) be matched to the ones of the
Beta distribution, the behaviour of nHR can be then be approximated by the Beta distri-
bution, as discussed in [20].
Finally, probability of detection for a Hadamard ratio-based spectrum sensor is
expressed as:
PHR
d,PnHR\cHR jH1
ðÞ¼FðcHRÞð52Þ
The next step is to define the probability of false alarm for the Hadamard Ratio-based
sensor. For this case, [25] studies the first two positive moments of (45) and proceeds
similarly to the abode mathematical methods. For this case, the two variables a2and b2are
given as a function of two positive moments of a beta distributed random variable:
a2¼M1M2M
1
ðÞ
M2
1M
2ð53Þ
b2¼1M
1
ðÞM
2M
1
ðÞ
M2
1M
2ð54Þ
Indeed, given the definition of a probability of false alarm PFA,Pr nHR \cHR jH0
fgand
using (46), we have:
PFA ’ZcHR
0
1
Bða2;b2Þta21ð1tÞb21dt
¼~
Bða2;b2;cHRÞ¼Bcða2;b2Þ
Bða2;b2Þ
ð55Þ
5 Performance Metric: SNR Walls
In order to properly sense a frequency channel, the sensor has to lead with a tradeoff
between prior knowledge of the signal, sensibility and computational complexity [35]. In
CR, system performance is usually evaluated via receiver operating characteristics (ROC)
analysis, which plots the dependency between probability of detection and false alarm.
Real-world scenarios need the highest Pdpossible for a given Pf(usually Pf¼0:1).
Figure 5shows a region that every CR sensor should target. Moreover, [1] and [35]
5018 L. Claudino, T. Abra
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analyze a few ways of increasing performance in CR sensing; however, due to real case
uncertainties, a new effect turns in when looking at the sample complexity. At some limit
point, the ‘‘sample complexity blows up to infinity as the detector sensitivity approaches
certain critical values’’ [1]. This phenomenon is known as SNR Wall. Figure 6illustrates a
generic sensor with a SNR wall located at 46 dB; the black dashed line indicates how this
sensor should hypothetically behave.
1
Figure 6also leads to an interpretation that a sensor
with SNR wall is non-robust to noise, once it needs an infinity number of samples to
achieve a desirable performance for SNRs below the wall.
It is also possible to quantize this sample complexity by isolating the number of samples
in function of the usual variables of a CR spectrum sensing, including Pf,Pd,SNR and rg.
Herein, we are going to apply the SNR wall metric for EnS, MfS and CAV; however, the
Hadamard Ratio sensor, as seen in Sect. 4.4, does not have a closed expression for Pdand
Pfas a function of the number of samples, which precludes us to plot it together with the
other spectrum sensors.
5.1 SNR Wall for EnS
Given probabilities (13) and (14), the goal is to eliminate cED and find the value for N.
Authors in [35] also insert a factor q¼10x=10, which quantifies the level of uncertainty in
the noise power, scaling rgin an interval ½rg=q;qrg, where noise variance is allowed to
have xdB of uncertainty. The uncertainty modeling of a noise is used to give an idea of
approximated Gaussian noise (and not a precise one). The approximation consists in dis-
tributing the White noise (ga) moments over a closed interval
Eg2i
a

21
qiEg2i

;qiEg2i


;8i¼1;2;..., with gNð0;r2
gÞ, such approximated
00.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
Pd
Desired operation
Fig. 5 Desired operation for a CR sensor
1
In terms of linear dependence of the number of samples (log scale) increasing with the SNR (in dB)
decreasing.
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moments are close enough to nominal moments.
2
Hence, the following modified version of
the probabilities emerge from this approximation:
PED
f¼QcED qr2
g
ffiffiffiffi
2
N
rqr2
g
0
B
B
@1
C
C
Að56Þ
PED
d¼QcED ðSNR þr2
g=qÞ
ffiffiffiffi
2
N
rðSNR þr2
g=qÞ
0
B
B
@1
C
C
Að57Þ
From (56), cED ¼qrg1þffiffiffiffiffiffiffiffiffi
2=N
pQ1ðPED
fÞ

, and from the false alarm probability
Eq. (57), cED ¼Pþr2
g=q

1þQ1ðPED
dffiffiffiffiffiffiffiffiffi
2=N
pÞ

.
Eliminating cED, by assuming that in the interest region ð1þSNRÞ1, we finally get
the Sample Complexity for an Energy Detector:
NED ¼
2Q1ðPED
fÞQ1ðPED
dÞ
hi
2
SNR q21
q2

