Spectrum Sensing Techiniques for Cognitive Radios

Technical University of Crete, Greece
Department of Electronic and Computer Engineering

Spectrum Sensing Techniques
for
Cognitive Radios

Konstantinos E. Bountouris

Thesis Committee

Professor Athanasios P. Liavas (ECE)
Professor Michael Paterakis (ECE)
Assistant Professor Aggelos Bletsas (ECE)

Chania, September 2013


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September 2013

Πολυτεχνειο Κρητης
Τμημα Ηλεκτρονικων Μηχανικων και Μηχανικων Υπολογιστων

Τεχνικές Αίσθησης Φάσματος
για
Ευφυή Ραδιόφωνα

Κωνσταντίνος Ε. Μπουντούρης

Εξεταστική Επιτροπή

Καθηγητής Αθανάσιος Π. Λιάβας (ΗΜΜΥ)
Καθηγητής Μιχαήλ Πατεράκης (ΗΜΜΥ)
Επίκουρος Καθηγητής ΄Αγγελος Μπλέτσας (ΗΜΜΥ)

Χανιά, Αύγουστος 2013


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September 2013

Abstract
The tremendous ongoing growth of wireless digital communications has raised
spectrum shortage and security issues. In particular, the need for new spectrum
is the main obstacle in continuing this growth. Recent studies on radio spectrum usage have shown that pre-allocation of spectrum bands to specific wireless
communication applications leads to poor utilization of those allocated bands.
Therefore, research into new techniques for efficient spectrum utilization is being aggressively pursued by academia, industry and government. Such research
efforts have given birth to Cognitive Radio (CR). CR is the new key enabling
technology that is presented as a solution to the spectrum scarcity. CRs are unlicensed devices that, through their most important functionality, i.e. spectrum
sensing, sense the spectrum and they transmit without interfering with the licensed users. In order to do that, they use several spectrum sensing techniques.
These techniques are used to detect the presence or absence of the primary user’s
signal. Spectrum sensing for one CR user has many challenges to overcome, such
as multipath fading or shadowing. Thus, in that occasion we can utilize cooperative spectrum sensing. This type of sensing is realized in a CR network and
the presence or absence of the primary user’s signal is decided by many users or
a base station. In this thesis, we are giving important background information
about CRs and how we were lead to that technology. Moreover, we are going to
describe the problem of spectrum sensing, what are the spectrum holes and the
challenges that a CR must face in order to sense the RF spectrum efficiently. A
big part of this thesis is the profound study of the most important techniques for
sensing the spectrum and the comparison among them. Finally, we are discussing
Cooperative Spectrum Sensing; the way it can be implemented and the problems
that it can solve.

Περίληψη
Η τεράστια συνεχιζόμενη ανάπτυξη των ασύρματων ψηφιακών επικοινωνιών έχει
προκαλέσει έλλειψη στις ελεύθερες συχνότητες του ραδιοφάσματος αλλά επίσης και
σε θέματα ασφαλείας. Ειδικότερα, η ανάγκη για νέες ζώνες συχνοτήτων στο ραδιοφάσμα είναι το κύριο εμπόδιο στην συνέχιση αυτής της ανάπτυξης. Πρόσφατες
μελέτες σχετικά με τη χρήση του ραδιοφάσματος έχουν δείξει ότι η εκ των προτέρων
κατανομή των ζωνών του φάσματος σε συγκεκριμένες εφαρμογές ασύρματης επικοινωνίας οδηγεί σε κακή χρήση αυτών των κατανεμημένων ζωνών. Ως εκ τούτου, η
ακαδημαϊκή κοινότητα, η βιομηχανία και οι κυβερνήσεις επιδιώκουν την έρευνα για
νέες τεχνικές για την αποτελεσματικότερη χρήση του φάσματος. Τέτοιες ερευνητικές προσπάθειες έχουν γεννήσει την τεχνολογία των Cognitive Radios (CR). Με
τον όρο CR εννοούμε την νέα κύρια τεχνολογία που παρουσιάζεται ως λύση στην
έλλειψη φάσματος. Τα CRs είναι συσκευές οι οποίες δεν έχουν άδεια για χρήση της
συγκεκριμένης ζώνης συχνοτήτων στην οποία επιθυμούν να εκπέμψουν, ωστόσω
μέσω της πιο σημαντικής λειτουργίας τους, της αίσθησης του ραδιοφάσματος, μεταδίδουν χωρίς να παρεμβάλλουν τους χρήστες που έχουν πληρώσει και έχουν
άδεια να χρησιμοποιήσουν αυτή τη ζώνη συχνοτήτων. Για να το κάνουν αυτό,
χρησιμοποιούν διάφορες τεχνικές ανίχνευσης φάσματος. Αυτές οι τεχνικές χρησιμοποιούνται για την ανίχνευση της ύπαρξης ή της απουσίας του σήματος του
εξουσιοδοτημένου χρήστη. Η αίσθηση του φάσματος έχει πολλές προκλήσεις να
ξεπεράσει, όπως η πολλαπλή όδευση του σήματος ή η επισκίαση ενός χρήστη. ΄Ετσι, με την ευκαιρία αυτή μπορούμε να χρησιμοποιήσουμε τη συνεργατική αίσθηση
φάσματος. Αυτό το είδος της αίσθησης πραγματοποιείται σε ένα δίκτυο με πολλούς χρήστες CRs και η ύπαρξη ή η απουσία του σήματος του εξουσιοδοτημένου
χρήστη αποφασίζεται από πολλούς χρήστες ή έναν σταθμό βάσης με τον οποίο συνεργάζονται οι δευτερεύοντες χρήστες. Στην παρούσα εργασία, δίνουμε σημαντικές
πληροφορίες σχετικά με τα CRs και πώς έχουμε οδηγηθεί σε αυτή την τεχνολογία.
Επιπλέον, πρόκειται να περιγράψουμε το πρόβλημα της ανίχνευσης φάσματος, τι είναι
και πως δημιουργούνται οι τρύπες του φάσματος και οι προκλήσεις που πρέπει να
αντιμετωπίσει το CR προκειμένου να γίνει η λειτουργία της αίσθησης του φάσματος
ραδιοσυχνοτήτων αποτελεσματικά. ΄Ενα μεγάλο μέρος αυτής της διπλωματικής εργασίας είναι η εις βάθος μελέτη των πιο σημαντικών τεχνικών για την ανίχνευση του
φάσματος και η σύγκριση μεταξύ τους. Τέλος, συζητάμε τη συνεργατική αίσθηση
φάσματος, τον τρόπο με τον οποίο μπορεί να εφαρμοστεί και τα προβλήματα που
μπορεί να επιλύσει.

Acknowledgements
First of all, I would like to thank my family, Evangelos, Androniki, Athina, for
their support and encouragement in all these years. Without them I am not sure
if I could manage to receive my diploma.
I, also, would like to thank my friends in Chania, Christos, Dimitris, Dimitris, Dimosthenis, Giorgos, Manos, Nikos, Stathis, Vag, Vassilis, Viky for their
support and for the great moments that we had the last years.
Finally, I wish to thank my supervisor, professor Athanasios Liavas, for his
guidance and the choice of this challenging topic. Whenever I had questions he
was there to answer to me and I am grateful to him because I learned many
things.


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September 2013

Contents
1 Introduction
1.1 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Cognitive Radios
2.1 Introduction . . . . . . . . . . . .
2.2 The vision of Cognitive Radios . .
2.3 Definitions of Cognitive Radios .
2.3.1 Software-Defined Radio . .
2.4 Functions of Cognitive Radios . .
2.5 Applications of Cognitive Radios
2.6 IEEE 802.22 . . . . . . . . . . . .

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3 Spectrum Sensing and Analysis
3.1 Introduction . . . . . . . . . . . . . . . . . . .
3.2 Spectrum Sensing . . . . . . . . . . . . . . . .
3.3 Spectrum Holes . . . . . . . . . . . . . . . . .
3.3.1 Temporal Spectrum Holes . . . . . . .
3.3.2 Spatial Spectrum Holes . . . . . . . . .
3.4 Challenges of Spectrum Sensing . . . . . . . .
3.5 Classification of Spectrum Sensing Techniques
4 Spectrum Sensing Techniques
4.1 Introduction . . . . . . . . . . . . .
4.2 Neyman-Pearson Theorem . . . . .
4.3 Matched Filter Detection . . . . . .
4.3.1 Generalized Matched Filter


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September 2013

CONTENTS

4.3.2 Pilot-Based Detection . . . . . . . . . . . . . . . . . . . .
Energy Detection . . . . . . . . . . . . . . . . . . . . . . . . . . .
Covariance-Based Detection . . . . . . . . . . . . . . . . . . . . .

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5 Comparison
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Energy Detection vs Matched Filter Detection . . . . . . . . . . .
5.3 Energy Detection vs Matched Filter Detection vs Covariance Based
Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Cooperative Spectrum Sensing
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
6.2 General Concept . . . . . . . . . . . . . . . . . . .
6.2.1 Challenges . . . . . . . . . . . . . . . . . . .
6.3 Methods of Cooperative Spectrum Sensing . . . . .
6.3.1 Centralized Sensing . . . . . . . . . . . . . .
6.3.2 Distributed Sensing . . . . . . . . . . . . . .
6.3.3 External Sensing . . . . . . . . . . . . . . .
6.4 Practical Considerations about Cooperative Sensing

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7 Conclusion
7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References

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4.4
4.5


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September 2013

List of Figures
2.1
2.2
2.3
2.4

2.5
3.1

3.2

3.3
4.1
4.2
4.3
4.4

Bar Graph of the Spectrum Occupancy in Each Band in New York
City and Chicago, USA. . . . . . . . . . . . . . . . . . . . . . . .
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Spectrum Occupancy Measured in Each Band at Commission for
Communications Regulation Building, Dublin, Ireland. . . . . . .
7
Cognitive Radio duty cycle [“Advances in CR Networks: A survey”, Beibei Wang, K.J. Ray Liu] . . . . . . . . . . . . . . . . . . 11
Example of public safety and emergency responder teams within
the same geographical area operating on different center frequencies and potentially using different communication standards. [“Cognitive Radios Communications and Networks, p.10”] . . . . . . . . 14
IEEE 802.22 WRAN service topology . . . . . . . . . . . . . . . . 15
Various aspects of spectrum sensing for Cognitive Radio. [Yucek
and Arslan: “A survey of spectrum sensing algorithms for cognitive
radio applications”] . . . . . . . . . . . . . . . . . . . . . . . . . .
Spectrum holes for secondary communication. (a) Temporal spectrum holes and (b) spatial spectrum holes. [“Signal Processing in
Cognitive Radio”, J. Ma, G.Y. Li, B.H. Juang] . . . . . . . . . . .
The hidden licensed user problem in cognitive radio systems. . . .
PDFs for hypothesis testing problem. . . . . . . . . . . . . . . . .
Neyman-Pearson detector for deterministic signals (replica correlator). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Right tail probability for standard normal PDF. . . . . . . . . . .
Detection performance of matched filter for target PF A = 10−1 and
PF A = 10−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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September 2013

LIST OF FIGURES

Detection performance of matched filter for target PF A = 10−5 and
PF A = 10−7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.6

ROC curves for MF detector under different values of SN RdB . . .

