Sith-203_CH03

45

3Introduction 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 vari-ous 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 spectral- user 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

46 CognitiveRadioTechniques

environment. 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 prob-ability of false alarm while minimizing the complexity and time to sense/de-tect 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. Follow-ing 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

0

1

( ) under( )

( ) ( ) under

t Hr t

hs t t H

νν

ìïíïî

;=

+ ; (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 en-ergy 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 im-prove the detection performance of the energy detector.

3.2.1 Energy Detector

In energy-based detectors, the energy-metric of the received signal is com-puted over a given time period T, or equivalently over N samples in the dis-

IntroductiontoSpectrumSensingTechniques 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

0

0( ) ( )

t T

tr t r t dtξ

+= ò (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 re-ceived 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

2

1

2

22 1

( ) ( )[ ]

t

ts t s t dt

t t

αρσ

=- ò (3.3)

For the discrete signal r[n] = r(nTs) the energy-based test statistic is given by

1

0

[ ] [ ]N

sn

T r n r nξ-

=» å (3.4)

where, N is the total number of complex samples and is also known as the time-bandwidthproduct, 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 Nnumber of imaginary component samples present, giving us a total of 2Nsamples. The detection criteria based on the energy-based test statistic is then given by

0

1d

ξ λξ λ

; <ì= í ; ³î

(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


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],

1[ under ] ( 2 )D N wP Pr H Q TBξ λ ρ λ= > ; = , (3.6)

= > ; = Γ , /[ under ] ( 2)P Pr H TBξ λ λ0FA w (3.7)

where, 11( )( ) exp( )aN b

a b u u du¥ -

GG , = -ò is the regularized upper incomplete

Gamma function, G (.) is the Gamma function, QN(a,b) = b

¥ò uNexp(–(u2 +

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 prob-ability 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 perfor-mance improves with increasing values of r by achieving lower miss detection

1010 108 10 6 104 102 10 01010

10 8

10 6

10 4

10 2

10 0

Prof of False Alarm

Prof

ofM

issDe

tect

ion

= 0dB

= 7dB

= 10dB

N = 10

Figure 3.1 ComplementaryROCcurvesfortheenergydetectorforvarioussignaltonoiseratiolevels.


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 chan-nel effects, such as fading or shadowing. In the subsequent sections, we present the energy detector performance under various wireless channel conditions.

ThresholdSelection: 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 prob-ability 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

10 10 10 8 10 6 10 4 10 2 10 010 10

10 8

10 6

10 4

10 2

10 0

Prof of False Alarm

Prof

ofM

issDe

tect

ion

= 5 dB

N = 10

N = 30

N = 50

Figure 3.2 ComplementaryROCcurvesfortheenergydetectorforvariousvaluesoftime-bandwidthproductN.


derived the detection performance of energy detector1 for Rayleigh, Rice, and Nakagami types of fading channels with additive Gaussian noise, which we present here considering no diversity reception. Different types of distri-butions 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,

( ) ( )D NR

P Q a b f dρρ ρ ρ= ,ò (3.8)

where 2 wa TB= and b λ= . Note that the false alarm probability is un-changed from (3.7) because it does not depend on s(t) under H0.

3.2.3.1 RayleighChannel

The probability density function of g in a Rayleigh fading channel is given by

1

( ) exp for 0fγγγ γ

γ γæ ö

= - ³ç ÷è ø (3.9)

where [ ]Eγ 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

( )

12

0

22(1 )

0

1 1exp

2 2

exp exp2 2 2

NnN

Dn

nN

n

Pn

n

λ γγ

λ λ γγ

λ λγ

--

=

- +

=

æ ö- +æ ö æ ö= +ç ÷ ç ÷ ç ÷!è ø è ø è ø

é ùæ ö- -ê úæ ö´ - ç ÷ç ÷ê ú+ !è øè øê úë û

å

å (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 RiceChannel

The probability density function of g in a Rice fading channel is given by

01 (1 ) (1 )

( ) exp 2 for 0K K K K

f K Iγγ γγ γ

γ γ γ

æ öç ÷ç ÷è ø

æ ö+ + += - - ³ç ÷è ø

(3.11)

1. 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).


where, [ ]Eρ 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

2 (1 )

1 1D

K KP Q

K Kγ λ

γ γ

æ öç ÷ç ÷è ø

+= ,+ + + +

(3.12)

3.2.3.3 NakagamiChannel

The probability density function of g in a Nakagami type fading channel is given by