2ð58Þ
which grows with the inverse of SNR. Notice that the denominator of (58) is fixed;
however, at some point it goes to zero (depending on SNR and qvalues) and the number of
−60 −50 −40 −30 −20 −10 0
10−5
100
105
1010
1015
SNR[dB]
Number of samples
SNR Wall
Sample Complexity
Hypothetical
Sample
Complexity
Fig. 6 SNR Wall characteristics
2
For a better detailed description of the noise model and uncertainty models used in this work, please refer
to [35].
5020 L. Claudino, T. Abra
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samples tends to infinity. This simple mathematical analysis shows that, for SNR values
around and below this discontinuity the EnS is unrealizable.
In order to find the exact point of discontinuity, we have to set the denominator of (58)
to zero:
SNR q21
q2

2
¼0))SNRED
wall ¼q21
q2ð59Þ
5.2 SNR Wall for MfS
Similar to Sect. 5.1, a formula relating sample complexity and usual parameters is obtained
for a matched filter-based CR sensor. In this case, one more parameter may influence the
necessary number of samples, which is the percentage (h) of total power present in the pilot
tone. It is worth noting that SNR wall is an effect related to real world scenarios; hence,
[35] suggests that, in many cases, PU’s signal is multiplexed in time, what strongly limits
the coherence time. Also, [34] says that MfS should be divided in coherence blocks, each
one with Ncsamples. So, when analyzing the sample complexity of a MfS, it is fair enough
to divide it into two steps: firstly the signal is coherently sensed within each coherence time
(it keeps the noise uncertainty and boosts signal power by Nc). Secondly, the boosted signal
is detected via an Energy sensor.
A modification of (58) comes from the addition of variables hrepresenting the fraction
of pilot tone power and Nccorresponding to the influence of coherence time:
NMF ¼
2NcQ1ðPED
fÞQ1ðPED
dÞ
hi
2
hNcSNR q21
q2

2ð60Þ
A simple analysis of MfS states the ‘‘Energy Sensor’’ part still non-robust to noise
uncertainty; however, the coherent part boosts performance by a factor of Nch, where
h2Rj0h1
fg
is a fraction of the pilot tone’s total power. Similarly to the EnS case,
(60) also has a discontinuity where the number of samples tends to infinity, but this value is
also dependent on Ncand h. This dependence shifts the limit SNR to the left, meaning an
improvement of MfS detector performance regarding the ED.
To find the exact point of discontinuity, the denominator of (60) has been set to zero:
hNcSNR q21
q2

2
¼0))SNRMF
wall ¼q21
hNcq2ð61Þ
5.3 SNR Wall for CAV
For the covariance absolute value spectrum sensing detector, probabilities of detection and
false alarm are given by (33) and (32), respectively. Firstly, isolating cCAV in both
equations:
cCAV ¼
1þðL1Þffiffiffiffiffiffiffi
2
Np
r
1Q1PCAV
f

ffiffiffiffiffiffiffiffiffi
2=N
pð62Þ
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cCAV ¼
1þLSNR
1þSNR
1þffiffiffiffiffiffiffiffiffi
2=N
pQ11PCAV
d
 ð63Þ
Now, both equations are combines and a closed expression for sample complexity of a
CAV spectrum sensor is obtained:
NCAV ¼2/2
dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d22D/
p

2ð64Þ
where:
d¼Q11PCAV
d

þðL1Þ
ffiffiffi
p
pþQ1ðPfÞ1þLSNR
1þSNR

/¼2ðL1Þ
ffiffiffi
p
pQ11PCAV
d

and D¼LSNR
1þSNR
The exact point of discontinuity is obtained when the denominator of (64) is set to zero:
dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d22D/
q