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4.7

Performance of detection for the generalized MF for a variety of
target PF A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.8

ROC for the generalized MF for a variety of values of EN RdB . . .

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4.9

PDF for central chi-squared random variable. . . . . . . . . . . .

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4.10 PDF for non central chi-squared random variable with varying degrees of freedom (ν) and noncentrality parameter λ = 4. . . . . .

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4.11 ROC curves for coherent detection for different values of SN RdB .

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4.12 Performance of detection for the ED for a variety of target PF A . .

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4.13 ROC for the ED for a variety of values of SN RdB . . . . . . . . . .

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4.5

4.14 ROC for the MME detection for different values of the SN R in dB. 49
5.1
5.2
5.3
5.4
5.5

6.1

6.2
6.3

Comparison of Energy Detector and Matched Filter Detector for
SN R = −6 dB . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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SN R = 0 dB . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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SN R = 2 dB . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Comparison of Energy Detector, Matched Filter Detector and MaxMin Eigenvalue Detection for SN R = −2.4 dB. . . . . . . . . . .

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Comparison of Energy Detector, Matched Filter Detector and MaxMin Eigenvalue Detection SN R = 3 dB. . . . . . . . . . . . . . .

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Cooperative spectrum sensing in CR networks. CR1 is shadowed
over the reporting channel and CR3 is shadowed over the sensing
channel. [Letaief and Zhang: “Cooperative Communications for
Cognitive Radio Networks”] . . . . . . . . . . . . . . . . . . . . .

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ROC curves for fusion rules in centralized cooperative spectrum
sensing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Complementary ROC curves for fusion rules in centralized cooperative spectrum sensing. . . . . . . . . . . . . . . . . . . . . . . .

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September 2013

LIST OF FIGURES

6.4

6.5

Principles of hard combination schemes (a) One-bit counting scheme
and (b) two-bit hard combination scheme. [Ma et al.: “Signal Processing in Cognitive Radio”] . . . . . . . . . . . . . . . . . . . . .
Schematic representation of the AF cooperation scheme in a decentralized CR network. [Ma et al.: “Signal Processing in Cognitive
Radio”] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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September 2013

LIST OF FIGURES


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September 2013

Chapter 1
Introduction
As wireless digital communications continue to grow driven by consumers’ interest in wireless services, more and more spectrum resources will be needed. On
the one hand, the increased diversity (voice, short message, Web, multimedia
etc) and demand of high quality-of-service (QoS) applications have resulted in
overcrowding of the officially allocated spectrum bands which leads to poor user
satisfaction. On the other hand, major licensed bands, such as those allocated for
television broadcasting, amateur radio and telemetry data, have been found to
be largely underutilized, resulting in spectrum wastage. The above were derived
by a survey of spectrum utilization made by the Federal Communications Commission (FCC) and published in November 2002 [1]. FCC is the main regulatory
body for distributing spectrum bands to licensed users in USA. To overcome these
problems, the FCC has been considering more flexible and comprehensive uses of
the available spectrum, through the use of the Cognitive Radio (CR) technology.
CRs are wireless devices that are used for the improvement of spectrum utilization. They achieve that by letting a secondary user (SU), also referred as an
unlicensed user, to exploit a spectrum band when it is not used by a primary
user (PU), also referred as a licensed user. PUs have higher priority than SUs or
legacy rights on the usage of a specific part of the spectrum. The spectrum bands
that are not used by the PUs are called spectrum holes. CRs have the ability to
sense and adapt to the environment continuously in order to detect the presence
of the PUs’ signal. Once they detect the PUs’ signal, they stop transmitting in


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September 2013

1. INTRODUCTION

that spectrum band and they continue to sense the spectrum in order to find
another spectrum hole for their transmission.
Among the many functionalities of a CR (they will be discussed later in more
details), the most important is spectrum sensing, as mentioned above. It is the
most important functionality because if a CR senses well its environment, the
spectrum will be utilized more efficiently, as well as there will be high QoS for
the PUs (no collisions, interference etc). The problem of spectrum sensing is to
decide whether there is PU’s signal or not. The detection or not of the primary
signal (the signal of the PU) can be realized from the CR by using the spectrum
sensing techniques. There are several algorithms for the detection of the primary
signal, but in this thesis we focus on “Matched Filter Detection” (MF), “Energy
Detection” (ED) and, finally, “Covariance Based Detection” and a variation of
it.
Traditional wireless networks have predominantly used direct point-to-point
or point-to-multipoint (e.g., cellular) topologies. The difference between these
traditional methods and cooperative spectrum sensing is that the latter method
allows different users or nodes in a wireless network to share resources and to
create collaboration through distributed transmission and processing, in which
each user’s information is sent out not only by the user but also by the collaborating users. This method promises significant capacity and multiplexing gain
increase in wireless networks as well as a new form of space diversity to combat
the detrimental effects of severe fading and shadowing.

1.1

Thesis Outline

The rest of the thesis is organized as follows: in Chapter 2 we are giving important
background information about CRs and how we were lead to that technology.
Furthermore, the different definitions, the applications, the functionalities of CR
and a brief description of IEEE 802.22 are going to be discussed. In Chapter 3
we are going to describe the problem of spectrum sensing, what are the spectrum
holes and the challenges that a CR must face in order to sense the RF spectrum
efficiently. In Chapter 4 we are going to discuss in depth the most important
techniques for sensing the spectrum. We are analyzing the model, the decision


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September 2013

1.1 Thesis Outline

statistic and we are deriving the performance of these techniques. Moreover, we
are giving in figures the performance of the detectors. In Chapter 5 we are going
to compare the different spectrum sensing techniques and the findings are going
to be discussed. In Chapter 6 Cooperative Spectrum Sensing, the way it can be
implemented and the problems that it can solve are going to be briefly discussed.
Chapter 7 serves as an epilogue to this thesis.


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September 2013

1. INTRODUCTION


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September 2013

Chapter 2
Cognitive Radios
2.1

Introduction

In this chapter we shall give some background information about the Cognitive
Radios. In section 2.2, we discuss the background of CRs and the reasons which
lead to the capturing of that idea. In section 2.3, we show the different definitions
for CRs and in section 2.4 we are discussing the main functionalities of a CR. In
section 2.5, we point out the most important applications of the CRs. Finally,
the working group that has been formed by IEEE (802.22 WRAN) is going to be
discussed briefly in section 2.6.

2.2

The vision of Cognitive Radios

The need for higher data rates is increasing as a result of the transition from
voice-only communications to multimedia type applications. The requirements
for this heavy load of data are large and it is obvious that the current static
frequency allocation schemes cannot accommodate them. As a result, we must
find new techniques for exploiting the available spectrum more efficiently.
Cognitive radio is the new key enabling technology that enables next generation communication networks to utilize the spectrum more efficiently in an
opportunistic way without interfering with the PUs. In a report by the Shared
Spectrum Company (SSC) in 2007 it was shown that the spectrum was not used


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September 2013

2. COGNITIVE RADIOS

Figure 2.1: Bar Graph of the Spectrum Occupancy in Each Band in New York
City and Chicago, USA.

effectively in almost all currently deployed frequency bands in USA (the same
results were derived from measurements in other countries as well). Figures 2.1
and 2.2 show the spectrum occupancy for the region of bands in the 30 MHz to 3
GHz with the measurements taken in New York City and Chicago (USA) and in
Dublin, Ireland (EU) for the period 16-18 April 2007; these results are from the
report of SSC. The spectrum occupancy in Dublin, Ireland is similar to the ones
in Chicago and New York. This proves that the inefficient usage of frequency
spectrum is a problem not only in USA, but also in European countries. Thus,
CRs is a solution to spectrum scarcity.
The term Cognitive Radio was first introduced in the pioneering work of


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September 2013

2.2 The vision of Cognitive Radios

Figure 2.2: Spectrum Occupancy Measured in Each Band at Commission for
Communications Regulation Building, Dublin, Ireland.


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September 2013

2. COGNITIVE RADIOS

Joseph Mitola III [2]. In Mitola’s dissertation (KTH Royal Institute of Technology, Stockholm, Sweden, 2000 ) and a number of publications [3], he envisioned
such a self-reconfiguring radio and dubbed the term Cognitive Radio for it. According to Mitola’s early vision, a CR would be realized through the integration
of model-based reasoning with software radio and would be trainable in a broad
sense, instead of just programmable. In analogy with the mental process of
cognition, Mitola also outlined a cognitive cycle through which such radio can
reconfigure itself through an ongoing process of awareness (both of itself and
the outside world), perception, reasoning, and decision making (Fig. 2.3). The
concept of CR emphasizes enhanced quality of information and experience for
the user, with cognition and reconfiguration capabilities as a means to this end.
Today, however, CR has become an all-encompassing term for a wide variety of
technologies that enable radios to achieve various levels of self-configuration, and
with an emphasis on different functionalities, ranging from ubiquitous wireless
access, to automated radio resource optimization, to dynamic spectrum access
for a future device-centric interference management, to the vision of an ideal CR.
The main characteristics of CRs are reconfigurability and intelligent adaptive
behavior. Here by intelligent adaptive behavior we mean the ability to adapt
without being a priori programmed to do this; that is, via some form of learning. From this it follows that cognitive radio functionality requires at least the
following capabilities:
• Flexibility and agility, the ability to change the waveform and other radio

operational parameters on the fly. In contrast, there is a very limited extent that the current multichannel multiradio (MC-MR) can do this. Full
flexibility becomes possible when CRs are built on top of SDRs (2.3.1). Another important requirement to achieve flexibility, which is less discussed,
is reconfigurable or wideband antenna technology.

• Sensing, the ability to observe and measure the state of the environment,
including spectral occupancy. Sensing is necessary if the device is to change
its operation based on its current knowledge of RF environment.


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September 2013

2.3 Definitions of Cognitive Radios

• Learning and adaptability, the ability to analyze sensory input, to recognize
patterns, and modify internal operational behavior based on the analysis of

a new situation, not only based on precoded algorithms but also as a result
of a learning mechanism.