11( ) exp for 0

( )

mmm m

fm

γγγ γ γ

γ γ-æ ö æ ö

= - ³ç ÷ ç ÷G è ø è ø (3.13)

where, m is the Nakagami parameter and [ ]Eγ γ= . Again, by using (3.8) authors in [6] have derived a closed form expression for the detection prob-ability given by

1

1 1 11

( 2) (1 )N um

Du u

β-

=

/ -exp 1

2 2P A F m u

λ λ λ βæ ö æ ö= + - ; + ;ç ÷ ç ÷è ø è øå (3.14)

where, ( )m mβ γ= / + and 1F1(.;.;.) is the confluent hypergeometric function, and A1 for integer values of m is given by

21

1 10

m

im

--

=

(1 ) (1 )exp (1 )

2 2 2m i

m iA L Lλβ λ β λ ββ β β-

é ù- - - -æ ö æ ö æ ö= - + -ê úç ÷ ç ÷ ç ÷è ø è ø è øê úë ûå

(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 chan-nels were presented in the previous section. Here we present the same for re-ceived 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


(3.10), (3.12) and (3.14)], and then average it out for all values of γ . The detection probability therefore is given by

|=

=

∫

∫

( ) ( )

( )

D d

D

P P f d f d

P f d

γ γ γ

γ

γ γ γ γ

γ γ (3.16)

where, Pd is the detection probability under Gaussian channel, ( )fγ 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 chan-nel (without shadowing), and ( )fγ γ is probability density function describ-ing the shadowing component modeled as a Gamma distribution given by

exp( )

γΩ

Ω

− − /= , ≥

Γ

1

( ) for y 0( )

k

ky y

f yk

(3.17)

where, k and W are the parameters describing the shadowing model. Con-sidering a Rayleigh fading channel, the detection probability for the energy detector for the Gamma distributed shadowing model then given by

2

0

0

2

0

1exp( )

2 2

1 1 1( 1) 1 1

2( )

exp( 2) 1 1( 1) 1 1

2( )

nN

Dn

n

kn

nN

kn

Pn

k N U k N k nnk

n k N U n k N knk

λ λ

λ

λ λ

-

=¥

=-

=

æ ö= - ç ÷è ø!

-æ ö æ ö+ G - + - + ; - + ;ç ÷ ç ÷è ø è ø! ΩG Ω

- / æ ö æ ö- G + - + + - + ; + ;ç ÷ ç ÷è ø è ø! ΩG Ω

å

å

å

(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 Uncertainty2

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

2 The authors would like to thank Andrea Mariani (Ph.D. student, University of Bologna) for his con-tribution to Section 3.3.


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 is chosen in order to guarantee a target false alarm rate, DES

FAP , and can be obtained inverting the analytical expression of the false alarm probability. From (3.7) we get

( )12 DESCFAR w FATB Pλ -= G , (3.19)

In this approach, the threshold selected depends on the noise power level, s2. The actual noise power is generally unknown, so we assume that the receiver has

its estimate 2

σ that is typically obtained through a calibration process, and in general, is different from s2. Therefore, in practical applications, we always must consider the adoption of an ED with estimated noise power (ENP) in place of the ideal ED. The adoption of

2σ for threshold setting can cause severe

performance degradations. If the uncertain value s2 is obtained as noise power estimate, threshold mismatch can be avoided including the statistic of the es-timator 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 designcurves [9–11, 13]. The design curve is the relation between the SNR and the number of samples N required to guarantee the desired detec-tion performance, DES

FA FAP P< and DESD DP P> . 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


the probability of false alarm and probability of detection. For the ideal ED, it can be approximated as [10]

( )( )

1 1

1 1

11

1

DESFA N

min ED DESD N

Q PSNR

Q P

-

, -

+-

+ (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 re-duced, increasing the observation time. The ideal ED design curve is plotted in Figure 3.3 (continuous curve), with 0 1DES

FAP = . and 0 9DESDP = . . 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 degrada-tion of the detector performance. In particular, in some practical situations, the design curve has a lower SNR limit, under which the detection is impos-sible even if the observation time tends to infinity. This is the so called SNRwall 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

101 102 103 104 10530

20

10

0

10

20

Ideal EDENP-ED, M = NENP-ED, M

= 1000

BWB-ED, = 1 dB

N

SNR

min

[dB]

Figure 3.3 DesigncurvesfortheidealED,ENP-EDwith = 0.1PDESFAP and 0.9PDES

DP = .ThecorrespondingBWBcurvewith 2 2

max min/ 1 dBρ σ σ= = isalsoshown.


limited range, defined by ( )2 2min maxσ σ, , that contains also the real noise power

level s 2 [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 esti-mated noise power assumes the lowest value 2

minσ , while for the probability of detection it assumes the highest value 2

maxσ . Then the corresponding design curve is given by

( )( )

1 12

2 1 1

11

1

DESFA Nmax

min BWB DESmin D N

Q PSNR

Q P

σσ

-

, -

+× -

+ (3.21)

that gives raise to the SNR wall

2

2lim 1 0maxmin BWB

N minSNR

σσ

,®¥

= - > (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 consid-ered 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 is determined by the choice of ( )2 2

min maxσ σ, .