2
¼0))2D/ ¼0
2LSNR
1þSNR

1ðL1Þ
ffiffiffi
p
pQ1ð1PdÞ

¼0ð65Þ
There are two possibilities for the denominator to be set to zero: a) L¼1; b) L¼0. This
shows that, for fixed and valid values of Land L, the sample complexity for a CAV
detector will not present a discontinuity point in terms of SNR.
Authors of [35] and [34] extended their investigation on SNR wall optimization in and
showed that, for flat fading channels,
3
feature detectors are robust to noise uncertainty and
don’t have a SNR wall.
It is worth noting that Eq. (64) is proposed herein for first time; the numerical results
discussed in Sect. 6.5 demonstrate accuracy with the above analysis, once there is no
abrupt asymptotic behavior in sample complexity. This means that for our case of study,
the CAV does not present a SNR wall.
6 Numerical Results
This section firstly brings an individual analysis for representative spectrum sensing
detection schemes. Performance versus complexity analysis is carried out starting with
ROC graphics, i.e. detection false alarm probabilities, as well as detection probability 
threshold, considering specific AWGN scenarios. The advantages and disadvantages or
each one method have been highlighted. For every realization, a zero-mean Gaussian
distributed data sequence is generated and its variance is chosen to be r2
x. In order to
simulate a simple channel, AWGN is added to transmitted data sequence and then all
analysis are evaluated using the received signal.
3
The channel scenario case studied herein for the CAV detector.
5022 L. Claudino, T. Abra
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Additionally, as more realistic representation of real world scenarios, multipath Ray-
leigh channels have been introduced and SS detection schemes such as HrS and EnS are
compared in term of ROC and computational complexity.
Firstly, individual results for each sensor are comprehensively discussed. Subsequently,
a broad comparison with all sensor is done under AWGN effect. Finally, HrS and EnS are
analysed and compared considering more realistic Rayleigh channels.
6.1 Energy Detector
Detection probability dependence is given by Eq. (14). Indeed, the most significant
parameters are threshold and SNR. Figure 7shows that SNR is an extremely important
factor, once for lower SNR values the probability of detection reaches 1 only when PED
fis
close to 1. Therefore, higher system effectiveness is achieved for better values of SNR,
because for low Pfthe detector has already achieved PED
d1.
Equation (14) firstly shows that somehow the threshold affects probabilities of detection
and false alarm. A basic understanding is that l1and r2
1are constants dependent on noise
and cED is varying; hence, as cED increases, PED
ddecreases. The relationship on these
variables is depicted in Fig. 8. Therefore, a correct threshold is set based on test statistics
and correct estimation of the SNR. From this graph, it is observed that if the threshold is
too high and transmitted signals have not enough energy to overcome this value, the
spectrum sensor will identify every signal as a noise; consequently, the channel will always
be sensed as idle.
Variation of PED
daccording to values of SNR is shown in Fig. 9. For this simulation a
target PED
f¼0:1 has been set in order to find an adequate value for cED and assumed a
sensing period with N¼2000 samples. Threshold levels for EnS are directly related to
noise variance and consequently the actual SNR value. Indeed, each SNR value sets a cED
aiming to establish a suitable detection probability for the system. Also, under the system
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
ED
Pd
ED
SNR=−15dB
SNR=−13dB
SNR=−11dB
SNR=−9dB
Fig. 7 ROC for an Energy detector with N ¼1000 samples
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configuration of Fig. 9(number of samples and false alarm probability), one can conclude
that ED is not recommended for scenarios where the SNR is less than 15 dB, once the
probability of detection is lower than 0.5.
Finally, in order to have a broad view about the behavior of PED
d, all main variables are
related in a single 3-D surface on Fig. 10. The simulation has been done for a target
probability of false alarm PED
f¼0:1. For an EnS detector, a reasonable number of samples
ranges from 500 to 1500, but also SNR has a strong effect on PED
d. For instance, if the CR is
working in a 10 dB scenario, a sensing with N¼1000 samples should result in
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
γED
Pd
ED
SNR=−12dB
SNR=−10dB
SNR=−8dB
SNR=−7dB
SNR=−6dB
Fig. 8 Relationship between threshold and probability of detection
−40 −35 −30 −25 −20 −15 −10 −5 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR[dB]
Pd
ED
Fig. 9 PED
ddependency on SNR and set threshold for N¼2000 and PED
f¼0:1
5024 L. Claudino, T. Abra
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PED
d0:6; however, it is desirable a greater rate of detection. So, a sensing phase with
1500 samples could achieve PED
d0:1.
6.2 Matched Filter
Similarly to EnS, behavior of MfS and its various parameters have been analyzed in order
to identify their influence on sensor’s performance. Firstly, probabilities of detection and
false alarm for AWGN channels have been evaluated in terms of ROC. Figure 11 offers an
overall performance idea of a MfS. A first comparison already pointed out that MfS can
easily operate in much lower SNR scenarios than a EnS, once MfS ranges from SNR
¼30 dB to 20 dB, while EnS results in the same characteristics for 15\SNR
\9 dB. Corroborating this found, [4] states that an energy sensor is much more
degraded due to noise uncertainty than a traditional matched filter.
Figure 12 relates probability of detection and SNR for a MfS. From (18), cMF is directly
related to probability of false alarm and noise variance. So, in a real scenario, for an
optimal detection, the threshold has to be recalculated at each sensing process, once it is a
function of the noise strength at (SNR ¼r2
x
r2
n), which may have an instantaneous fluctuation.
Hence, for this simulation, at each new SNR value, a cMF is calculated and then inserted
into (19), generating the performance curve of Fig. 12.
Figure 13 depicts how PMF
dbehaves with changes in number of samples and SNR.
Comparing to EnS case, the MfS is able to work satisfactorily under low SNR scenarios
(30 dB). Indeed, for the same N¼1500 samples needed for EnS, MfS is able to provide
a good performance under a 20 dB scenario. As a conclusion, matched filter spectrum
sensing presents a working margin 10 dB greater than EnS.
Fig. 10 Probability of detection for EnS considering dependency on number of samples Nand SNR and
fixed PED
f¼0:1
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5025
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6.3 Covariance Absolute Value Sensor
The CAV detection presented in Sect. 4.3 has its own probabilities of detection and false
alarm. Equations (32) and (33) show explicitly that system’s performance is highly related
to threshold, number of samples, SNR and also the correlation coefficient of received
samples. Hence, it is important to analyze how these factors affect the quality of spectrum
sensing.
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
MF
Pd
MF
SNR=−30dB
SNR=−28dB
SNR=−26dB
SNR=−24dB
SNR=−22dB
Fig. 11 ROC for a MF detector
−80 −70 −60 −50 −40 −30 −20 −10 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR[dB]
Pd
MF
Fig. 12 Probability of detection analysis for different values of threshold and SNR with N¼2000 samples
and PMF
f¼0:1
5026 L. Claudino, T. Abra
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123

