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Faculty of Electrical Engineering, Mathematics and Computer Science

Circuits and SystemsMekelweg 4,

2628 CD DelftThe Netherlands

http://ens.ewi.tudelft.nl/

CAS-2009-1393448

M.Sc. Thesis

Spectrum Sensing Issues for CognitiveRadio

Sina Maleki

Abstract

In this thesis, first, we address the problem of energy efficiency forspectrum sensing. We propose a combined censoring and ”on/off”scheme as an energy efficient technique for cognitive radio net-

works. We maximize the lifetime of the spectrum sensing system byminimizing the energy consumption of the system subject to a specificdetection performance constraint. We show that our proposed tech-nique is more energy efficient than the traditional pure censoring andpure ”on/off” schemes. Second, we address the problem of wide-bandspectrum sensing at low SNR. Energy detector is known to be sensi-tive to noise uncertainty, hence it is not reliable at low SNR. Here,we propose a two-stage spectrum sensing technique consisting of acoarse and a fine sensing stage. In the coarse sensing stage, we locatethe possible empty channels within a frequency band using an energydetector and then in the fine sensing stage, we make a final decisionabout the emptiness of the reported channels from the coarse sensingstage using a cyclostationary detector. Our simulation results showthat under a certain noise uncertainty, two-stage spectrum sensingoutperforms both the energy detector and the cyclostationary detec-tor in terms of the detection performance and mean detection time.However, increasing the noise uncertainty leads to a decreasing SNRrange where our proposed technique performs better than the energyand cyclostationary detector.

Spectrum Sensing Issues for Cognitive Radio

Thesis

submitted in partial fulfillment of therequirements for the degree of

Master of Science

in

Electrical Engineering

by

Sina Malekiborn in Zahedan, Iran

This work was performed in:

Circuits and Systems GroupDepartment of TelecommunicationsFaculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of Technology

Delft University of Technology

Copyright c© 2009 Circuits and Systems GroupAll rights reserved.

Delft University of TechnologyDepartment of

Telecommunications

The undersigned hereby certify that they have read and recommend to the Facultyof Electrical Engineering, Mathematics and Computer Science for acceptance a thesisentitled “Spectrum Sensing Issues for Cognitive Radio” by Sina Maleki inpartial fulfillment of the requirements for the degree of Master of Science.

Dated: March 25, 2009

Chairman:Prof.dr.ir. Alle-Jan Van der Veen

Advisors:Dr. Ashish Pandharipande

Dr. ir. Geert Leus

Committee Members:Dr. Homayoon Nikookar

Abstract

In this thesis, first, we address the problem of energy efficiency for spectrum sens-ing. We propose a combined censoring and ”on/off” scheme as an energy efficienttechnique for cognitive radio networks. We maximize the lifetime of the spectrum

sensing system by minimizing the energy consumption of the system subject to a spe-cific detection performance constraint. We show that our proposed technique is moreenergy efficient than the traditional pure censoring and pure ”on/off” schemes. Second,we address the problem of wide-band spectrum sensing at low SNR. Energy detectoris known to be sensitive to noise uncertainty, hence it is not reliable at low SNR. Here,we propose a two-stage spectrum sensing technique consisting of a coarse and a finesensing stage. In the coarse sensing stage, we locate the possible empty channels withina frequency band using an energy detector and then in the fine sensing stage, we makea final decision about the emptiness of the reported channels from the coarse sensingstage using a cyclostationary detector. Our simulation results show that under a certainnoise uncertainty, two-stage spectrum sensing outperforms both the energy detector andthe cyclostationary detector in terms of the detection performance and mean detectiontime. However, increasing the noise uncertainty leads to a decreasing SNR range whereour proposed technique performs better than the energy and cyclostationary detector.

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Acknowledgments

Although my name appears as the sole author of the thesis, in reality a numberof people are responsible for the work. First and foremost, I would like to thankmy thesis advisors, Dr. Ashish Pandharipande, and Dr. Geert Leus. They

introduced me to the topics of statistical signal processing and cognitive radio and theysteered my research efforts to attack interesting and potentially solvable problems. Imust thank Ashish, for his great efforts in making my papers and my thesis readable,and teaching me the process of good scientific research. Many thanks Geert, for youralways positive attitude and for helping me to improve my writing. Working withAshish and Geert has been very inspiring: their energy, dedication, creative ideas andexcellent organization. I acknowledge Dr. Homayoon Nikookar and Prof. A.-J. vander Veen for their participation in my MSc thesis committee. The outcomes of the lastyear of interaction with these people did not get reflected in the thesis, but I feel theydeserve to be mentioned anyway. I could not have wished for better collaborators andcoaches. Your contributions, detailed comments and insights have been of great valuefor me. I am also grateful for the opportunity to be part of the research group at Philips.

My warmest thanks go to my friends, very specially, Arash Vafanejad, RahmanDoostmohammadi, Vincent D. Lange, Nikolai Blanic and Ermmana Conte for makingme forget for brief periods of time about my work and my thesis.

Finally, and most importantly, I would like to express my gratitude and humility tomy parents and my only sister Atena. Even thousands of kilometers apart, they havebeen present through every step of my life, providing support in difficult times. Theyhave been a constant source of inspiration, and this thesis is dedicated to them.

