Introduction to Spectrum Sensing Techniques

3
Introduction to Spectrum
S­ensing Technique­s
The topic of spectrum sensing and primary user detection has gained a great
deal of interest in the context of cognitive radios for dynamic spectrum access
networks. Spectrum sensing is one of the crucial functionalities of a cognitive
radio in order to learn the radio environment. In literature, one, can find various spectrum sensing techniques [1, 2] which, in general, could be classified as
(1) energy-based sensing, (2) cyclostationary feature-based sensing, (3) matched
filter-based sensing and (4) other sensing techniques. Different techniques serve
different purposes based on their advantages and drawbacks. The energy-based
sensing is the simplest method to sense the environment in a blind manner; the
cyclostationary-based sensing may require some information about the spectraluser signal characteristics; and the matched filter-based sensing requires the
complete information of the spectral-user signal, which are presented in detail
in this chapter. Some of the other techniques, such as the covariance-based
method and the eigenvalue-based method, are also presented.
3.1 Introduction
The recent interest in cognitive radio-related research has attracted a great
deal of interest in spectrum sensing and detection of radio users in the
45
46
Cognitive Radio Techniques
e­ nvironment. The key objective behind spectrum sensing and detection is to
see how reliably one could detect the radio users given a particular scenario
with an acceptable payoff or trade-off. In other words, the main objective is
to maximize the probability of detection without losing much on the probability of false alarm while minimizing the complexity and time to sense/detect the radio. In this section, we present various methods and techniques to
detect the radio users in the environment.
Let us define the signal model to be used in the rest of the chapter. Following from the previous chapter, we define two hypothesis H0 and H1 to represent
the presence of a radio signal, the corresponding signal model is given by
ν(t ); under H 0
ïî hs(t )+ν(t ); under H1
ì
ï
r (t ) = í
(3.1)
where r(t) is the complex baseband of the sensed radio signal, s(t) is the received
primary user signal, and n(t) is the additive bandlimited complex Gaussian noise
with a noise power of s 2 (including the real and imaginary noise components)
over a bandwidth of Bw (Hz). The channel component h has an amplitude and
phase shift associated with it given by h = aÐq°. Various models can be adopted
for the received radio signal s(t) without the noise component, depending on the
considered wireless channel. In the subsequent sections, we consider different
channel models and present their corresponding detection performances.
3.2 Spectrum Sensing with Energy Detection
The energy based spectrum sensing and detection is the simplest method for
detecting primary users in the environment in a blind manner [3]. The energy detector is computationally efficient and could also be used conveniently
with analog and digital signals, that is at the RF/IF stages or at the base band.
It also has a well-known drawback in the detection performance when the
noise variance is unknown to the sensing node. When the signal-to-noise
ratio is very low, it would be hard distinguish between the radio signal and
noise signal, therefore the knowledge of the noise power can be used to improve the detection performance of the energy detector.
3.2.1 Energy Detector
In energy-based detectors, the energy-metric of the received signal is computed over a given time period T, or equivalently over N samples in the dis-
Introduction to Spectrum S­ensing Technique­s
47
crete domain, and is used as the test statistic for the detection, where T = NTs
and Ts is the signal sampling period. From the GLRT in the previous chapter
it can be shown that the energy detector is optimum when s(t) is zero mean
complex Gaussian [4]. Considering the signal model given by (3.1) the test
statistic for the energy detector is given by
ξ=ò
t0 +T
t0
r (t )r�(t )dt (3.2)
where, r�(t ) is the complex conjugate of r(t) and t0 Î R+ is an arbitrary
starting time. The signal-to-noise ratio r is then defined based on the received signal s(t) assuming the signal is present throughout within the time
period of consideration t1 < t £ t2 for some t1, t2 Î R+, given by
ρ=
t2
α2
s(t )�s (t )dt ò
2
σ [t 2 - t1 ] t1
(3.3)
For the discrete signal r[n] = r(nTs) the energy-based test statistic is given
by
ξ » Ts
N -1
å r[n]r�[n]
(3.4)
n=0
where, N is the total number of complex samples and is also known as
the time-bandwidth product, which is a metric that defines the performance
of the energy based detector [3]. If T is the total sensing duration, then the
time-bandwidth product is given by TBw = NTs fs = N, where f s = 1/Ts is the
bandwidth of the discrete baseband signal r[n]. Note that in (3.4) there are
essentially N number of real component samples and N number of imaginary
component samples present, giving us a total of 2N samples. The detection
criteria based on the energy-based test statistic is then given by
ì0;
d =í
î1;
ξ< λ
ξ³ λ
(3.5)
Choosing the appropriate value for the threshold l is a challenging task,
which we present later in this section.