Influence of SNR on ROC curves is presente in Fig. 14. Indeed, for values of SNR
around 13:5 dB, CAV sensing method almost reaches an ideal detection, with PCAV
f¼0
and PCAV
d¼1. Additionally, comparing Figs. 7and 14, one can identify which system has
better ROC performance. An EnS reaches an excellent performance under SNR ¼9 dB,
while a CAV sensor does it with much less energy, as indicated in Fig. 15, i.e., under
SNR ¼13:5 dB.
Notice that not only SNR affects CAV spectral sensing detector. Also smoothing factor
and the preset threshold do it. A CAV sensor is based on how strong correlated the samples
are. Hence, if there is a scenario with a fixed SNR, the higher Lis, the more efficient the
−40
−30
−20
−10
500
1000
1500
0
0.2
0.4
0.6
0.8
1
SNR [dB]
N. samples
Pd
MF
Fig. 13 Probability of detection for a MfS
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
CAV
Pd
CAV
SNR=−14dB
SNR=−13.5dB
SNR=−13dB
SNR=−12.5dB
SNR=−12dB
Fig. 14 ROC for a CAV detector with L¼10, L¼2 and N¼10;000
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5027
123

detection will be. Figure 16 illustrates it. With a graph of PCAV
dSNR and different values
for the overall correlation strength L, for example, if SNR ¼16 dB a system with a
correlation strength of 2 has PCAV
d¼0:1, while the detector with L¼4 has Pd’1.
Previous results in the literature have already pointed out that CAV spectrum sensing
detectors need much higher number of samples when compared to EnS and MfS. Aiming
to corroborate it, Fig. 17 relates the main factor that may influence CAV performance in
terms of PCAV
d. This numerical result has been obtained for middle correlated AWGN
channels, i.e., L¼3, while the normalized correlation coefficient b
Lchanges according
to the SNR level. Indeed, from Fig. 17, given SNR ¼14 one can identify the CAV
sensor needs at least 9 times more samples than EnS and MfS. If SNR increases 2 dB,
around 12 dB, \6000 samples would satisfy a PCAV
d[0:8; however, it still a huge
number of samples, which may exceed the sensing time and consequently shorten the
transmission phase.
6.4 Hadamard Ratio Test
Literature for Hadamard ratio spectrum sensing is yet very limited; performance results for
this sensor are different from the ones present on previous sessions. A HrS performance for
a system with one primary signal operating under SNR ¼½15;8dB, nR¼4 SUs and
N¼½1000samples is presented in Fig. 18.
In order to compare the ROC with all previous cases dhas been set to 1 in Fig. 19a. As
analyzed in Sect. 4.4, performance of this sensor is enhanced according to number of PUs
and SUs present in the system. Hence, an analysis with nT¼1 will not make use of HrS’
full performance. Figure 19b shows how a simple increase in the number of PUs nT¼3
may enhance overall sensor’s performance.
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
CAV
Pd
CAV
SNR=−16dB
SNR=−15.5dB
SNR=−15dB
SNR=−14.5dB
SNR=−13.5dB
Fig. 15 ROC for a CAV detector with L¼10, L¼3 and N¼10;000
5028 L. Claudino, T. Abra
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123