2.3

Definitions of Cognitive Radios

CR has drawn great attention due to its potential for solving current spectrum
shortage problems and enhancing radio communication performance. These result in many academic institutions and industries generating various definitions
for CR, according to their own needs, based on the original definition by Mitola
in 1999. In this section we are going to point out the most popular definitions
for CR:
By Joseph Mitola “A radio that employs model based reasoning to achieve a
specified level of competence in radio-related domains.”
By Simon Haykin “Cognitive Radio is an intelligent wireless communication
system that is aware of its surrounding environment and uses the methodology of understanding-by-building to learn from the environment and adapt
its internal states to statistical variations in the incoming RF stimuli by
making corresponding changes in certain operating parameters (e.g. transmit power, carrier-frequency and modulation strategy) in real time, with two
primary objectives in mind
• highly reliable communications whenever and wherever needed;
• efficient utilization of the radio spectrum”.
By FCC “A cognitive radio is a radio that can change its transmitter parameters
based on interaction with the environment in which it operates”.
From the first and the second definition six words stand out: awareness, intelligence, learning, adaptability, reliability and efficiency. These are the cognitive
capabilities that a CR must have and thanks to the advances of digital signal
processing (DSP), networking, machine learning, computer software (SW) and


9

September 2013

2. COGNITIVE RADIOS

computer hardware (HW). Except of these cognitive capabilities, a CR has another one which is borrowed from by a platform known as Software-Defined Radio
(SDR). On this platform the CR is built.
In the subsection 2.3.1 we give a brief description of what an SDR is.

2.3.1

Software-Defined Radio

A SDR is a radio in which the properties of carrier frequency, signal bandwidth,
modulation and network access are defined by SW. It is a general-purpose device
in which the same radio tuner and processors are used to implement many waveforms at many frequencies. The advantage of this approach is that the equipment
is more versatile and cost-effective. Additionally, it can be upgraded with new
SW for new waveforms and new applications after sale, delivery and installation.

2.4

Functions of Cognitive Radios

A typical duty cycle of CR, as illustrated in Figure 2.3, includes detecting spectrum white space, selecting the best frequency bands, coordinating spectrum
access with other users and vacating the frequency when a primary user appears.
Such a cognitive cycle is supported by the following functions:
• spectrum sensing and analysis,
• spectrum management and handoff,
• spectrum allocation and sharing.
Through spectrum sensing and analysis, CR can detect the spectrum white
space, i.e. a portion of frequency band that is not being used by the primary users,
and utilize the spectrum. On the other hand, when primary users start using the
licensed spectrum again, CR can detect their activity through sensing, so that no
harmful interference is generated due to SUs’ transmission. After recognizing the
spectrum white space by sensing, spectrum management and handoff function
of CR enables SUs to choose the best frequency band and hop among multiple
bands according to the time varying channel characteristics to meet various QoS


10

September 2013

2.4 Functions of Cognitive Radios

Figure 2.3: Cognitive Radio duty cycle [“Advances in CR Networks: A survey”,
Beibei Wang, K.J. Ray Liu]

requirements. For instance, when a PU reclaims his/her frequency band, the SU
that is using the licensed band can direct his/her transmission to other available
frequencies, according to the channel capacity determined by the noise and interference levels, path loss, channel error rate, holding time, and etc. In dynamic
spectrum access, a SU may share the spectrum resources with PUs, other SUs,
or both. Hence, a good spectrum allocation and sharing mechanism is critical
to achieve high spectrum eﬃciency. Since PUs own the spectrum rights, when
SUs co-exist in a licensed band with PUs, the interference level due to secondary
spectrum usage should be limited by a certain threshold. When multiple SUs
share a frequency band, their access should be coordinated to alleviate collisions
and interference.


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September 2013

2. COGNITIVE RADIOS

2.5

Applications of Cognitive Radios

Because CRs are able to sense, detect and monitor the surrounding RF environment such as interference and access availability and reconfigure their own
operating characteristics to best match outside situations, cognitive communications can increase spectrum efficiency and support higher bandwidth service.
Thus, there are many application in which a CR can be employed. The most
popular and useful are discussed:
For military communications The capacity of military communications in
limited by radio spectrum scarcity because static frequency assignments
freeze bandwidth into unproductive applications, where a large amount of
spectrum is idle. CR using dynamic spectrum access can relieve the spectrum congestion through efficient allocation of bandwidth and flexible spectrum access. Therefore, CR can provide military with adaptive, seamless
and secure communication.
Public safety A CR can be implemented to enhance public safety and homeland
security. A natural disaster or terrorist attack can destroy existing communication infrastructure, so an emergency network becomes indispensable to
aid the search and rescue. As a CR can recognize spectrum availability and
reconfigure itself for much more efficient communication, this provides public safety staff with dynamic spectrum selectivity and reliable broadband
communication to minimize information delay. Moreover, CR supports interoperability between various communication systems. By adaptation to
the different network, CR can sustain multiple service types.
In Figure 2.4, an example of public safety teams is shown. Members of Team
A employ a communications standard operating on a carrier frequency that
is different from the communication equipment employed by both Teams
B and C. Thus, unless these teams are coordinated with respect to operating parameters and communication standards, effective communications
between them would be nearly impossible.


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September 2013

2.6 IEEE 802.22

Commercial purposes Finally, another very promising application of CR is
in the commercial markets for wireless technologies. Since CR can intelligently determine which communication channels are in use and automatically switches to an unoccupied channel, it provides additional bandwidth
and versatility for rapidly growing data applications. Moreover, the adaptive and dynamic channel switching can help avoid spectrum conflict and
expensive redeployment. As CR can utilize a wide range of frequencies,
some of which has excellent propagation characteristics, CR devices are
less susceptible to fading related to growing foliage, buildings, terrain and
weather. When frequency changes are needed due to conflict or interference, the CR frequency management software will change the operating
frequency automatically even without human intervention. Additionally,
the radio software can change the service bandwidth remotely to accommodate new applications. As long as no end-user hardware needs to be
updated, product upgrades or configuration changes can be completed simply by downloading newly released radio management software. Thus, CR
is viewed as the key enabling technology for future mobile wireless services
anywhere, anytime and with any device.

2.6

IEEE 802.22

IEEE 802.22 standard is known as cognitive radio standard because of the cognitive features it contains. The standard is still in the development stage. One of
the most distinctive features of the IEEE 802.22 standard is its spectrum sensing
requirement. IEEE 802.22 based wireless regional area network (WRAN) devices
sense TV channels and identify transmission opportunities. The functional requirements of the standard require at least 90% probability of detection and at
most 10% probability of false alarm for TV signals with - 116 dBm power level
(approximately 0.001 pW ) or above. The sensing is envisioned to be based on
two stages: fast and fine sensing. In the fast sensing stage, a coarse sensing algorithm is employed, e.g. energy detector. The fine sensing stage is initiated based
on the fast sensing results. Fine sensing involves a more detailed sensing where


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September 2013

2. COGNITIVE RADIOS

Figure 2.4: Example of public safety and emergency responder teams within the
same geographical area operating on different center frequencies and potentially
using different communication standards. [“Cognitive Radios Communications
and Networks, p.10”]

more powerful methods are used. Several techniques that have been proposed
and included in the draft standard include energy detection, waveform-based
sensing (PN511 or PN63 sequence detection and/or segment sync detection), cyclostationary feature detection, and matched filtering. A base station (BS) can
distribute the sensing load among subscriber stations (SSs). The results are returned to the BS which uses these results for managing the transmissions. Hence,
it is a practical example of centralized collaborative sensing. Another approach
for managing the spectrum in IEEE 802.22 devices is based on a centralized
method for available spectrum discovery. The BSs would be equipped with a
global positioning system (GPS) receiver which would allow its position to be
reported. The location information would then be used to obtain the information
about available TV channels through a central server. For low-power devices
operating in the TV bands, e.g. wireless microphone and wireless camera, external sensing is proposed as an alternative technique. These devices periodically
transmit beacons with a higher power level. These beacons are monitored by
IEEE 802.22 devices to detect the presence of such low-power devices which are
otherwise difficult to detect due to the low-power transmission. Figure 2.5 shows


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September 2013

2.6 IEEE 802.22

Figure 2.5: IEEE 802.22 WRAN service topology

the service topology for the IEEE 802.22 WRAN.


15

September 2013

2. COGNITIVE RADIOS


16

September 2013

Chapter 3
Spectrum Sensing and Analysis
3.1

Introduction

Through spectrum sensing, CRs can obtain useful information about their surrounding radio environment, such as the presence of PUs and appearance of
spectrum holes. Only with this information a CR can adapt its transmitting and
receiving parameters, like transmission power, frequency, modulation schemes
etc., in order to achieve eﬃcient spectrum utilization and avoid interference to
the PUs’ signals. Therefore, spectrum sensing and analysis is a critical step towards dynamic spectrum management.

3.2

Spectrum Sensing

Spectrum sensing enables the capability of a CR to measure, learn and be aware of
the radio’s operating environment, such as the spectrum availability and power,
noise temperature, interference status etc. When a certain frequency band is
detected as not being used by the primary licensed user of the band at a particular time in a particular position (spectrum hole), SUs can utilize the spectrum,
i.e. there exists a spectrum opportunity. Therefore, spectrum sensing can be
performed in the time, frequency, space and code dimensions. With the recent
development of transmit beamforming, multiple users can utilize the same channel/frequency at the same time in the same geographical location. Thus, in the


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September 2013

3. SPECTRUM SENSING AND ANALYSIS

case that a PU does not transmit in all directions, extra spectrum opportunities
can be created for SUs in the directions where the PU is not operating.
Spectrum sensing helps CRs to gain awareness of their radio environment, in
a manner that they know if a band is used by a PU in a geographical area. This
awareness can be obtained by using beacons, by using geolocation and databases
or by performing local spectrum sensing at cognitive radios. Recently, the latter
method is used more than the others because of its broader application and lower
infrastructure requirement.
Figure 3.1 shows the various aspects of spectrum sensing for CRs. In this chapter, we are going to analyze the phenomenon of spectrum holes in section 3.3, the
challenges of spectrum sensing for CRs in section 3.4 and, finally, a classification
according to the requirements that each method needs in order to be implemented
will be discussed in section 3.5.

Figure 3.1: Various aspects of spectrum sensing for Cognitive Radio. [Yucek and
Arslan: “A survey of spectrum sensing algorithms for cognitive radio applications”]

3.3

Spectrum Holes

Spectrum Hole is defined as a licensed spectrum band that can be used by Cognitive Radio users without interfering the primary users.