3.2.2 Energy Detector in Gaussian Channel
In order to compute the detection probability and the false alarm probability,
we consider the distribution of the test statistic x. For the Gaussian channel
with h = 1 Ð 0°, the energy based test statistic x follows a non central and a
48
Cognitive Radio Techniques
central chi-squared distribution under H0 and H1 respectively with 2N d­egrees
of freedom [3]. Using the distributions of the test statistic under H0 and H1, we
can derive the detection probability and the false alarm probability as [6],
PD = Pr[ξ > λ ; under H1 ] = Q N ( 2TBw ρ , λ )
(3.6)
PFA = Pr[ξ > λ; under H 0 ] = Γ(TBw , λ / 2)
(3.7)
¥
where, G( a , b ) = G(1N ) ò u a -1 exp( -u )du is the regularized upper incomplete
b
¥
Gamma function, G(.) is the Gamma function, Q N (a,b) = ò uN exp(–(u2 +
b
a2)/2)IN–1(au)/aN–1du is the generalized Marcum Q-function, and IN–1(.) is
the modified Bessel function of first kind with order N – 1.
Let us look at some results for the detection performance of the energy
detector in the additive Gaussian noise channel by plotting the complementary
receiver operating characteristics (C-ROC) curve. The C-ROC depicts the probability of false alarm in the x-axis and probability of miss detection in the y-axis.
Figure 3.1 shows the C-ROC curves for the energy detector for various values of
signal to noise ratio levels r. As we observe from the figure, the detection performance improves with increasing values of r by achieving lower miss detection
10
0
10
2
10
4
10
6
10
8
Prof of Miss Detection
 = 0dB
 = 7dB
 = 10dB
N = 10
10
10
10
10
8
10
10
6
10
4
Prof of False Alarm
10
2
10
0
Figure 3.1 C
omplementary ROC curves for the energy detector for various signal to noise
ratio levels.
49
Introduction to Spectrum S­ensing Technique­s
10
Prof of Miss Detection
10
0
N = 10
2
10
4
10
6
10
8
10
10
N = 30
N = 50
 = 5 dB
10
10
10
8
10
6
10
4
Prof of False Alarm
10
2
10
0
Figure 3.2 C
omplementary ROC curves for the energy detector for various values of timebandwidth product N.
probabilities for lower false alarm probabilities when r increases. Figure 3.2, on
the other hand, shows the C-ROC curves for various values of N, and again we
observe that the detection performance improves with increasing values of N.
Note that the analytical results presented here do not consider the wireless channel effects, such as fading or shadowing. In the subsequent sections, we present
the energy detector performance under various wireless channel conditions.
Threshold Selection: The detection and false alarm probabilities depend
on the threshold l, and hence it is necessary to choose an appropriate value
based on our requirements. The detection probability also depends on the
signal’s power and the time-bandwidth product, whereas the false alarm probability depends only on the time-bandwidth product apart from the threshold.
Therefore, one approach to choose the threshold for a given time-bandwidth
product is to select l to meet the desired false alarm probability.
3.2.3 Energy Detector in Fading Channels
The energy detector performance varies when the received signal component
s(t) in (3.1) undergoes different types of fading. The authors in [5–7] have
50
Cognitive Radio Techniques
derived the detection performance of energy detector for Rayleigh, Rice,
and Nakagami types of fading channels with additive Gaussian noise, which
we present here considering no diversity reception. Different types of distributions for the signal-energy-to-noise-power-spectral-density-ratio g = a 2Es /
N0 = Nr are considered to derive the detection performance under different
channel models. The corresponding probability density functions are then
averaged over (3.6) to compute the detection probability, given by,
PD = ò Q N ( a ρ , b ) f ρ ( ρ )dρ
(3.8)
R
where a = 2TBw and b = λ . Note that the false alarm probability is unchanged from (3.7) because it does not depend on s(t) under H0.
3.2.3.1 Rayleigh Channel
The probability density function of g in a Rayleigh fading channel is given
by
æ γö
1
(3.9)
f γ (γ ) = exp ç - ÷ for γ ³ 0
γ
è γø
where γ = E[ γ ] is the mean signal-to-noise ratio. Then by using (3.8) a closed
form expression for the detection probability can be derived, given by
N-2
1 æ λ ö æ1+ γ ö
æ -λ ö
PD = exp ç
÷å ç ÷ +ç
÷
2
n
è
ø n =0 ! è 2 ø è γ ø
n
é
ê æ -λ
´ êexp ç
2 + 2γ
êë è
N- 2
ö
æ -λ ö
exp
ç
÷
å
÷
è 2 ø n =0
ø
N -1
(
)
λγ nù
2(1+γ ) ú
n!