6.5 SNR Walls in Cognitive Radio Sensors
At this point, seen each sensor characteristics and ROCs curves have already been studied,
what gives an overview about its performance in scenarios of interest. Now, the next step is
to analyze the sample complexity for each sensor via SNR wall graphs and study which
presents better performance in a specific scenario. From the definition, a SNR wall is the
SNR limit for which each analyzed spectrum sensing detector is able to perform without
the necessity of using a number of sample tending to infinity. Figure 20 depicts the SNR
walls for three sensors: EnS, MfS and CAV. A SNR wall for HrS is impractical because a
few approximation have been done; hence, there is no theoretical expression relating
number of samples and SNR.
−22 −20 −18 −16 −14 −12 −10 −8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR[dB]
Pd
CAV
¡L=0
¡L=1
¡L=2
¡L=3
¡L=4
¡L=5
Fig. 16 Probability of detection versus SNR for different values of correlation strength
−17 −16 −15 −14 −13 −12 −11
6000
8000
10000
12000
0
0.2
0.4
0.6
0.8
1
SNR [dB]
N. samples
Pd
CAV
Fig. 17 Probability of detection for a CAV detector
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5029
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Firstly, a greater susceptibility to noise interference is observed in the EnS case, once its
SNR wall is located at around 13:5 dB and it has to use an extremely high number of
samples to keep its characteristics within an acceptable limit.
On the other hand, MfS’ characteristics shows that the sample complexity boost of the
coherent stage shifts SNR wall by around 30 dB, what gives an expressive working
margin before sample complexity tends to infinity. For example, in very low-SNR sensing
scenarios, i.e., ½30;25dB, MfS is a suitable choice if a number of samples as large as
100,000 or 10,000 is available inside the sensing time period.
Finally and differently from the other cases, CAV sensor does not have a SNR wall;
however, more samples are needed than MfS for low-SNR sensing scenarios. Another
important analysis similarly presented in is that the EnS does not require any assumptions
of the signal; consequently, the SNR wall is located at higher SNR. In contrast, MfS needs
several assumptions
4
of the signals under spectrum sensing; however, it presents a SNR
wall much lower than EnS. Presenting an intermediate sample complexity, CAV spectrum
sensor only makes structural assumption of the signal (medium/high correlated signals),
what may be the best choice as CRN Spectrum sensor in several practical scenarios of
interest.
Next Sect. 6.6 provides numerical analysis for four sensors applied to some real case
constraint scenarios.
6.6 Performance Analysis of ED, MF CAV and HR Sensors
A spectrum sensing system is usually applied to a real CRNs. Indeed, performance of SS
methods under some specific constraints is one of the most important points while
designing a CR network. In order to fairly compare previous analyzed sensors, optimal
parameter values for each sensor have been selected and compared. The adopted system
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
γHD
Pd
HD
M=6,N=20
M=6,N=50
M=60,N=100
Fig. 18 Probability of detection versus threshold of a HrS for a MIMO system with uncalibrated receivers;
Rayleigh channels
4
Actually MfS needs an entire pilot sequence.
5030 L. Claudino, T. Abra
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123