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September 2013

3.3 Spectrum Holes

In general, spectrum holes can be divided into two categories: temporal and
spatial spectrum holes. A further analysis is following and Figure 3.2 shows
temporal (a) and spatial (b) spectrum holes.

3.3.1

Temporal Spectrum Holes

A temporal spectrum hole means that there is no transmission over the spectrum
band of interest during the time of sensing. Thus, this band can be utilized by
CR in the current time slot. The PUs and the SUs are located in the same area,
in the sense that there can be interference between them. The CR avoids that by
exploiting the spectrum holes in time, in order not to interfere the licensed user.
Consequently, it is relatively easy to detect the presence or absence of the primary
user activity since CRs only need to have a similar detection sensitivity as regular
primary receivers and the only thing that is mandatory to do is to identify the
presence of the primary signal, rather than demodulating and decoding it. So,
there is no need for high complexity in signal processing.

3.3.2

Spatial Spectrum Holes

A spatial spectrum hole exists when the spectrum band of interest is occupied by
the primary transmission only in a restricted geographical area. Thus, this band
can be utilized by CRs only when they appear outside of this area. The diﬀerence
between temporal and spatial holes is that for the CRs to be able to use the latter
they must be outside of the transmission coverage area of the PUs. Since there
are no PUs outside the coverage area, secondary communication over the licensed
band is allowed if and only if the CR does not interfere with the operation of the
PU inside the coverage area. In this case, the detection of the PU’s signal from
the SU is a diﬃcult task, because the SU falls out of the coverage area of the PU’s
transmission. Therefore, it is comprehensible that the CR needs high complexity
in signal processing, because is it obligatory that the PU’s transmission will be
detected at any location where there would be interference.


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September 2013


Figure 3.2: Spectrum holes for secondary communication. (a) Temporal spectrum
holes and (b) spatial spectrum holes. [“Signal Processing in Cognitive Radio”, J.
Ma, G.Y. Li, B.H. Juang]


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September 2013

3.4 Challenges of Spectrum Sensing

3.4

Challenges of Spectrum Sensing

In this section we are about to point out some challenges and other issues that
spectrum sensing must face so as the CR to have a proper operation.
Hardware Requirements Spectrum sensing for CR applications requires high
sampling rate, high resolution analog-to-digital converters (ADC) with large
dynamic range and high speed signal processors. On the one hand, the noise
interference problem is easier for these purposes as receivers are tuned to
receive signals that are transmitted over a desired bandwidth. Moreover,
simple receivers are capable of processing narrowband baseband signals with
low complexity and power consumption. On the other hand, CR terminals
are required to process transmission over a much wider band for utilizing
any opportunity. Hence, CR should be able to capture and analyze a relatively larger band for identifying spectrum opportunities. Thus, additional
requirements on the components in radio frequency (RF) bands, such as
antennas and power ampliﬁers, are needed and they must operate in a wide
range of frequencies. Also, high speed processors (DSPs or FPGAs) with
low computationally complexity are necessary.
Hidden Primary User Problem This is a very serious problem for a CR user
and it can be caused by many factors including severe multipath fading and
shadowing observed by secondary users while scanning for primary users’
transmissions. Figure 3.3 shows an illustration of a hidden node problem
where the dashed circles show the operating ranges of the primary user and
the cognitive radio device. In this example, the CR causes unwanted interference to the PU because the CR is outside of the transmission coverage
area of the PU. We can tackle this problem by applying Cooperative Spectrum Sensing. In Chapter 6 we discuss the Cooperative Spectrum Sensing.
Sensing Periodicity While utilizing a white space, the SU should continue to
periodically sense the desired band (e.g. every Tp ) in case a PU starts to
transmit. The sensing period, Tp , determines the maximum time during
which the CR will not be aware of a reappearing PU and may interfere
with it. Therefore, Tp plays a key role for the QoS of the licensed user.


21

September 2013


Figure 3.3: The hidden licensed user problem in cognitive radio systems. [Yucek
and Arslan: “A survey of spectrum sensing algorithms for cognitive radio applications”]

The CR cannot simultaneously sense the band and transmit, so secondary
transmission and sensing of the band must be combined properly. While
from the regulator’s perspective it suffices for the SU to monitor the band
and make a decision whether there is or not a PU signal once every Tp , for
the CR it is desired to maintain sensing time well below Tp , in order to have
time for its transmission.
Noise Uncertainty It is not always available for a CR to know a priori the noise
power, so the receiver must estimate it by itself. Unfortunately, calibration
errors as well as changes in thermal noise caused by temperature variations
limit the accuracy with which noise power can be estimated. Thus, the
detection sensitivity, defined as the minimum SN R at which the PU’s signal
can be accurately detected, must be calculated with the worst case noise
assumption which leads to a more sensitive detector.

3.5

Classification of Spectrum Sensing Techniques

Several techniques have been proposed for a CR to detect the primary signal
in order to utilize in an efficient way the spectrum and each one has different


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September 2013

3.5 Classification of Spectrum Sensing Techniques

requirements so as to be implemented. These methods can be classified into
three general categories: (a) methods requiring both primary signal and noise
power information, (b) methods requiring only noise power information (semiblind
detection) and (c) methods requiring no information on primary signal or noise
power (blind detection). For example, Likelihood Ratio Test (LRT), Matched
Filter (MF) and Cyclostationary Detection (CSD) belong to category (a); Energy
Detection (ED) and Wavelet-Based Detection are semiblind methods and belong
to category (b) and finally blind methods are the Eigenvalue-Based Detection,
Covariance-Based Detection and Blindly Combined ED and belong to category
(c).
In chapter 4 we shall show the characteristics as well as the performance of
some of the above methods; for the MF detection and a variation of it, the ED
and finally the Covariance-Based detection and a variation of that method.


23

September 2013



24

September 2013

Chapter 4
Spectrum Sensing Techniques
4.1

Introduction

In this section we are going to present the most important and widely used sensing
methods for the CRs. The presentation is relative to the information that each
method is needed so as to be implemented, i.e. first the method that needs both
PU’s signal and noise information (4.3), then the semiblind detection (4.4) and
finally the blind detection (4.5). But first of all we are discussing the NeymanPearson theorem (4.2) which is the basis for the design of detectors of signals in
noise.

4.2

Neyman-Pearson Theorem

A common approach to simple hypothesis testing is based on the Neyman-Pearson
(NP) theorem. The simple hypothesis testing arises when the Probability Density
Function (PDF) of each assumed hypothesis is completely known. NP theorem
is used typically in sonar and radar systems.
The NP theorem Before continuing to the spectrum sensing techniques, it is
mandatory to explain how the NP theorem works. An example will give us
a good explanation.
Assume that we have a random variable (RV) whose PDF is either N(0, 1)
or N(1, 1). By the notation N(µ, σ 2 ) we mean that this random variable


25

September 2013

4. SPECTRUM SENSING TECHNIQUES

Figure 4.1: PDFs for hypothesis testing problem.

has a Gaussian (Normal) distribution with mean µ and variance σ 2 . So, we
have only one observation of that RV, i.e. x[0] and we must determine if
its mean is 0 or 1. Thus, we have to choose among two hypothesis:
H0 : µ = 0
H1 : µ = 1

(4.1)

where H0 is the null hypothesis and H1 is the alternative hypothesis. This
problem is known as the binary hypothesis test and in detection theory for
signals is a key problem. The PDFs under each hypothesis are shown in
Figure 4.1, with the diﬀerence in means causing the PDF under H1 to be
shifted to the right.
Now, we must decide one in favor of the two hypotheses. It is diﬃcult to
decide based in only one sample but a good approach would be to decide
H1 if x[0] > 1/2 because if this is happening then the observed sample is
more likely if H1 is true. We call the value 1/2 as our threshold (usually
referred as γ) in this example with which we compare our observed data
in order to decide one of the two hypothesis. We can make two types of
errors. If we decide H1 but H0 is true we make a false alarm error. In
the other hand, if we decide H0 while H1 is true we make a miss detection


26

September 2013

4.2 Neyman-Pearson Theorem

error. The threshold is a very important feature of the detection theory as
it determines the performance of the detection method.
We can convert the binary hypothesis problem (4.1) to the signal detection
problem, which will occupy us in the next sections:
H0 : x[0] = w[0]

(4.2)

H1 : x[0] = s[0] + w[0],

Deciding H1 when H0 is true can be thought of as a false-alarm. Generally,
in the implementation of the detectors we want very small values of probability of false-alarm (PF A ) or P r{H1 |H0 }. On the other hand, we wish to
maximize the probability of detection (PD ) or P r{H1 |H1 }. NP approach
maximizes the PD for a ﬁxed PF A . By writing P r{Hi |Hj } we mean that
we choose the hypothesis Hi when the hypothesis Hj is true.

To return to the signal detection problem (4.2) we can constrain PF A by
choosing the threshold γ since
PF A = P r{H1 |H0 }
= P r{x[0] > γ|H0 }
∞

1
1
√ exp − t2 dt
2
2π

=

(4.3)

γ

γ−µ
√
σ2
= Q(γ),
=Q

because x is a Gaussian RV and in the case of H0 µ = 0 and σ 2 = 1. As an
example, if PF A = 10−3 then γ = 3, because Q−1 (PF A ) = 3. We therefore


27

September 2013


decide H1 if x[0] > 3. Furthermore, with this choice we have
PD = P r{H1 |H1 }
= P r{x[0] > γ|H1 }
∞

1
1
√ exp − (t − 1)2 dt
2
2π

=

(4.4)

γ

γ−µ
√
σ2
= Q(γ − 1) = Q(2) = 0.023,
=Q

because x is a Gaussian RV and in the case of H1 µ = 1 and σ 2 = 1.