ú
úû
(3.10)
Note that in [6] the authors have considered a total of N samples (N/2 for the
inphase and N/2 for the quadrature), whereas we have considered a total of
2N samples (N for the inphase and N for the quadrature).
3.2.3.2 Rice Channel
The probability density function of g in a Rice fading channel is given by
æ
1+ K
(1 + K )γ ö æç K (1 + K ) γ ö÷
f γ (γ ) =
exp ç - K for γ ³ 0
÷ø I 0 ç 2
÷
γ
γ
γ
è
è
ø
(3.11)
. In [6] and [7], the authors have a considered a different energy-based test statistic which is a scaled
version of that presented in (3.2).
Introduction to Spectrum S­ensing Technique­s
51
where, ρ = E[ ρ] is the mean signal-to-noise ratio and K is the Rician factor.
Then by using (3.8) authors in [7] have derived a closed form expression for
the detection probability for N=1, given by
æ
PD = Q ç
ç
è
2K γ
λ(1 + K ) ö÷
,
1 + K + γ 1 + K + γ ÷ø
(3.12)
3.2.3.3 Nakagami Channel
The probability density function of g in a Nakagami type fading channel is
given by
m
æ mγ ö
1 æ m ö m -1
f γ (γ ) =
γ
exp ç for γ ³ 0
ç
÷
G(m ) è γ ø
è γ ÷ø
(3.13)
where, m is the Nakagami parameter and γ = E [γ ]. Again, by using (3.8)
authors in [6] have derived a closed form expression for the detection probability given by
N -1
(λ /2)u
λ(1 - β ) ö
æ λö
æ
PD = A1 + β m exp ç - ÷ å
1F1 ç m;1 + u;
÷ (3.14)
è 2ø
è
u
2 ø
u =1
where, β = m/(m + γ ) and 1F1(.;.;.) is the confluent hypergeometric function,
and A1 for integer values of m is given by
m-2
æ λβ ö é m -1
æ - λ(1 - β ) ö
æ - λ(1 - β ) ö ù
A1 = exp ç β Lm -1 ç
+ (1 - β ) å β i Li ç
ê
÷
÷
÷ø ú
è 2m ø ê
è
ø
è
2
2
úû
i =0
ë
(3.15)
where, Li(.) is the Laguerre polynomial of degree i. The authors in [6, 7] have
also presented similar analytical results for the detection performance of the
energy detector for the case of diversity reception in fading channels.
3.2.4
Energy Detector in Fading Channels with Shadowing
The detection performance of the energy detector for small scale fading channels were presented in the previous section. Here we present the same for received signals undergoing fading and shadowing simultaneously. The authors
in [8] present the detection probability in closed-form considering Gamma
distributed shadowing model under Rayleigh and Nakagami fading channels.
They show that the detection probability for the shadowing case with fading
can derived by considering γ as a Gamma distributed random variable (the
shadowing component) in the expressions for PD under fading channels [in
52
Cognitive Radio Techniques
(3.10), (3.12) and (3.14)], and then average it out for all values of γ . The
detection probability therefore is given by
PD = ∫ Pd f γ |γ (γ )dγ f γ ( γ )d γ
= ∫ PD f γ (γ )d γ
(3.16)
where, Pd is the detection probability under Gaussian channel, f γ |γ (γ ) is the
probability density function of of g under a given fading channel conditioned
on γ , PD is the detection probability under fading and Gaussian noise channel (without shadowing), and f γ (γ ) is probability density function describing the shadowing component modeled as a Gamma distribution given by
y k −1 exp( − y /Ω )
(3.17)
, for y ≥ 0
Γ(k )Ω k
where, k and W are the parameters describing the shadowing model. Considering a Rayleigh fading channel, the detection probability for the energy
detector for the Gamma distributed shadowing model then given by
fγ ( y) =
λ N -2 1 æ λ ö
PD = exp( - ) å ç ÷
2 n = 0 n! è 2 ø
n
+
¥
1
1 æ -λ ö
1ö
æ
G(k - N + 1)U ç k - N + 1; k - n + 1; ÷
÷
k å n! ç
è
Ωø
G(k )Ω n = 0 è 2 ø
-
exp( -λ /2) N - 2 1 æ λ ö
1ö
æ
G(n + k - N + 1)U ç n + k - N + 1; k + 1; ÷
÷
k å n! ç
è
Ωø
G(k )Ω n = 0 è 2 ø
n
n
(3.18)
where, N < k + 1 and U(.;.;.) is the confluent hypergeometric function of the
second kind. The authors in [8] also present a closed form expression for the
detection probability for the energy detector considering Nakagami fading
channel with Gamma distributed shadowing model.