and channel configuration are described according to the values depicted in Table 2. The
simulation trial has considered a LOS (line of sight) AWGN channel transmission of a
microphone signal operating in a TV band with a power of 50 mW and bandwidth of
200 kHz. For this system configuration, the CAV correlation coefficient is then normalized
by the signal and noise variances, as defined in Eq. (35), so it ranges between jb
Lj1.
Performance analysis for SS detectors operating under realistic mobile NLOS channels,
such as Rayleigh fading are discussed in Sect. 6.7.
Figure 21 depicts the spectrum sensing performance for several sensors under AWGN
interference hypothesis. The correlation coefficient is set to 0:09\b
L\0:15. Again,
notice that EnS is not efficient for low SNR scenarios, once it is based on an accurate
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
HD
Pd
HD
SNR=−15dB
SNR=−12dB
SNR=−10dB
SNR=−8dB
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
HD
Pd
HD
SNR=−15dB
SNR=−14dB
SNR=−12dB
(a)
(b)
Fig. 19 ROC for a HrS with N¼1000 and nR¼4: anT¼1; bnT¼3
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5031
123

estimation of the noise power. On the other hand, CAV and MfS also depend on other
characteristics of the received signal. MfS requires a pilot sequence given by PU, while
CAV relies on sensing a correlated channel. The ROC performance curves demonstrated
that for low SNR scenarios, MfS is much more efficient than CAV; however, for high/
medium correlated channels, CAV is able to achieve higher probabilities of detection. For
the HrS detector, the above graph shows that utilization of a MIMO CRN may enhance
−50 −40 −30 −20 −10 0
10−5
100
105
1010
1015
SNR[dB]
Number of samples
EnS
MfS
CAV
SNR Wall
(MfS)
SNR Wall
(EnS)
Fig. 20 Sample complexity for CRN sensors
Table 2 Adopted parameters
values for the spectrum sensing
system
Parameter Adopted Value
SU: microphone signal
Tx power 50 mW
Channel AWGN, LOS
Frequency band TV sub-band, BW ¼200 KHz
General SS detector parameters
Number of samples N2½1;10103
SNR range SNR 2½30;10
Threshold Varies for each sensor
Target Pf0.1
CAV detector
CAV correlation coefficient 0:09\b
L\0:15
Smoothing factor length L¼10
HrS detector
nTf1;3g
nR3
5032 L. Claudino, T. Abra
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123

performance of spectrum sensing phase. For example, HrS with nT¼3 presents a much
higher performance than for the case with nT¼1 and same SNR range.
To sum up, the graph shows that, for the proposed channel, the best detector is the
Matched Filter Sensor, once the acceptable results of Pdand Pfare achieved under low
ranges of SNR (around 24 dB).
6.7 Performance Comparison Under Realistic NLOS Channels
This section is devoted to compare two former sensors applied to realistic wireless
channels. Section 6.6 has compared all previous studied sensors operating under AWGN
channels, which is not the most accurate representation of real transmission channels for
CRNs. For future 5G and CR systems, realistic MIMO channels must be studied in term of
SS performance. In order to analyze it, this section includes Rayleigh multipath fading and
AWGN noise in signal’s formulation, which are known to represent a more accurate
version of real scenarios. The path-loss influence can be overcome by increasing trans-
mission power; hence will not be deeply considered in this article.
Two sensors have been chosen for this simulation. EnS due its low computational
complexity and HrS because it is a robust sensor based on the accurate GLR theory,
although it is more complex to implement. Other sensors present intermediate results either
in terms of complexity or accuracy. All parameters necessary and respective values for this
simulations are shown in Table 3.
Numerical results depicted in Fig. 22 demonstrate that HrS presents higher performance
than EnS, in terms of detection probability. Considering the target Pf, EnS has not
achieved Pd0:8 for SNR ¼12 dB, while HrS presents Pd’0:97 for SNR ¼5 dB. This
fact shows that statistic test based on likelihood function is actually much more accurate
than tests based only on signal’s energy. As a disadvantage, the HrS is known to be more
complex than EnS. Hence, the choice of which sensor should be used may depend not only
on detection probabilities, but also considering other factors, such as the available trans-
mission power and processing resources.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
Pd
EnS, SNR=-12dB
MfS, SNR=-30dB
MfS, SNR=-24dB
CAV, SNR=- 14 .5 dB, ΥL=0.10825
CAV, SNR=- 14 .5 dB, ΥL=0.12991
HrS, SNR =-10 dB, d=1
HrS, SNR =-10 dB, d=3
Fig. 21 ROC comparison for EnS, MfS, CAV and HrS
Spectrum Sensing Methods for Cognitive Radio Networks: A Review 5033
123