4.3

Matched Filter Detection

If SUs know information about a PU’s signal a priori, then the optimal detection
method is the matched filter since it maximizes the SNR of the received signal.
The MF correlates the already known primary signal with the received signal to
detect the presence of the PU and thus maximizes the SNR in the presence of
additive noise. The advantage of MF detection is the short time that it needs in
order to achieve a good detection performance compared to the other techniques,
such as a low probability of false alarm and missed detection, since the MF needs
less received samples. MF implementation complexity and power consumption
is too high, because that detector needs receivers for all types of signals and
corresponding receiver algorithms to be executed.
Matched filtering requires perfect knowledge of the PU’s signal, e.g. the operating frequency, bandwidth, modulation type and order, pulse shape, packet
format etc. If wrong information is used for matched filtering the detection performance will be degraded, which leads to malfunction of the CR concept and
from the PU’s perspective, leads to low QoS for the licensed users.
The development of the detector follows.
Model The detection problem is to distinguish between the two hypotheses:
H0 : x[n] = w[n],
H1 : x[n] = s[n] + w[n],


28

n = 0, 1, . . . , N − 1
n = 0, 1, . . . , N − 1

(4.5)

September 2013

4.3 Matched Filter Detection

where w[n] is White Gaussian Noise (WGN) with variance σ 2 and the source
signal s[n] is assumed a known deterministic one and Gaussian distributed.
x[n] is the received signal. WGN is deﬁned as a zero-mean Gaussian process
with constant spectral density.
Decision Statistic The NP detector decides H1 if the likelihood ratio exceeds a
threshold γ (we are going to analyze later in this section how the threshold
is calculated) or
L(x) =

p(x|H1 )
>γ
p(x|H0 )

(4.6)

where x = [x[0] x[1] . . . x[N − 1]]T
Taking the PDFs of the two hypotheses, putting them in eq. (4.6) and after
some mathematical calculations we manage to evaluate the decision statistic
T (x) of the MF detector. Thus, the detector decides H1 if:
N −1

T (x) =

x[n]s[n] > γ

(4.7)

n=0

where γ is a new threshold. This means that in eq. (4.7) if T (x) is greater
than the threshold, then the detector has detected a PU’s signal.
The detector in eq. (4.7) is referred to as a correlator or replica-correlator
since we correlate the received signal with a replica of the signal. In Figure 4.2 the replica-correlator detector is shown.
Performance We now determine the detection performance. Speciﬁcally, we
will derive PD for a given PF A . Using the eq. (4.7) we decide H1 if
N −1

T (x) =

x[n]s[n] > γ
n=0

.
Under both hypotheses, x[n] is Gaussian and T (x) is also Gaussian as it
is a linear combination of Gaussian random variables. By E(T ; Hi ) we


29

September 2013


Figure 4.2: Neyman-Pearson detector for deterministic signals (replica correlator).

denote the expected value and by var(T ; Hi ) we denote the variance under
hypothesis Hi . Then we have:
N −1

E(T ; H0 ) = E

w[n]s[n]

=0

n=0

N −1

N −1

var(T ; H0 ) = var

w[n]s[n]

N −1
2

var(w[n])s [n] = σ

=
n=0

n=0

s2 [n] = σ 2 E

2
n=0

where E is the energy of the source signal s[n].
N −1

E(T ; H1 ) = E

(s[n] + w[n])s[n]

=E

n=0

and ﬁnally the variance under hypothesis H1 is:
N −1

var(T ; H1 ) = var

(s[n] + w[n])s[n]

= σ2E

n=0

Thus, the distributions of the test statistic under either hypotheses, H0 and
H1 are, respectively:

T ∼


N(0, σ 2 E) under H0 ,
N(E, σ 2 E) under H1

30

September 2013


Now, we are going to calculate the performance of the MF detector, by
calculating the probability of false alarm and the probability of detection.
As the probability of false alarm (PF A ) is defined when there is no signal, i.e.
only noise, and we detect signal, from the distribution of the test statistic
T under hypothesis H0 we have:
γ
√
σ2E

PF A = P r{H1 |H0 } = P r{T > γ |H0 } = Q

.

(4.8)

The probability of detection (PD ) is defined when in the received signal
there is source signal with noise and we detect the source signal. From the
distribution of the test statistic T under hypothesis H1 we have:
PD = P r{H1 |H1 } = P r{T > γ |H1 } = Q

γ −E
√
σ2E

.

(4.9)

Thus, equations (4.8) and (4.9) give us the theoretical performance of the
MF detector. Subsequently, we are going to calculate the threshold, which
is a very important component of the detector as, in a way, it determines
the performance of the detector.
Since we do not know if there is signal or not, it is difficult to set the
threshold based on the PD . So, we, usually, calculate it based on the PF A .
Hence, based on eq. (4.8) we have for the threshold γ :
√
γ = Q−1 (PF A ) σ 2 E.

(4.10)

We can do that because Q(x) = 1 − Φ(x) and Φ(x) is monotonically in-

creasing, so Q(x) is monotonically decreasing and has an inverse Q−1 (·).
Figure 4.3 shows the values of the Q(x) function.
Returning to the calculation of the performance of the MF detector, we
have from combining the equations (4.9) and (4.10) the evaluation of the
probability of detection of the MF detector. That is:
PD = Q

√

σ 2 EQ−1 (PF A )
√
−
σ2E


E
σ2

31

= Q Q−1 (PF A ) −

E
σ2

.

(4.11)

September 2013


Right tail probability for standard normal PDF
1
0.9
0.8
0.7

Q(x)

0.6
0.5
0.4
0.3
0.2
0.1
0
−5

0
x

5

Figure 4.3: Right tail probability for standard normal PDF.

Simulation The detection performance and the Receiver Operating Characteristics (ROC) are shown in figures. In Figures 4.4 and 4.5 we can see the performance of the MF detector for different values of target PF A , for PF A = 10−1
and PF A = 10−3 in the first case and for PF A = 10−5 and PF A = 10−7 in the
second case. As we can observe from these figures, if we want to increase the
detection performance we can always increase the PF A and/or increase the
EN R, which is the energy-to-noise ratio, and we can do that by increasing
N −1

the signal energy. We define EN R as 10log10 (E/σ 2 ) and E =

s2 [n].
n=0

Another way to show the performance of a detector is the ROC in which
the PD is plotted versus PF A . Each point of the curve corresponds to a
value of the set (PD , PF A ) for a given threshold γ. As γ increases, PD and
PF A decrease and, as γ decreases, PD and PF A increase. One characteristic
of the ROC curve is that it should be always above the 45o line. Figure 4.6
shows the ROC for the MF detector for different values of the SN R, where


32

September 2013


2

SN RdB = 10log10 σs .
σ2

4.3.1

Generalized Matched Filter

The MF is an optimal detector for a known signal in WGN. In this subsection
we model the noise as correlated noise. Thus, we now assume that w ∼ N(0,C),
where C is the covariance matrix.

H0 : x[n] = w[n],
H1 : x[n] = s[n] + w[n],

n = 0, 1, . . . , N − 1
n = 0, 1, . . . , N − 1

(4.12)

where s[n] is the source signal and is assumed known. The covariance matrix
C is, also, assumed known.
Decision Statistic To determine the NP detector we again determine the likelihood ratio test (LRT) with
p(x|H1 ) =

1
(2π)N/2 det1/2 (C)

p(x|H0 ) =

1
exp − (x − s)T C−1 (x − s)
2

1
(2π)N/2 det1/2 (C)

1
exp − xT C−1 x
2

(4.13)

(4.14)

where we have noted that under H0 , x ∼ N(0, C) and under H1 , x ∼
N(s, C).

We decide H1 if
l(x) = ln

p(x|H1 )
> lnγ.
p(x|H0 )

(4.15)

But
1
(x − s)T C−1 (x − s) − xT C−1 x
2
1
= − xT C−1 x − 2xT C−1 s + sT C−1 s − xT C−1 x
2
1
= xT C−1 s − sT C−1 s
2

l(x) = −


33

(4.16)

September 2013


Detection performance for a matched filter
1
0.9

Probability of detection PD

0.8
0.7
0.6
0.5
0.4

PD theoretical PFA=10−1

0.3

PD simulation PFA=10−1

0.2


0.1
0

0

5
10
Energy-to-noise-ratio(dB)

15
E
10log10( σ2 )

20

Figure 4.4: Detection performance of matched filter for target PF A = 10−1 and
PF A = 10−3 .
Detection performance for a matched filter
1

0.8

0.9


0.7

PD theoretical PFA=10

0.6


−7

0.5
0.4
0.3
0.2
0.1
0

0

5
10
Energy-to-noise-ratio(dB)

15
E
10log10( σ2 )

20

Figure 4.5: Detection performance of matched filter for target PF A = 10−5 and
PF A = 10−7 .
34
September 2013


Receiver Operating Characteristic for different values of SNR
1
0.9

Probability of Detection

0.8
0.7
0.6
0.5
SNR=0 dB
SNR=−9.5 dB
SNR=−14 dB

0.4
0.3
0.2
0.1
0

0

0.2

0.4
0.6
Probability of False Alarm

0.8

1

Figure 4.6: ROC curves for MF detector under different values of SN RdB .

or by incorporating the non-data dependent term into the threshold we
decide H1 if
T (x) = xT C−1 s > γ.

(4.17)

The detector of eq. (4.17) is referred to as a generalized replica-correlator.
The replica is the modified signal s = C−1 s.
Performance The generalized MF decides H1 if
T (x) = xT C−1 s > γ .
Under either hypotheses the test statistic is Gaussian, as it is a linear transformation of x. Then, to derive the PD we do the same things as in MF
detector. We have:


35

September 2013


E(T |H0 ) = E(wT C−1 s) = 0
E(T |H1 ) = E (s + w)T C−1 s = sT C−1 s
var(T |H0 ) = E (wT C−1 s)2 = E(sT C−1 wwT C−1 s) =
sT C−1 E(wwT )C−1 s = sT C−1 s
and ﬁnally,
var(T |H1 ) = sT C−1 s
This means that:
T ∼

N(0, sT C−1 s),
under H0
−1
−1
N(sT C s, sT C s), under H1

Thus, we have for the PF A and for the threshold γ :

PF A = P r{H1 |H0 } = Q

√

γ
sT C−1 s

⇒ γ = Q−1 (PF A )

sT C−1 s,
(4.18)

and the PD for a target PF A is
PD = P r{H1 |H1 } = Q

γ − sT C−1 s
√
sT C−1 s

(4.19)

and with the help of eq. (4.18) we can transform the eq. (4.19) into:
PD = Q Q−1 (PF A ) −

sT C−1 s .

(4.20)

So, we derived the threshold and the PD for the generalized MF detector
and now we are ready to show the detection performance of that detector
based on the above equations and on simulations.