3.3 Energy Detection and Noise Power Uncertainty
If the noise power level is perfectly known at the receiver, the energy director
can work with arbitrary values of probability of detection and probability of false
The authors would like to thank Andrea Mariani (Ph.D. student, University of Bologna) for his contribution to Section 3.3.
Introduction to Spectrum S­ensing Technique­s
53
alarm, even in low SNR regimes, by using a sufficiently long observation time.
H­owever, in real systems we do not have a perfect knowledge of the noise power
level, causing critical implications for energy detection design. The main two
problems derived from noise uncertainty are ED threshold setting [9] and the so
called SNR wall [10–12].
3.3.1 ED Threshold Mismatch
The typical approach for setting the threshold in energy detection is given by
the constant false alarm rate (CFAR) strategy, in which the threshold value
DES
is chosen in order to guarantee a target false alarm rate, PFA
, and can be
obtained inverting the analytical expression of the false alarm probability.
From (3.7) we get
(
)
DES
λ CFAR = 2 G -1 TBw , PFA
(3.19)
In this approach, the threshold selected depends on the noise power level, s 2.
The actual noise power is generally unknown, so we assume that the re­ceiver has
2
its estimate σ� that is typically obtained through a calibration process, and in
general, is different from s 2. Therefore, in practical applications, we always
must consider the adoption of an ED with estimated noise power (ENP) in
2
place of the ideal ED. The adoption of σ� for threshold setting can cause severe
performance degradations. If the uncertain value s 2 is obtained as noise power
estimate, threshold mismatch can be avoided including the statistic of the estimator in the probability of false alarm and probability of detection formulas
[9, 10, 13].
3.3.2 SNR Wall
An alternative representation of the performance of the ED is given by the so
called design curves [9–11, 13]. The design curve is the relation between the
SNR and the number of samples N required to guarantee the desired detecDES
tion performance, PFA < PFA
and PD > PDDES . Note that, given the sampling
frequency, the number of samples is proportional to the time needed for the
detection task. Then, the design curve can also be considered as the minimum
signal-to-noise ratio, SNRmin, needed to fulfil the detection specification for a
given sensing time. The design curve can be derived from the expressions of
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Cognitive Radio Techniques
the probability of false alarm and probability of detection. For the ideal ED,
it can be approximated as [10]
SNRmin,ED �
( )
(P )
DES
1 + Q -1 PFA
1
N
1 + Q -1
1
N
DES
D
- 1
(3.20)
where Q –1(.) is the inverse of the Gaussian tail function. For the ideal ED,
the minimum SNR satisfying the target detection performance can be reduced, increasing the observation time. The ideal ED design curve is plotted
DES
in Figure 3.3 (continuous curve), with PFA
= 0.1 and PDDES = 0.9. Note
that, when N is sufficiently high, the design curve has asymptotically a linear
trend on a log-log scale, with a slope of –5 dB/decade [13, 14]. In practical
implementations however, the noise uncertainty can cause a severe degradation of the detector performance. In particular, in some practical situations,
the design curve has a lower SNR limit, under which the detection is impossible even if the observation time tends to infinity. This is the so called SNR
wall phenomenon.
In presence of noise uncertainty, a very popular design strategy adopted
in literature is to consider; the estimated noise variance is constrained into a
20
Ideal ED
ENP-ED,
ENP-ED,
BWB-ED,
SNR min [dB]
10
M = N
M = 1000
 = 1 dB
0
10
20
30
10
1
10
2
10
3
N
10
4
10
5
PDES
= 0.1 and PDPDES = 0.9. The
Figure 3.3 D
esign curves for the ideal ED, ENP-ED with PFA
2
2
/σ min
= 1 dB is also shown.