As an example of ENP-ED, assume that M noise only samples, wn with n = 0,…,M– 1, are available at the receiver.3 Then we can adopt the maxi-mum likelihood noise power estimator defined by

σ

−

== ∑

12

0

[ ] [ ]M

sn

T w n w n (3.23)

The variance of 2

σ is s 2/M. In this case, the design curve of the ENP-ED is given by [27]

σσ

− +

, − − +

+⋅ −+

12

2 1

11

1

DES N MFA NMmax

min ENP ED DES N Mmin D NM

Q PSNR

Q P (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 ENP-ED with = .0 1DES

FAP and 0 9DESDP = . . As can be seen, when M = N (the num-

ber 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 corresponding BWB-ED design curve with 2 2 1max minρ σ σ= / = 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, identify-ing 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.


In the context of cognitive radios, we consider using such analysis for spec-trum sensing and primary user detection [17–20], in which case some de-gree 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 fundamen-tals 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

( ) ( ) [ ( )]x xE t E t mT E x t= + = (3.25)

and

( ) ( ) [ ( ) ( )]x xR t R t mT E x t x tτ τ τ, = + , = + (3.26)

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 peri-odic autocorrelation function can be expressed in terms of the Fourier series given by

( ) ( )exp(2 )x xR t R j tα

ατ τ π α

¥

=-¥, = å (3.27)

where,

1

( ) lim ( ) ( )exp( 2 )2 2

xTT

R x t x t j t dtT

α τ ττ π α®¥

= + - -ò (3.28)

The expression in (3.28) is known as the cycleautocorrelation. Using the Wie-ner relationship, we can define the cyclic power spectrum (CPS) or the spec-tral correlation function as,

( ) ( )exp( 2 )x xS f R j f dα α τ π τ τ¥

-¥= -ò (3.29)


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 do-main 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

0

00

2

20

1 1 1( ) lim lim ( ) ( )

Tx T TTT T

S f X t f t f dtXT T

αα α

/

- /®¥ ®¥= , + , -ò (3.30)

where, ( )T t uX , is the complex conjugate of XT(t,u), and XT(t,u) is given by

2

2( ) ( )exp( 2 )

t TT

t TX t u x v j uv dvπ

+ /

- /, = -ò (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

0.02

050

S x

0

50 50

0

50

(Hz)f(Hz)

Figure 3.4 CyclicspectraldensityforBPSKwithasignaltonoise(power)ratioof0dBestimatedover2000BPSKsymbols.


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

0.04

0.06

0.02

0

S x

0

50 50

0(Hz)

f(Hz)

50 50

Figure 3.5 CyclicspectraldensityforBPSKwithasignaltonoise(power)ratioof0dBestimatedover20BPSKsymbols.


0

1

( ) ( )

( ) ( ) ( )

r

r s

H S f S f

H S f S f S f

α αν

α α αν

: =

: = + (3.32)

where, ( )S fαν is the CPS of the additive noise u(t), and ( )sS fα 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

0

( ) ( )r rf

S f fSα α

α αξ

, ¹= å å (3.33)

where, ( )r fS α is the conjugate of ( )rS fα . The detector is then given by

0

1d

ξ λξ λ

; <ì= í ; ³î

(3.34)

An important point to note here is that one needs sufficient number of sam-ples to get a good estimate of the CPS and hence this method is not so com-putationally efficient. Furthermore, when insufficient number of samples are used the detection performance will tend to get worse due to the poor esti-mate 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 kÎ, k ¹ 0 and ± 2f 0 + k/T0 for "kÎ . Therefore, if the primary user signal falls into one of the signal categories men-tioned above, the cognitive radio device can use the signal information to com-pute 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 tra-ditional matched filter detection technique deployed in digital receivers. Obviously for match filter based spectrum sensing a complete knowledge


of the primary user signal is required (such as the modulation format data rate, carrier frequency, pulse shape, etc). The matched filter detection tech-nique 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

( ) 0

( ) 0

s T t t Th t

elsewhere

- ; £ £ì= í ;î

(3.35)

Figure 3.6 depicts matched filter based spectrum sensing method for pri-mary 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

0 ( )

( )1 ( )

nTd nT

nT

ξ λξ λ

; <ì= í ; ³î

(3.36)

The matched filter-based detector gives better detection probability compared to the previously discussed methods using the energy detector and the cyclo-stationary 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 men-tioned 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.

r(t)

t = T

h(t) = s(T t)

Figure 3.6 Matchedfilterbasedspectrumsensinganddetectionofprimaryusers.