36

September 2013


Simulation The detection performance of the generalized MF is summarized
in Figure 4.7 and in Figure 4.8 the ROC is shown. In the first figure, we
can see the curves that are created from the theoretical expressions of the
PD , i.e. from eq. (4.20) and the curves that are created via simulation.
We plot the PD versus the EN RdB which is defined as 10log10 (sT C−1 s).
We can see that the theoretical and the simulation are matched for both
the values of PF A . Also, we can observe that when the PF A increases,
the detection probability increases as well. This happens because when a
detector throws false alarm frequently this means that it will detect the
signal properly more frequently. The first figure is derived for covariance
4 0
matrix C =
and the second figure is derived for covariance matrices
0 9
9 0
1 0
1 0
CEN R1 =
, CEN R2 =
, CEN R3 =
.
0 16
0 4
0 1

4.3.2

Pilot-Based Detection

Most wireless communication systems exhibit certain known patterns, such as
pilot tones, preambles, midambles, spreading codes etc, which are used to assist
control, equalization, synchronization, continuity or reference purposes. These
pilot tones are transmitted periodically. Even though perfect information of a
PU’s signal may not be attainable, if a certain pattern is known from the received
signals, pilot-based detection can be used to decide whether there is the signal of
the licensed user or not. A brief description of pilot-based detection follows.
Model There are two hypotheses:

H0 : y(n) = w(n),
H1 : y(n) = hp(n) + w(n),

0≤n≤N −1
0≤n≤N −1

(4.21)

where p(n) is the pilot sequence, w(n) is the white noise, h is the unknown
quasi-static block fading channel from the PU to the CR user. If we define
1
Pp =
N


37

N −1

n=0

|p(n)|2

(4.22)

September 2013


Probability of Detection - Generalized Matched Filter
1
0.9

Probability of Detection PD

0.8
0.7
0.6

PD theoretical, PFA1e−7
PD simulation, PFA=1e−7

0.5

PD theoretical, PFA=1e−1
PD simulation, PFA=1e−1

0.4
0.3
0.2
0.1
0

0

2

4

6

8
10
12
14
Energy-to-noise-ratio (dB)

16

18

20

Figure 4.7: Performance of detection for the generalized MF for a variety of target
PF A .

as the average power of the pilot signal, then the instantaneous SN R is
given by
γ=

|h|2 Pp
2
σn

(4.23)

2
where σn is the noise power.

Decision Statistic Using the Generalized Likelihood Ratio Test (GLRT) the
NP detector decides H1 if the likelihood ratio exceeds a threshold γ or

L(y) =


ˆ
p(y; hM L |H1 )
>γ
p(y|H0 )

38

(4.24)

September 2013


ROC for generalized matched ﬁlter for diﬀerent values of SNR
1
0.9


0.8
0.7
0.6
ENR = −7.6 dB
ENR = 0.9 dB
ENR = 6.5 dB

0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 4.8: ROC for the generalized MF for a variety of values of EN RdB .

We, then, take the logarithms of the two PDFs and after some mathematical
calculations the test statistic of the coherent detection yields:

Y =

2
2
N P p σn

2

N −1
∗

(4.25)

y(n)p (n)
n=0

which under H0 and H1 becomes:

2
N −1



∗

w(n)p (n) ,
under H0
 N P2 σn
2

p
n=0
Y =
2
N −1

 2N Pp

∗
2

w(n)p (n) , under H1

2 h +
2
σn
N Pp σn

n=0

and we make the decision from the above test statistic by comparing it with
a predetermined threshold γ, which is chosen that way to satisfy a target
probability of false alarm.


39

September 2013


Under H0 , the test statistics Y of that detector follows a central chi-squared
distribution with two degrees of freedom. This happens because the expected value of Y under H0 is 0 and its variance is 2 because it is a complex
number squared, with real (Re) part and imaginary (Im) part. Re ∼ (0, 1)

and Im ∼ (0, 1) are summed, thus the test statistic under H0 has expected
value equal to 0 and variance equal to 2.
Under H1 , Y has a noncentral chi-squared distribution with two degrees of
freedom and a non centrality parameter µ = 2N γ. Summarizing the above,
we have

fY (Y ) =

under H0
χ2 ,
2
2
χ2 (µ), under H1
ν

x2
i

The central chi-squared distribution arises as the PDF of x where x =
i=1

where xi ∼ N(0, 1) and the xi s are independent and identically distributed.
On the other hand, the noncentral chi-squared distribution arises as the
ν

PDF of x where x =
i=1

x2 where xi ∼ N(µi , 1). Then x has a noncentral
i

chi-squared PDF with ν degrees of freedom and a noncentrality parameter
ν

µ2 . Figures 4.9 and 4.10 show some examples of the PDFs for
i

λ =
i=1

central and non central chi-squared RVs, respectively.
Performance The performance of the coherent detection is calculated experimentally.
Simulation The performance and the ROCs for a variety of values of instantaneous SN R in db are shown in Figure 4.11 for diﬀerent values of SN RdB .
As we can see from this ﬁgure when SN R increases the detection performance of the coherent detection increases.


40

September 2013


Figure 4.9: PDF for central chi-squared random variable.

Figure 4.10: PDF for non central chi-squared random variable with varying degrees of freedom (ν) and noncentrality parameter λ = 4.


41

September 2013


Receiver Operating Characteristic for different values of SNR
1
0.9


0.8
0.7
0.6
0.5
SNR = −8.4 dB
SNR = −3.9 dB
SNR = 2 dB

0.4
0.3
0.2
0.1
0

0

0.2

0.4
0.6

0.8

1

Figure 4.11: ROC curves for coherent detection for different values of SN RdB .

4.4

Energy Detection

Energy Detection (also known as radiometry) is the simplest spectrum sensing
technique and is widely used when there is no a priori information on the source
signal. It simply treats the PU’s signal as noise and decides on the presence or
absence of the primary signal based on the energy of the observed signal. Since
it does not need any a priori knowledge of the primary signal, the ED is robust
to the variation of the primary signal. Two significant advantages of the ED is
that it does not involve complicated signal processing and has low complexity.
Despite its advantages, ED has some drawbacks. It has not good performance under low SN R conditions and there is an inability in differentiating the
interference from other SUs sharing the same channel and the PU. This leads to
frequently triggering false-alarm. Moreover, ED is not appropriate method for
detecting spread spectrum signals.


42

September 2013

4.4 Energy Detection

In section 4.3 we assumed deterministic signals. In this section, we are going
to analyze the ED assuming random signals. The analysis of the Energy Detector
follows.
Model We model the source signal s[n] as a zero mean, white, WSS Gaussian
2
random process with variance σs and the noise w[n] is WGN with variance
2
σ 2 and independent of the signal. That is, s ∼ N(0, σs ) and w ∼ N(0, σ 2 ).

The detection problem is to distinguish between the two hypotheses:
H0 : x[n] = w[n],
H1 : x[n] = s[n] + w[n],

n = 0, 1, . . . , N − 1
n = 0, 1, . . . , N − 1

(4.26)

Decision Statistic The NP detector decides H1 if the likelihood ratio exceeds a
threshold γ (we are going to analyze later in this section how the threshold
is calculated) or

L(x) =

p(x|H1 )
>γ
p(x|H0 )

(4.27)

From the above assumptions, we have for the received signal
x = [x0 , x1 , , . . . , , xN −1 ]T under H0 x ∼ N(0, σ 2 I) and under H1 x ∼
2
N(0, (σs + σ 2 )I). So, now, from eq. (4.27) we are going to evaluate the deci-

sion statistic for the ED taking the PDFs of the two hypotheses. Eq. (4.27)
becomes:
N −1
1
2
[2π(σs +σ 2 )]

N
2

exp

L(x) =

− 2(σ21 2 )
s +σ

x2 [n]
n=0

N −1
1
(2πσ 2 )

N
2

1
exp − 2σ2

(4.28)

x2 [n]
n=0

and after some mathematical calculations to the eq. (4.28) the decision
statistic for the ED yields:
N −1

x2 [n] > γ

T (x) =

(4.29)

n=0


43

September 2013


Performance We can observe from eq. (4.29) that the test statistic measures
the energy of the received data and compares it to a threshold. If the signal
is present, the energy of the received data increases. By dividing the test
2
statistic T (x) with σ 2 in the ﬁrst case and with σ 2 + σs in the second case,

the distribution of the statistic becomes:
T (x)
∼ χ2
under H0
N
σ2
T (x)
∼ χ2
N
2
σs + σ 2

under H1

(4.30)

(4.31)

Hence, from (4.30), (4.31) and (4.29), for a given threshold γ , we are able
to compute the probability of false alarm and the probability of detection of
the ED. The PF A is when there is only noise but the detector detects PU’s
signal and the PD is when there is PU’s signal and noise and the detector
detects it. Thus:
PF A = P r{H1 |H0 }
= P r{T (x) > γ |H0 }
T (x)
>γ
= Pr
σ2
γ
= Qχ2
N
σ2
and

(4.32)

PD = P r{H1 |H1 }
= P r{T (x) > γ |H1 }
T (x)
= Pr
>γ
2
σs + σ 2
γ
.
= Q χ2
2 + σ2
N
σs

(4.33)

If we deﬁne the SN R as the ratio of the power of the source signal to the
2
power of the noise, i.e. σs /σ 2 , then from eq. (4.33) we can see that the
detection performance increases as the SN R increases. We show that:
PD = Qχ2
N


44

γ /σ 2
2
σs /σ 2 + 1

(4.34)

September 2013

4.5 Covariance-Based Detection

2
So, when σs /σ 2 increases, the argument of the Qχ2 decreases and the probN

ability of detection increases.
Now, we are going to evaluate the threshold. For its evaluation we use
the recursive algorithm from the Problem 5.1 in p. 176 from the book
Fundamentals of Statistical Signal Processing-Detection Theory by Steven
Kay. Then, we have

PF A = exp −

γ
2σ 2

N
2

r

γ
2σ 2

−1

1 +
r=1

(4.35)



r!

And then by letting γ = γ /2σ 2 and rearranging terms we have:

γ = −lnPF A + ln 1 +

N
2

−1

r=1

r



(γ ) 
r!

(4.36)

Finally, we can evaluate the threshold γ by using the fixed point iteration:

γk+1 = −lnPF A + ln 1 +

N
2

−1

r=1

r



(γk ) 
r!

(4.37)

and begin the iteration with γ0 = 1.
Simulation The detection performance of the ED for two values of target PF A
is shown in Figure 4.12. Also, in Figure 4.13 the Receiver Operating Characteristic for different values of SN R in dB is shown. In the first figure we
can see the curves that are created from the theoretical types of the PD ,
i.e. from eq. (4.33) and the curves that are created via simulation. We can
see that the theoretical and the simulation are matched for both values of
PF A .

4.5

Covariance-Based Detection

The key idea behind covariance-based detection is that the PU’s signal received
at the CR user is usually correlated because of the dispersive channels, the utility


45

September 2013


Energy detector performance
1
0.9

PD theoretical, Pfa=1e−2
PD simulation, Pfa=1e−2


0.8

P theoretical, P =1e−5

0.7

PD simulation, Pfa=1e−5

D

fa

0.6
0.5
0.4
0.3
0.2
0.1
0
−10

−5

0
SNR (db)

5

10

Figure 4.12: Performance of detection for the ED for a variety of target PF A .

of multiple receive antennas or even over-sampling. Such correlation can be used
by the CR user to diﬀerentiate the signal of the licensed user from white noise.
Covariance-based detector determines the presence or absence of the primary
signal based on the covariance matrix of the received signal. Speciﬁcally, based
on the ratio of maximum eigenvalue to minimum eigenvalue of the covariance
matrix of the received signal we can detect the signal existence.
The analysis of the maximum-minimum eigenvalue (MME) detection follows.