corresponding BWB curve with ρ = σ max
Introduction to Spectrum S­ensing Technique­s
(
55
)
2
2
, σ max
limited range, defined by σ min
, that contains also the real noise power
2
level s [11, 12, 14]. This design strategy is called “bounded worse behavior”
(BWB). In this situation, the common approach is to consider a worst case
strategy, in which the probability of false alarm is evaluated when the esti2
mated noise power assumes the lowest value σ min
, while for the probability of
2
detection it assumes the highest value σ max . Then the corresponding design
curve is given by
SNRmin,BWB �
(
(
DES
2
1 + Q -1 PFA
σ max
×
2
σ min
1 + Q -1 PDDES
)
)
1
N
1
N
- 1
(3.21)
that gives raise to the SNR wall
lim SNRmin,BWB =
N ®¥
2
σ max
- 1 > 0
2
σ min
(3.22)
Due to the adoption of this design strategy and noise uncertainty model, an
idea that is raised into the spectrum sensing community is that the SNR wall
phenomenon is an unavoidable problem in practical applications.
3.3.3 Existence of the SNR Wall
Recently, it has been demonstrated that the SNR wall can be avoided if the
ENP has a sufficient accuracy [10, 13]. In particular, the two conditions for
avoiding the SNR wall are:
1. The correct statistic of the noise power estimator must be considered in the evaluation of the decision threshold.
2. The variance of the ENP must decrease faster then 1/N when the
observation time grows.
Note that, even if the second condition cannot be satisfied, the adoption of
the correct statistical model of the problem allows to predict the correct value
of the SNR wall. In a situation in which the two conditions above cannot
be satisfied, the BWB approach is the unique solution; however, not only it
always predicts the presence of the wall, but it also generally overestimates its
value [10]. Indeed, as we can see from (3.22), in this case the SNR wall value
2
2
,σ max
is determined by the choice of σ min
.
(
)
56
Cognitive Radio Techniques
As an example of ENP-ED, assume that M noise only samples, wn with
n = 0,…,M – 1, are available at the receiver. Then we can adopt the maximum likelihood noise power estimator defined by
2
σ� = Ts
M −1
∑ w[n]w�[n]
(3.23)
n =0
2
The variance of σ� is s 2/M. In this case, the design curve of the ENP-ED is
given by [27]
SNRmin,ENP − ED
DES 
2
1 + Q −1  PFA

σ max


� 2 ⋅
−
1
DES
σ min 1 + Q  PD 


N +M
NM
N +M
NM
− 1
(3.24)
It is easy to see that, in accordance to the condition ii, the SNR wall does not
occur (i.e., limN®¥SNRmin,ENP–ED = 0) only if M is an increasing function of
N.
Figure 3.3 shows and compares performance of an ideal ED and ENPDES
ED with PFA
= 0.1 and PDDES = 0.9. As can be seen, when M = N (the number of samples used to estimate noise power) is equal to the number of samples
used for detection, the ENP-ED does not exhibit the SNR wall (according to
condition ii) and the slope of the design curves is the same. In this situation,
only a loss of around 1.5 dB, when N > 100, is noticeable. On the contrary, if
M = 1000 is fixed with respect to N, the SNR wall occurs. For comparison, the
2
2
corresponding BWB-ED design curve with ρ = σ max
/σ min
= 1 dB is also
shown. As can be seem, the BWB-based ED design may lead to an incorrect
threshold design.
3.4 Spectrum Sensing with Cyclostationary Feature Detection
In wireless communications, the transmitted signals show very strong cy­
clostationary features based on the modulation type, carrier frequency, and
data rate, especially when excess bandwidth is utilized. Therefore, identifying the unique set of features of a particular radio signal for a given wireless
access system can be used to detect the system based on the cyclostationary
analysis at the cognitive radio node. The cyclostationary feature analysis is a
well developed and treated topic in the literature of signal processing [15, 16].
3. These samples can be captured in a signal free time window or in a free frequency band.
Introduction to Spectrum S­ensing Technique­s
57
In the context of cognitive radios, we consider using such analysis for spectrum sensing and primary user detection [17–20], in which case some degree of source signal knowledge may be required. For a sufficient number
of samples, this method can perform better than the energy-based detection
method when the cyclostationary features are properly identified. However,
the main drawback with this method is the complexity associated with it and
the requirement for a large sample set for better estimation and precision
of the features in the frequency domain. We present some of the fundamentals of cyclostationary feature analysis below and show how it can be used as
a spectrum sensing technique to detect primary users in the environment for
cognitive radio networks.