3.6.1 Covariance-Based Method

The covariance of wireless signals and the additive noise component are gen-erally 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

(0) (1) ( 1)

(1) (2) ( 2)ˆ ( )

( 1) ( 2) (0)

L

R R … R L

R R … R Lu v

…

R L R L … R

-é ùê ú-ê ú, =ê ú . . ..ê ú- -ë û

R (3.37)

and for a sample size of N the elements of the sample covariance matrix are given by

1

0

1( ) [ ] [ ] for 0 1 1

N

n

R l r n r n l l … LN

-

== - = , , , -å (3.38)

In the absence of a primary user signal (under hypothesis H0), the non-diagonal element of the covariance matrix ˆ LR is theoretically zero, whereas 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

11 1

21

1 ˆ ( )

1 ˆ ( )

L L

Lu v

L

Lu

T u vL

T u uL

= =

=

= | , |

= | , |

å å

å

R

R (3.39)

and the detection criteria to make the decisions d to decide on H0 or H1 is given by

0 1 2

1 1 2

0 decide on ifˆ1 decide on if

H T Td

H T T

λλ

; ; / <ì= í ; ; / ³î

(3.40)


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

∈ λ∈

= max1

minT ≷ (3.41)

known as the max-min eigenvalue (MME) technique for some threshold l1, and

ξ

∈=

minT (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 meth-ods 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 ir-regularities/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


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 sens-ing and detection in cognitive radio networks [24, 25]. Parametric and non-parametric 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 spec-trum 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 MultitaperMethod

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 fre-quency 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.

f(Hz)

Edges

Figure 3.7 Concept of edge detection of narrowband spectral bands using wavelettransforms.


3.6.4.2 FilterBankMethod

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 com-munications with filter bank structure in the receivers this method could be con-veniently 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 en-ergy detector method, to partial context aware methods, such as the cyclosta-tionary 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 sig-nal 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 perfor-mance 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 chap-ter, various other strategies are the topics of the next few chapters.

References

[1] Yucek, T., and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Ra-dio Applications,” IEEECommunicationsSurveysandTutorials, Vol. 11, No. 1, 2009, pp. 116–130.

[2] Kandeepan, S., et al., Project Report–“D2.1.1: Spectrum Sensing and Monitoring,” EUWB Integrated Project, European Commission funded project (EC: FP7-ICT-215669), May 2009, http://www.euwb.eu, accessed August 4, 2012.

[3] Urkowitz, H., “Energy Detection of Unknown Deterministic Signals,” Proc. of theIEEE, Vol. 55, No. 4, 1967, pp. 523–531.


[4] Lim, T. J., R. Zhang, Y. C. Liang, and Y. Zeng, “GLRT-Based Spectrum Sensing for Cognitive Radio,” Proc.ofIEEEGLOBECOM, New Orleans, LA, 2008.

[5] Kostylev, V. I., Energy Detection of a Signal with Random Amplitude,” Proc.IEEEInt.Conf.onCommun.(ICC02), New York, 2002, pp. 1606–1610.

[6] Digham, F., M. S. Alouini, and M. K. Simon, “On the Energy Detection of Unknown Signals over Fading Channels,” IEEETransactionsonCommunications, Vol. 55, No. 1, 2007, pp. 21–24.

[7] Digham, F., M. S. Alouini, and M. K. Simon, “On the Energy Detection of Unknown Signals over Fading Channels,” inProc.ofIEEEICC, Alaska, 2003.

[8] Atapattu, S., C. Tellambura, and H. Jiang, “Performance of an Energy Detector over Channels with Both Multipath Fading and Shadowing,” IEEETransactionsonWirelessCommunications, Vol. 9, No. 12, 2010, pp. 3662–3670.

[9] Mariani, A., A. Giorgetti, and M. Chiani, “Energy Detector Design for Cognitive Ra-dio Applications,” Proc.IEEEInt.WaveformDiversity&DesignConference, Niagara, NY, 2010, pp. 53–57.