H0 : x[n] = w[n],
N

H1 : x[n] =
k=0


n = 0, 1, . . . , N − 1

h[k]s[n − k] + w[n],

46

n = 0, 1, . . . , N − 1

(4.38)

September 2013


ROC for diﬀerent values of SNR, Energy Detector
1
0.9


0.8
0.7

SNR = −6 dB
SNR = 0 dB
SNR = −3.5 dB

0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 4.13: ROC for the ED for a variety of values of SN RdB .

where h is the channel response from source signal to the receiver, s[n] is
the PU’s signal, w[n] is the additive noise and x[n] is the received signal in
the CR receiver. Based on the received signals with little information on
the source signals, noise power and channel responses a sensing algorithm
should make a decision on the existence or the absence of the PU’s signal.
For a good detection algorithm (obviously for every algorithm discussed in
this thesis) we want the PD to be high and the PF A to be low.
Decision Statistic The next step that we must do in this algorithm is to compute the covariance matrix of the received signal, that is:
R(Ns ) =

1
Ns

L−1+Ns

x(n)x† (n)

(4.39)

n=L

where Ns is the number of collected samples, L is the number of consecutive


47

September 2013


outputs of the received signal and the superscript † denotes the transcon-

jucate (or Hermitian) of the complex signal x(n).

After the computation of R matrix from eq. (4.39) we must find its eigenvalues and obtain the maximum and the minimum eigenvalue of the matrix.
Let λmax and λmin be the maximum and the minimum eigenvalue, respectively. Subsequently, we can make our decision from the two hypotheses of
eq. (4.38) based on the ratio λmax /λmin .
Thus, if λmax > γλmin signal exists, i.e. hypothesis H1 . Otherwise, signal
does not exist, i.e. hypothesis H0 . In the previous cases, γ is the threshold
and we are going to show later the way that is evaluated.
Performance The threshold, theoretically, is computed from the next equation
for a given PF A :
√
√
( Ns + L)2
√
γ= √
( Ns − L)2

√
√
( Ns + L)−2/3 −1
1+
F2 (1 − PF A )
(Ns L)1/6

(4.40)

where F2 (·) is the CDF of the 2nd order Tracy-Widom distribution.
Generally, it is difficult to obtain a closed form expression of the detection
probability PD = P r{λmax > γλmin |H1 }, so in the next figures the detection
performance and the ROCs are computed experimentally.

Simulation The Receiver Operating Characteristic for the MME detector for
two values of the SN R in dB is shown in Figure 4.14. From that figure
we can observe that when the SN R increases, the detection performance
increases as well. Furthermore, we can see that for low SN R the red curve
does not fall under the 45o line, which means that, still, in this case the
detection performance is satisfactory.
The values of the channel h (with dimension (N + 1, 1)) for which the
following ROC was produced are:


48

September 2013


Values of channel h
0.2321 + 0.1188i
−1.7022 − 0.55962i
−0.5913 + 0.7218i
1.1470 − 0.5950i
0.8434 − 1.0207i
0.1451 + 1.7469i

MME Detector - ROC PDet

vs Pfa

1
0.9
0.8
0.7

PDet

0.6
0.5
SNR = 6.9 dB
SNR = 0.9 dB

0.4
0.3
0.2
0.1
0

0

0.2

0.4

0.6

0.8

1

Pfa

Figure 4.14: ROC for the MME detection for diﬀerent values of the SN R in dB.


49

September 2013



50

September 2013

Chapter 5
Comparison
5.1

Introduction

In this Chapter we are going to compare the diﬀerent spectrum sensing techniques
discussed in Chapter 4.

5.2

Energy Detection vs Matched Filter Detection

In this section we are comparing the performance of the ED to the one of the MF
Detector. In the experiment we create a random signal and then we use it for
the evaluation of the detection performance of each of these two methods. We
compute the threshold and the test statistic of each of the methods (with the
same signal we created before) and then we evaluate the PD and the PF A in the
same way as in Chapter 4. Visually, the comparison of ED and MF is shown in
Figure 5.1 for SN R = −6 dB, in Figure 5.2 for SN R = 0 dB and in Figure 5.3
for SN R = 2 dB.

From these ﬁgures we can observe that the MF has better detection performance than the ED for any SN R. This is reasonable, as in the MF detection
we know information about the PU’s signal a priori and the MF correlates the
already known primary signal with the received signal to detect the presence of
the PU. On the other hand, ED has no a priori information on the source signal.


51

September 2013

5. COMPARISON

ROC for comparison of ED and MF. SNR = −6 dB

1
0.9


0.8
0.7
0.6
Energy Detection

0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 5.1: Comparison of Energy Detector and Matched Filter Detector for
SN R = −6 dB
It simply treats the PU’s signal as noise and decides on the presence or absence
of the primary signal based on the energy of the observed signal.

5.3

Energy Detection vs Matched Filter Detection vs Covariance Based Detection

In this section we compare the performances of the ED, the MF Detector and
the Covariance-Based Detection. In the experiment we create a random signal
and then we use it for the evaluation of the detection performance of each of
these three techniques. Also, we have a channel, assumed known, and the useful
signal is the result of the convolution of the signal we created with the values of
the channel. The received signal is the summation of the useful signal plus the


52

September 2013

5.3 Energy Detection vs Matched Filter Detection vs Covariance
Based Detection

ROC for comparison of ED and MF. SNR = 0 dB
1
0.9


0.8

Energy Detection

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

SN R = 0 dB

noise. For the MF detection we assume the useful signal as known. In Figure 5.4
we show the ROCs for the three methods for SN R = −2.4dB and in Figure 5.5

for SN R = 3dB. From these ﬁgures we can observe that the MF detection has
almost excellent performance for low SN R as well as for higher SN R. This is
because we have perfect knowledge of the signal and the channel. Moreover, we
can see that the ED has better performance than the MME detector. In this case
we deﬁne SN R as 10log10


2
||h||2 σs
σ2

.

53

September 2013

5. COMPARISON

ROC for comparison of ED and MF. SNR = 2 dB
1
0.9


0.8

Energy Detection

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

SN R = 2 dB


54

September 2013

5.3 Energy Detection vs Matched Filter Detection vs Covariance
Based Detection

ROC for comparison of ED, MF Detection and MME Detection, SNRdB = −2.4
1
0.9


0.8
0.7
0.6
0.5
0.4
0.3
Energy Detection Sim. Thresh.
Energy Detection Theor. Thresh.
Max−Min Eig. Detection

0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 5.4: Comparison of Energy Detector, Matched Filter Detector and MaxMin Eigenvalue Detection for SN R = −2.4 dB.
ROC for comparison of ED, MF Detection and MME Detection, SNRdB = 3
1

0.9


0.8
0.7
0.6
0.5
0.4
0.3
Energy Detection Sim. Thresh.
Energy Detection Theor. Thresh.
Max−Min Eig. Detection

0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 5.5: Comparison of Energy Detector, Matched Filter Detector and MaxMin Eigenvalue Detection SN R = 3 dB.


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5. COMPARISON


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Chapter 6
Cooperative Spectrum Sensing
6.1

Introduction

Spectrum sensing using a single CR has a number of limitations. First of all,
the sensitivity of a single sensing device might be limited because of energy constraints. Furthermore, the CR might be located in a deep fade of the PU signal,
and as such might miss the detection of this PU. Moreover, although the CR
might be blocked from the PU’s transmitter, this does not mean it is also blocked
from the PU’s receiver, i.e. the hidden terminal problem which was described in
section 3.4. As a result, the PU is not detected but the secondary transmission
could still signiﬁcantly interfere at the PU’s receiver. Figure 6.1 shows that CR3
is shadowed by a high building over the sensing channel (PU to the CR) and that
CR1 is shadowed over the reporting channel (CR to Base Station).

6.2

General Concept

By taking advantage of the independent fading channels (i.e., spatial diversity)
and multiuser diversity, cooperative spectrum sensing is proposed to improve the
reliability of spectrum sensing, increase the detection probability to better protect
a PU and reduce false alarm to utilize the idle spectrum more eﬃciently. The
concept of cooperative spectrum sensing is to use multiple sensors and combine
their measurements into one common decision.


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6. COOPERATIVE SPECTRUM SENSING

Figure 6.1: Cooperative spectrum sensing in CR networks. CR1 is shadowed over
the reporting channel and CR3 is shadowed over the sensing channel. [Letaief
and Zhang: “Cooperative Communications for Cognitive Radio Networks”]

The merit of cooperative spectrum sensing primarily lies in the achievable
space diversity brought by the sensing channels, namely, sensing diversity gain,
provided by the multiple CRs. Even though one CR may fail to detect the signal
of the PU, there are still many chances for other CRs to detect it. With the
increase of the number of cooperative CRs, the probability of missed detection
for all the users will be extremely small. Another merit of cooperative spectrum
sensing is the mutual benefit brought forward by communicating with each other
to improve the sensing performance. When one CR is far away from the primary
user, the received signal may be too weak to be detected by this CR. However, by
employing a CR that is located nearby the PU as a relay, the signal of the PU can
be detected reliably by the far user. There are mainly three relaying protocols:
• Amplify-and-forward (AF). In AF, the received signal is amplified and re-

transmitted to the destination. The advantage of this protocol is its simplicity and low cost implementation. But the noise is also amplified at the


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6.3 Methods of Cooperative Spectrum Sensing

relay.
• Decode-and-forward (DF). In DF, the relay attempts to decode the received
signals. If successful, it reencodes the information and retransmits it.

• Compress-and-forward (CF). CF attempts to generate an estimate of the

received signal. This is then compressed, encoded, and transmitted in the
hope that the estimated value may assist in decoding the original codeword
at the destination.

6.2.1

Challenges

There also exist several challenges on cooperative spectrum sensing. For instance,
secondary users can be low-cost devices only equipped with a limit of amount of
power, so they can not aﬀord very complicated detection hardware and high
computational complexity. In wideband cooperative sensing, multiple secondary
users have to scan a wide range of spectrum channels and share their detection
results. This results in a large amount of sensory data exchange, high energy
consumption, and an ineﬃcient data throughput. If the spectrum environment is
highly dynamic, the sensed information may even be stale due to user mobility,
channel fading, etc. Furthermore, another challenge in the implementation of
cooperative sensing is the issue of user reliability. For instance, a single malicious
user may prevent a cognitive radio network (CRN) from accessing a white space
by sending false reports to the band manager.