3.4.1 Cyclostationarity Analysis
A random process x(t) is classified as a wide sense cyclostationary process if the
mean and autocorrelation are periodic in time with some period T, given by
E x (t ) = E x (t + mT ) = E[ x (t )]
(3.25)
Rx (t , τ ) = Rx (t + mT ,τ ) = E[ x(t )x�(t + τ )]
(3.26)
and
where, t is the time variable, t is the lag associated with the autocorrelation
function, x�(t ) is the complex conjugate of x(t), and m is an integer. The periodic autocorrelation function can be expressed in terms of the Fourier series
given by
¥
å
Rx (t , τ ) =
Rxα (τ )exp(2 π jα t )
(3.27)
α =-¥
where,
Rxα (τ ) = lim
1
ò
T ®¥ T T
τ
τ
x(t + )x�(t - )exp( -2 π jα t )dt 2
2
(3.28)
The expression in (3.28) is known as the cycle autocorrelation. Using the Wiener relationship, we can define the cyclic power spectrum (CPS) or the spectral correlation function as,
S xα ( f ) = ò
¥
-¥
Rxα (τ )exp( - j 2 π f τ )dτ (3.29)
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Cognitive Radio Techniques
The CPS in (3.29) is a function of the frequency f and the cycle frequency a
and any cyclostationary features can be detected in the cyclic frequency domain a property that is exploited to be used as a spectrum sensing technique.
An alternative expression for (3.28) for the ease of computing the CPS is
given by
1
T0 ®¥ T ®¥ T0T
S xα ( f ) = lim lim
T0 / 2
ò-T /2 XT (t , f
0
+
1
1
) X�T (t , f - )dt (3.30)
α
α
where, X�T (t , u ) is the complex conjugate of XT (t,u), and XT (t,u) is given by
XT (t , u ) = ò
t +T / 2
t -T / 2
x(v )exp( -2 jπ uv )dv
(3.31)
Expression in (3.30) is also known as the time-averaged CPS, which achieves
the theoretical CPS when computed over a sufficient number of samples.
Frequency-averaged CPS can also be derived similar to the time-averaged one
as given in [21].
Let us observe some examples for the CPS. Figure 3.4 depicts a CPS
plot for BPSK modulated signal estimated over 2,000 symbols at a signal
0.04

Sx
0.02
0
50
50
f(Hz)
0
0
50
(Hz)
50
Figure 3.4 C
yclic spectral density for BPSK with a signal to noise (power) ratio of 0 dB
estimated over 2000 BPSK symbols.
59
Introduction to Spectrum S­ensing Technique­s
0.06

Sx
0.04
0.02
0
50
50
f(Hz)
0
0
(Hz)
50 50
Figure 3.5 C
yclic spectral density for BPSK with a signal to noise (power) ratio of 0 dB
estimated over 20 BPSK symbols.
to noise ratio of 0 dB. Figure 3.5 on the other hand depicts the same for
an estimation over 20 BPSK symbols at the same signal-to-noise ratio level.
These figures clearly show how the estimate of the CPS varies depending on
the number of samples used, and we observe that with a poor estimate of the
CPS noise can be seen at cyclic frequencies other than a = 0 (Figure 3.5).
With a better estimate of the CPS (Figure 3.4), we can clearly identify the
cyclic frequency components and the additive noise component appearing at
a = 0. Therefore, using the CPS one could detect the presence of the primary
user provided that the CPS is estimated properly. In the next section, we see
how the CPS can be used to detect the presence of primary users by cognitive
radios.
3.4.2 Cyclostationary Feature-Based Detector
In order to use the cyclostationary features to perform spectrum sensing in
wireless communications, we can rewrite the hypothesis equation for the
presence of a primary user signal considering the CPS as
60
Cognitive Radio Techniques
H 0 : Srα ( f ) = Sνα ( f )
H1 : Srα ( f ) = Ssα ( f ) + Sνα ( f )
(3.32)
where, Sνα ( f ) is the CPS of the additive noise u(t), and Ssα ( f ) is the CPS
of the primary user signal s(t). Since n(t) is not a cyclostationary process, the
CPS of n for a ¹ 0 is zero. Based on this, we can derive the test statistic for
the detector in the discrete domain as
ξ=
å å Srα ( f )S�αr ( f )
(3.33)
α ,α ¹ 0 f
where, S�αr ( f ) is the conjugate of Srα ( f ). The detector is then given by
ì0;
d =í
î1;
ξ< λ
ξ³λ
(3.34)
An important point to note here is that one needs sufficient number of samples to get a good estimate of the CPS and hence this method is not so computationally efficient. Furthermore, when insufficient number of samples are
used the detection performance will tend to get worse due to the poor estimate of the CPS.