[10] Mariani, A., A. Giorgetti, and M. Chiani, “Effects of Noise Power Estimation on En-ergy Detection for Cognitive Radio Applications,” IEEETransactionsonCommunica-tions, Vol. 59, Issue 12, 2011, pp. 3410–3420.

[11] Sonnenschein, A., and P. M. Fishman, “Radiometric detection of spread-spectrum sig-nals in noise of uncertain power,” IEEEJournalonAerospaceElectronicSystems, Vol. 28, Issue 3, 1992, pp. 654–660.

[12] Tandra, R., and A. Sahai, “SNR Walls for Signal Detection,” IEEEJournalOfSelectedTopicsInSignalProcessing, Vol. 2, No. 1, 2008.

[13] Mariani, A., A. Giorgetti, and M. Chiani, “SNR Wall for Energy Detection with Noise Power Estimation,” Proceeding of IEEE International Conference on Communications(ICC), Kyoto, Japan, 2011.

[14] Tandra, R., and A. Sahai, “Fundamental limits on detection in low SNR under noise uncertainty,” ProceedingsofIEEEInt.ConferenceonWirelessNetworks,CommunicationandMobileComputing, Maui, HI, 2005, pp. 464–469.

[15] Gardner, W. A., “Exploitation of spectral redundancy in cyclostationary signals,” IEEESignalProcessingMagazine, Vol. 8, Issue 2, 1991, pp. 14–36.

[16] Gardner, W. A., A. Napolitano, and L. Paura, “Cyclostationarity: Half a Century of Research,” SignalProcessing, Vol. 86, 2006, pp. 639–697.

[17] Sutton, P. D., K. E. Nolan, and L. E. Doyle, “Cyclostationary Signatures in Practical Cognitive Radio Applications,” IEEEJournalonSelectedAreasinCommunications, Vol. 26, Issue 1, 2008, pp. 13–24.

[18] Dandawate, A. V., and G. B. Giannakis, “Statistical Tests for Presence of Cyclostation-arity,” IEEETransactionsonSignalProcessing, Vol. 42, No. 9, 1994, pp. 2355–2369.


[19] Kyouwoong, K., I. A. Akbar, K. K. Bae, J-S. Urn, C. M. Spooner, et al., “Cyclostation-ary Approaches to Signal Detection and Classification in Cognitive Radio,” IEEEInter-nationalSymposiumonNewFrontiersinDynamicSpectrumAccessNetworks(DySPAN), Dublin, Ireland, 2007, pp. 212–215.

[20] Kandeepan, S., G. Baldini, and R. Piesiewicz, “Experimentally Detecting IEEE 802.11n Wi-Fi Based on Cyclostationarity Features for Ultra-Wide Band Cognitive Radios,” IEEEPersonalIndoorandMobileRadioCommunications(PIMRC)Conference, Tokyo, Japan, 2009.

[21] Gardner, W. A., “Measurement of Spectral Correlation,” IEEETransactionsOnAcous-tics,Speech,AndSignalProcessing, Vol. ASSP-34, No. 5, 1986, pp. 1111–1123.

[22] Zeng, Y., and Y. C. Liang, “Spectrum-Sensing Algorithms for Cognitive Radio Based on Statistical Covariances,” IEEETransactionsOnVehicularTechnology, Vol. 58, No. 4, 2009, pp. 1804–1815.

[23] Zeng, Y., and Y. C. Liang, “Eigenvalue-Based Spectrum Sensing Algorithms for Cognitive Radio,” IEEE Transactions On Communications, Vol. 57, No. 6, 2009, pp. 1784–1793.

[24] Tian, Z., and G. B. Giannakis, “A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios,” ProceedingsofIEEE/ICSTConferenceonCROWNCOM, Myko-nos, Greece, 2006.

[25] Kay, S. M., ModernSpectralEstimation:TheoryandApplication, Englewood Cliffs, NJ: Prentice Hall, 1999.

[26] Stoica, P., and R. Moses, SpectralAnalysisofSignals, Pearson/Prentice Hall, 2005.

[27] Thomson, D. J., “Spectrum estimation and harmonic analysis,” ProceedingsoftheIEEE,Vol. 70, No. 9, 1982, pp. 1055–1096.

[28] Thomson, D. J., MultitaperAnalysisofNonstationaryandNonlinearTimeSeriesData, Cambridge University Press, 2000.

[29] Farhang-Boroujeny, B., “Filter Bank Spectrum Sensing for Cognitive Radios,” IEEETransactionsonSignalProcessing, Vol. 56, No. 5, 2008, pp. 1801–1811.

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