6.3

Methods of Cooperative Spectrum Sensing

Cooperation can be among cognitive radios or external sensors can be used to
build a cooperative sensing network. In the former case, cooperation can be
implemented in two fashions: centralized or distributed. These two methods and
external sensing are discussed in the following sections.


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6.3.1

Centralized Sensing

In centralized sensing, cooperative spectrum sensing consists of a base station
(BS) or an access point (AP). The BS or AP collects sensing information from
cognitive devices, identifies the available spectrum and broadcasts this information to other CR (i.e., the presence or absence of the PU’s signal) or directly
controls the cognitive radio traffic. The goal is to mitigate the fading effects of
the channel and increase detection performance. In the case of a large number of
users, the bandwidth required for reporting becomes huge. In order to reduce the
sharing bandwidth, local observations of cognitive radios are quantized to one bit
(hard decisions). Furthermore, only the cognitive radios with reliable information
are allowed to report their decisions to the central unit. Hence, some sensors are
censored. Censoring can be implemented by simply using more threshold values
instead of one.
Generally, the sensing information combination at the BS can be categorized
by soft combination and hard combination techniques.
Soft Combination In soft combination, also known as data fusion, the CR users
send their original sensing data (measurements) to the base station without
quantization. While soft combination requires large overhead to feedback
the sensing data, it has excellent detection performance. Soft combination
can be performed as described above:
1. Every CR performs its own local spectrum sensing measurements independently.
2. All of the CRs forward their measurements (data) to AP.
3. The common receiver fuses the CR decisions and makes a final decision
to infer the absence or presence of the PU.
Hard Combination In order to minimize the communication overhead and
hence the bandwidth required for the transmission of the data from the
CRs to the AP, users may only report their final 1-bit decisions rather than
the actual measurements. In hard combination schemes, also called decision
fusion, the CR users send quantized sensing information to the BS and the


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BS deploys a fusion rule to make the final decision, i.e. whether there is or
not the PU’s signal. While local hard decision at the CR users causes information loss and performance degradation, it greatly reduces the amount
of feedback.
The simplest hard combination scheme is the one-bit counting scheme, in
which each CR user sends one-bit information to the base station regarding
its observed energy is above a predetermined threshold. Specifically, if each
user only sends one-bit decision (“1” for signal present and “0” for signal
absent) and no other information is available at the central processor, some
commonly adopted decision fusion rules are described as follows.
1. “Logical-OR (LO)” Rule: If one of the decisions is “1” the final decision is “1”. Assuming that all decisions are independent, then the
probability of detection and probability of false alarm of the final deciM

sion are PD = 1−

M

(1−PD,i ) and PF A = 1−
i=1

(1−PF A,i ) respectively,
i=1

where PD,i and PF A,i are the probability of detection and probability
of false alarm for user i, respectively.
2. “Logical-AND (LA)” Rule: If and only if all decisions are “1”, the
final decision is “1”. The probability of detection and probability of
M

false alarm of the final decision are PD =

M

PD,i and PF A =
i=1

PF A,i
i=1

respectively.
3. “K out of M” Rule: If and only if K decisions or more are “1”, the final
decision is “1”. This includes “Logical-OR (LO)” (K = 1), “LogicalAND (LA)” (K = M), and “Majority” (K = M/2 ) as special cases.
The probability of detection and probability of false alarm of the final
decision are
M −K

PD =
i=0

and

M −K

PF A =
i=0


M
(1 − PD,i )M −K−i (1 − PD,i )K+i
K +i
M
(1 − PF A,i )M −K−i (1 − PF A,i )K+i
K +i

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ROC in Cooperative Sensing. SNR = −6 db, 10 users

1
0.9


0.8
AND−rule
OR−rule
MAJORITY−rule K=6

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4
0.5
0.6
0.7

0.8

0.9

1

Figure 6.2: ROC curves for fusion rules in centralized cooperative spectrum sensing.

respectively.
In the following ﬁgures we show the ROCs for the three above rules. In
Figure 6.2 we plot the probability of detection versus the probability of
false alarm and in Figure 6.3 we plot the probability of missed detection
(PM ISS ) versus the probability of false alarm. The probability of missed
detection is deﬁned as PM ISS = 1 − PD . Our experiment is implemented for

10 CR users in the Cognitive Radio Network (CRN) and a fusion center that
collects the binary decisions from these CRs. We choose for the MajorityRule the value of the factor K = 6.
In the literature, a new two bit hard combination scheme has been proposed [16]. With this scheme a better detection performance can be achieved.


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Complementary ROC in Cooperative Sensing. SNR = −6 db, 10 users

1
0.9

Probability of Miss Detection

0.8
AND−rule
OR−rule
MAJORITY−rule K=6

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.2

0.4
0.6

0.8

1

Figure 6.3: Complementary ROC curves for fusion rules in centralized cooperative
spectrum sensing.

Figure 6.4 shows the one-bit and two-bit hard combination schemes. We
can see that in the second case the observed energy is divided into four
regions by three thresholds λ1 , λ2 , λ3 .

6.3.2

Distributed Sensing

In the case of distributed sensing, cognitive nodes share information among each
other but they make their own decisions as to which part of the spectrum they
can use. Distributed sensing is more advantageous than centralized sensing in
the sense that there is no need for a backbone infrastructure and it has reduced
cost.
Figure 6.5 shows a schematic representation of the AF cooperation scheme in
a decentralized CR network. In the ﬁgure, P denotes the primary user and CR


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September 2013


Figure 6.4: Principles of hard combination schemes (a) One-bit counting scheme
and (b) two-bit hard combination scheme. [Ma et al.: “Signal Processing in
Cognitive Radio”]

user U1 is sending data to CR user U3, while CR user U2 acts as an AF relay
for U1. The AF cooperation scheme consists of two stages or time slots: in the
ﬁrst time slot U1 transmits while U2 listens; in the second time slot U2 transmits
while U1 keeps silent. Thus orthogonal transmission of U1 and U2 is guaranteed.
Since continuous spectrum sensing is required during the process of secondary
communication between the CR users, actually U1 does not idle the second time
slot away. Instead, U1 listens to its partner U2 and decides whether the received
signal contains the primary signal in the second time slot.

6.3.3

External Sensing

Another technique for obtaining spectrum information is external sensing. In external sensing, an external agent performs the sensing and broadcasts the channel
occupancy information to CRs. External sensing algorithms solve some problems
associated with the internal sensing where sensing is performed by the cognitive
transceivers internally. The main advantages of external sensing are overcoming
hidden primary user problem and the uncertainty due to shadowing and fading.


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6.4 Practical Considerations about Cooperative Sensing

Figure 6.5: Schematic representation of the AF cooperation scheme in a decentralized CR network. [Ma et al.: “Signal Processing in Cognitive Radio”]

Furthermore, as the cognitive radios do not spend time for sensing, spectrum
eﬃciency is increased. The sensing network does not need to be mobile and not
necessarily powered by batteries. Hence, the power consumption problem of internal sensing can also be addressed. External sensing is one of the methods
proposed for identifying primary users in IEEE 802.22 standard as well.

6.4

Practical Considerations about Cooperative
Sensing

Fading and Shadowing In practice, the reporting channels between the CRs
and the common receiver will also experience fading and shadowing (such as
CR 1 in Figure 6.1). This will typically deteriorate the transmission reliability of the sensing results reported from the CRs to the BS. For example,
when one CR reports a sensing result “1” (denoting the presence of the
PU) to the BS through a realistic fading channel, the BS will likely detect
it to be the opposite result “0” (denoting the absence of the PU) because of
the disturbance from the random complex channel coeﬃcient and random


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September 2013


noise. Eventually, the performance of cooperative spectrum sensing will be
degraded by the imperfect reporting channels.
Trade-off Between Sensing Duration and Performance Spectrum sensing
is significant in CRs in avoiding a collision with the licensed user and improving the licensed spectrum utilization efficiency. The former is characterized by the PD and the latter is measured by the PF A . The sensing duration
T is no doubt a key parameter to determine the sensing performance. A
longer sensing duration T can produce a better sensing performance but
results in longer waiting time for cognitive users to access the channel. An
extremely long sensing duration cannot be tolerated by an agile radio. From
the perspective of the cognitive users, a lower false alarm probability implies that there will be more chances for the licensed channel to be reused.
Assuming that the protection of the primary user is of the first priority in
CR networks, we can maximize the throughput of the cognitive users in
order to find an optimal sensing duration.
Trade-off Between Cooperation and Sensing In a CR network with a large
number of CRs, cooperative spectrum sensing may become impractical because in a time slot only one CR should send its local decision to the BS so
as to separate decisions easily at the receiver end. Hence, it may make the
whole sensing time intolerantly long. Obviously the fewer CRs involved in
cooperative spectrum sensing, the shorter the sensing duration. However,
a small number of CRs in cooperative spectrum sensing results in a small
sensing diversity order. This problem can be addressed by allowing the CRs
to send the decisions concurrently. But this may complicate the receiver
design when we try to identify the decisions from different CRs. Another
potential solution is to send the decisions on orthogonal frequency bands,
but this requires a large portion of the available bandwidth.


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Chapter 7
Conclusion
Cognitive Radio is the new key technology that serves as a solution to the spectrum scarcity. It is necessary that the CRs are used in wireless communications
in order to potentially improve the utilization eﬃciency of the radio spectrum.
By tuning the frequency to the temporarily unused licensed band and adapting
operating parameters to environment variations, CR technology provides future
wireless devices with additional bandwidth, reliable broadband communications
and versatility for rapidly growing data applications.
In this thesis we presented the fundamental concepts of CR technology and the
idea that lead us to that technology. We presented the prerequisite requirement
on deploying CR, i.e. spectrum sensing and we analyzed the basic detection
techniques in order to realize the sensing of the RF spectrum. Furthermore, we
presented cooperative spectrum sensing that serves as a solution to the challenges
that one CR user can face, i.e. multipath fading and shadowing.

7.1

Future Work

Research on spectrum sensing thus far has mainly focused on meeting the regulatory requirements for reliable sensing. An important venue for further research
is the interplay of spectrum sensing and higher-layer functionalities to enhance
the end user’s perceived QoS.


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7. CONCLUSION


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“Cognitive Radio: An Integrated Agent Architecture for

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Spectrum Sensing Techiniques for Cognitive Radios

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