If the target (primary user) signal information is somewhat known a priori
(such as the modulation type, code rate, symbol rate, etc.), then the test statistic
in (3.33) may be simplified to search for specific values of a corresponding to
the target signal. For analog amplitude, phase and frequency modulated signals
with a carrier frequency of f 0 the cyclic frequency components are observed at
± 2f 0, and for digital amplitude shift keying and (binary) phase shift keying
signals with symbol rate 1/T0 and a carrier frequency of f 0 the cyclic frequency
components are observed at k/T0 for k Î, k ¹ 0 and ± 2f 0 + k/T0 for "k Î .
Therefore, if the primary user signal falls into one of the signal categories mentioned above, the cognitive radio device can use the signal information to compute its test statistic targeting the specific values of a.
3.5 Spectrum Sensing with Matched Filter Detection
The matched filter detection based sensing is exactly the same as the traditional matched filter detection technique deployed in digital receivers.
Obviously for match filter based spectrum sensing a complete knowledge
Introduction to Spectrum S­ensing Technique­s
61
t=T
r(t)
h(t) = s(T  t)
Figure 3.6 Matched filter based spectrum sensing and detection of primary users.
of the primary user signal is required (such as the modulation format data
rate, carrier frequency, pulse shape, etc). The matched filter detection technique is a very well-treated topic in literature, and therefore, we just present
the fundamental results on matched filter detection in this section. Given a
real transmit signal waveform s(t) defined over 0 £ t £ T the corresponding
matched filter maximizing the signal to noise ratio at the output of the filter
sampler is given by
ì s(T - t ); 0 £ t £ T
(3.35)
h(t ) = í
0;
elsewhere
î
Figure 3.6 depicts matched filter based spectrum sensing method for primary user detection. Considering that a complete signal information of the
primary user signal is required in this case the matched filter method is not
really recommended by the system designers to suit our purpose here unless
when the complete signal information is known to the secondary user. Then
based on the test statistic x(nT ) at the output of the filter sampled every t =
nT seconds, the detector is given by
ì 0; ξ(nT ) < λ
d (nT ) = í
(3.36)
î 1; ξ(nT ) ³ λ
The matched filter-based detector gives better detection probability compared
to the previously discussed methods using the energy detector and the cyclostationary feature based detector; however as mentioned, it requires complete
signal information and needs to perform the entire receiver operations (such
as synchronization, demodulation, etc.) in order to detect the signal.
3.6 Other Spectrum Sensing Techniques
Many techniques have been proposed in literature, apart from the ones mentioned before in this chapter. In the rest of this section, we present some of
the other known techniques for spectrum sensing and primary user detection
in cognitive radio applications.
62
Cognitive Radio Techniques
3.6.1 Covariance-Based Method
The covariance of wireless signals and the additive noise component are generally different. The difference therefore is used to detect the presence of a
wireless signal by distinguishing from the noise signal. Zeng and Liang [22]
have proposed test statistics derived from the sample covariance matrix of
the received signal to perform signal detection. The sample covariance of the
received discrete signal r[n] is given by
é R(0)
ê R (1)
ê
ˆ
(
u
,
v
)
=
RL
ê
.
ê
ë R (L - 1)
R (1)
R (2)
.
R (L - 2)
…
…
…
…
R(L -1)
R(L -2)
..
R(0)
ù
ú
ú
ú
ú
û
(3.37)
and for a sample size of N the elements of the sample covariance matrix are
given by
R (l ) =
1
N
N -1
å r[n]r�[n - l ] for
l = 0,1,…, L - 1
(3.38)
n =0
In the absence of a primary user signal (under hypothesis H0), the non­
ˆ L is theoretically zero, whereas
diagonal element of the covariance matrix R
the diagonal elements contain the noise power. In the presence of a primary
user signal (under hypothesis H1), the nondiagonal elements would become
nonzero, and thus using this property of the covariance matrix, one could
detect the presence of the primary user signal. Based on this, Zeng and Liang
[22] have proposed the following test statistics given by
T1 =
1 L L
å å | Rˆ (u, v ) |
L u =1 v =1 L
T2 =
1 L
å | Rˆ (u, u ) |
L u =1 L
(3.39)
and the detection criteria to make the decisions dˆ to decide on H0 or H1 is
given by
ì 0; decide on H 0 ;
dˆ = í
î 1; decide on H1 ;
if T1/T2 < λ
if T1 /T2 ³ λ
(3.40)
Introduction to Spectrum S­ensing Technique­s
63
As per the above-mentioned detection mechanism, it is assumed that the
sensed wireless signals are correlated such that the resulting covariance matrix
is not diagonal when signal is present (under hypothesis H1).