7 Conclusion
This paper aims to analyze the spectrum sensing detectors available in the literature and
further compare them for specific scenarios. Each sensor has a parameter that dramatically
changes its performance. Numerical and analytical results demonstrate that EnS is not
designed to work in low SNR scenarios, mainly because it is based on received signal’s
energy; therefore, if noise levels are too high at receiver, the sensor may look at it as an
actual primary signal. On the other hand, CAV spectrum sensing detector is able to work in
low SNR scenarios; however, correlated primary signals are needed. A significant increase
in probabilities of detection for CAV is achieved by small gains in correlation b
, as seen in
results of Sect. 6.6.
MfS, as discussed in Sects. 6.2 and 6.6, results in better performance if compared to
EnS and CAV. The disadvantage of this SS technique is that a pilot sequence (or any
known signal) is needed at the receiver, which is not often available in CR networks.
Furthermore, one more factor to worry about is the SNR wall with results discussed in
Sect. 6.5. Results have confirmed that, for high-SNR scenarios, the EnS may be an
acceptable choice as a CRN spectrum sensor, once it has slightly higher sample complexity
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pf
Pd
HrS, SNR=0dB
HrS, SNR=5dB
EnS, SNR=8dB
EnS, SNR=12dB
Fig. 22 ROC comparison for EnS and HrS over Rayleigh channel
Table 3 SS system parameters
values deployed in more realistic
NLOS fading channels scenarios
Parameter Adopted value
Number of samples N¼1024
SNR range SNR 2½0;12
Threshold Varies for each sensor
Target Pf0.1
AWGN noise gCNð0;1Þ
PUs nT¼3
SUs nR¼12
5034 L. Claudino, T. Abra
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but does not rely on any knowledge of the signal. However, for medium/low-SNR sce-
narios, the MfS performs better than all others and even lower sample complexity is
needed.
If a MIMO CR network is suitable, the results from 6.6 have demonstrated that the more
PUs and SUs are actually sensing the spectrum, the higher performance is achieved by
HrS. Hence, for researches leading with MIMO systems, it is worth to have a close look at
this promising spectrum sensing technique. In order to motivate this direction of investi-
gation, realistic CRN scenarios have been analysed in Sect. 6.7. Numerical results indi-
cated that HrS is able to perform more accurate spectrum sensing under low SNR
scenarios; however, higher computational complexity is needed, if compared no EnS.
Acknowledgements This work was supported in part by the National Council for Scientific and Techno-
logical Development (CNPq) of Brazil under Grant 304066/2015-0, Fundac¸a
˜o Arauca
´ria under Grant
302/2012, and in part by State University of Londrina—Parana
´State Government (UEL), and CAPES/DS
scholarship.
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Lucas Claudino received his B.S. in Electrical Engineering from
Londrina State University (UEL) in 2016. Since 2013, he has been
engaged with telecommunication subjects at the Digital Signal Pro-
cessing and Telecommunications Lab. (UEL) and has undertaken an
internship at Swinburne University of Technology at the Centre for
Advanced Internet Architectures (CAIA) in 2014. His interests lie in
digital signal processing, internet architectures, cognitive radio,
resource alloation, heuristic and convex optimization aspects of 3G
and 4G systems, electronic systems and integrated circuit design.
Taufik Abra
˜o(IEEE Senior Member’12; IEEE Member’97) received
his B.S., M.Sc. and Ph.D., all in Electrical Engineering, from the
Polytechnic School of the University of Sa
˜o Paulo (EPUSP), Brazil, in
1992, 1996, and 2001, respectively. Since March 1997, he has been
with the Communications Group, Department of Electrical Engineer-
ing, Londrina State University (UEL), PR, Brazil, where he is currently
an Associate Professor in communications engineering. In 2012 (2nd
semester), he was an Academic Visitor at Communications, Signal
Processing and Control Research Group, University of Southampton,
UK. In 2007–2008, he was a postdoctoral researcher at the Department
of Signal Theory and Communications of the Polytechnic University
of Catalonia (TSC/UPC), Barcelona, Spain. Dr Abrao has participated
in several projects funded by government agencies and industrial
companies. He is involved in editorial board activities of three journals
in the communication area and he has served as TPC member in
several symposium and conferences in the field. Dr Abrao is a member
of the IEEE and SBrT. His research interests lie in communications and signal processing, including multi-
user detection and estimation, MC-CDMA and MIMO systems, cooperative communication and relaying,
resource allocation, heuristic and convex optimization aspects of 3G and 4G systems. He is authored or co-
authored of more than a 190 research papers published in specialized/international journals and conferences.
For more information, please, see the author’s personal HP: http://www.uel.br/pessoal/taufik/
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