3.6.2 Eigenvalue-Based Method
The eigenvalue-based method for spectrum sensing and detection is also
based on the computation of the covariance matrix of the sensed signal [22].
The eigenvalues of the covariance matrix are computed, and in turn, are used
to compute the test statistic as given in [22]. Two test statistics are proposed
by Zeng and Liang based on the maximum (Îmax) and the minimum (Îmin)
eigenvalues. The first test statistic is given by
T =
∈max
≷ λ1
∈min
(3.41)
known as the max-min eigenvalue (MME) technique for some threshold l1,
and
T =
ξ
∈min
(3.42)
known as the energy with minimum eigenvalue (EME) technique for some
threshold l2, where x is the energy of the sensed signal. The detection methods based on the test statistics above do not require the knowledge of the
noise power but are based purely on the sensed signal itself, thus considered
to be fully blind sensing techniques.
3.6.3 Wavelet-Based Edge Detection
The wavelet transform was proposed for spectrum sensing for detecting edges
in a wideband spectrum in the frequency domain for detecting one or more
narrowband users [23]. Wavelets transforms in general are used to detect irregularities/singularities in the power spectral density and thus proposed to
be used for detecting spectral irregularities or in other words varying power
levels in the spectral bands over a wide portion of the spectrum. This method
is well suited especially for ultrawideband based cognitive radios that has a
frequency band allocation from 3GHz – 10GHz with many narrowband
incumbent and other users lying within such as WiMAX, C-band satellite,
S-band satellite, Wi-Fi, and DECT. Figure 3.7 depicts the edge detection
graphically considering a wide portion of the spectra. The wavelet detection
64
Cognitive Radio Techniques
Edges
f(Hz)
Figure 3.7 C
oncept of edge detection of narrowband spectral bands using wavelet
­transforms.
method avoids the requirement to have complex bandpass architectures in
the receiver for detecting narrowband users for wideband sensing; however, it
requires high sampling rate when operating the discrete domain.
3.6.4 Spectral Estimation Methods
Traditional spectral estimation methods can also be used for spectrum sensing and detection in cognitive radio networks [24, 25]. Parametric and nonparametric techniques exist in literature for spectral analysis and estimation.
The former method requires a well-defined model for the sensed signal to get
good results and thus is not much considered in cognitive radio applications.
The nonparametric method is therefore considered to be suitable for spectrum sensing in cognitive radios which we briefly present here. We mainly
consider two nonparametric methods, first the multitaper method [26, 27],
and second the filter bank based method [28].
3.6.4.1 Multitaper Method
In the multitaper method–where taper indicating the windowing function
of the signal samples–orthonormal Slepian sequences are considered for
the tapers. The Slepian sequences have a distinguished property where most
of the energy of its Fourier transforms have their energy within a given frequency band for a finitie sample size. This allows one to trade the spectral
resolution for reduced variance of the spectral estimate without leaking signal
energy into adjacent bands. This, therefore, is considered to be a well-suited
technique for spectrum sensing in cognitive radio networks.
Introduction to Spectrum S­ensing Technique­s
65
3.6.4.2 Filter Bank Method
In the filter bank method, a set of bandpass filters with low side-lobes are used
to estimate the signal spectra. This is a very conventional method for spectral
estimation and could also possibly used for spectrum sensing in cognitive radios.
The major disadvantage of this method is obviously the requirement for many
bandpass filters in the receiver; on the other hand, considering multicarrier communications with filter bank structure in the receivers this method could be conveniently utilized for spectrum sensing without any additional requirements.
3.7 Summary
Spectrum sensing for cognitive radio networks is a very popular topic and
many basic techniques that are seen in the literature were presented in this
chapter. The presented techniques vary from blind methods, such as the energy detector method, to partial context aware methods, such as the cyclostationary feature detector method, and all the way to complete context aware
methods, such as the matched filter detection method.
The energy detector is the simplest and is optimal for uncorrelated signal samples with Gaussian distribution. The knowledge of the noise power is
also required to get improved detection performance for the energy detector;
when the noise power is not known precisely, the energy detector performance is limited by the SNR wall [12]. The covariance and the eigenvalue
based methods are more suitable for detecting wireless signals, considering
the signals are correlated in nature. The cyclostationary feature-based method
has better detection performance than the energy-based method, given that
the cyclic features are estimated properly, which requires larger set of samples.
Given the short falls of the spectrum sensing methods presented in this chapter, various other strategies are the topics of the next few chapters.
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