Sina MalekiDelft, The NetherlandsMarch 25, 2009

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Contents

Abstract v

Acknowledgments vii

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Spectrum Sensing Issues . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Outline and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Background discussion 72.1 Current Energy Efficient Techniques . . . . . . . . . . . . . . . . . . . 7

2.1.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Energy Efficient Techniques . . . . . . . . . . . . . . . . . . . . 9

2.2 Two-Stage Spectrum Sensing . . . . . . . . . . . . . . . . . . . . . . . 182.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Combined Censoring and ”On/Off” Scheme 233.1 Combined Censoring and ”On/Off” Scheme . . . . . . . . . . . . . . . 23

3.1.1 Detection Performance without Prior Knowledge . . . . . . . . . 243.1.2 Detection Performance with Prior Knowledge . . . . . . . . . . 263.1.3 Analysis and Problem Definition . . . . . . . . . . . . . . . . . 28

3.2 Energy Consumption Analysis . . . . . . . . . . . . . . . . . . . . . . . 313.2.1 IEEE 802.15.4/ZigBee . . . . . . . . . . . . . . . . . . . . . . . 333.2.2 Channel and Radio Model . . . . . . . . . . . . . . . . . . . . . 333.2.3 Optimal Sleeping and Censoring Rate . . . . . . . . . . . . . . . 34

3.3 Convex Analysis of the Problem . . . . . . . . . . . . . . . . . . . . . . 363.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Two-Stage Spectrum Sensing 454.1 Two-Stage Spectrum Sensing . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Coarse Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.1.2 Fine Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Analysis and Problem Formulation . . . . . . . . . . . . . . . . . . . . 504.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 504.2.2 Mean Detection Time Analysis . . . . . . . . . . . . . . . . . . 52

4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 Conclusions and further work 655.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Suggestions for further Work . . . . . . . . . . . . . . . . . . . . . . . . 66

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List of Figures

1.1 The NTIA’s Frequency Allocation Chart [1] . . . . . . . . . . . . . . . 21.2 Measurement of Spectrum Utilization (0-6 GHz) in the Downtown Berke-

ley [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Temporal Variation of the Spectrum Utilization (0-2.5 GHz) in the

Downtown Berkeley [25] . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Cooperative Spectrum Sensing Configuration . . . . . . . . . . . . . . . 82.2 ROC for N=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 ROC for N=5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 ROC for N=10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Feasible set of the problem (2.21) . . . . . . . . . . . . . . . . . . . . . 142.6 ROC for N=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.7 ROC for N=5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.8 ROC for N=10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.9 Feasible set of the problem (2.31) . . . . . . . . . . . . . . . . . . . . . 192.10 Block diagram of the cognitive radio proposed by Y. Hur et al [21] . . . 202.11 Two-stage sensing scheme of [20] . . . . . . . . . . . . . . . . . . . . . 20

3.1 Feasible µ and ρ for QFoc ≤ 0.1 and QDoc ≥ 0.7 . . . . . . . . . . . . . . 293.2 Feasible µ and ρ for QFoc ≤ 0.1 and QDoc ≥ 0.8 . . . . . . . . . . . . . . 303.3 Feasible µ and ρ for QFoc ≤ 0.1 and QDoc ≥ 0.9 . . . . . . . . . . . . . . 303.4 Feasible µ and ρ for QFoc ≤ 0.1 and QDoc ≥ 0.99 . . . . . . . . . . . . . 313.5 Feasible µ and ρ for QFoc ≤ 0.1 with Pr(H0) = 0.8 . . . . . . . . . . . . 323.6 Feasible µ and ρ for QFoc ≤ 0.1 with Pr(H0) = 0.2 . . . . . . . . . . . . 323.7 Energy Consumption of ZigBee for QFoc ≤ 0.1 . . . . . . . . . . . . . . 353.8 Energy Consumption Comparison for ZigBee . . . . . . . . . . . . . . . 353.9 Energy Consumption Comparison for WLAN 802.11/g at 1 Mbps . . . 363.10 Energy Consumption of ZigBee for QFoc ≤ 0.1 and Pr(H0)=0.8 . . . . 373.11 Energy Consumption Comparison for ZigBee and Pr(H0) = 0.8 . . . . 373.12 Energy Consumption of ZigBee for QFoc ≤ 0.1 and Pr(H0)=0.2 . . . . 383.13 Energy Consumption Comparison for ZigBee and Pr(H0) = 0.8 . . . . 38

4.1 Feasible set of (4.32) for Pf = 0.1 . . . . . . . . . . . . . . . . . . . . . 524.2 Detection Performance Comparison for ∆ = 0dB . . . . . . . . . . . . 534.3 Mean Detection Time Comparison for Pr(H0) = 0.2 . . . . . . . . . . . 544.4 Mean Detection Time Comparison for Pr(H0) = 0.8 . . . . . . . . . . . 554.5 Detection Performance Comparison for ∆ = 0.05dB . . . . . . . . . . 554.6 Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 0.05dB . 564.7 Mean Detection Time Comparison for Pr(H0) = 0.8 and ∆ = 0.05dB . 564.8 Detection Performance Comparison for ∆ = 0.1dB . . . . . . . . . . . . 574.9 Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 0.1dB . . 574.10 Mean Detection Time Comparison for Pr(H0) = 0.8 and ∆ = 0.1dB . . 584.11 Detection Performance Comparison for ∆ = 0.5dB . . . . . . . . . . . . 58

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4.12 Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 0.5dB . . 594.13 Mean Detection Time Comparison for Pr(H0) = 0.8 and ∆ = 0.5dB . . 594.14 Detection Performance Comparison for ∆ = 1dB . . . . . . . . . . . . 604.15 Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 1dB . . . 604.16 Mean Detection Time Comparison for Pr(H0) = 0.8 and ∆ = 1dB . . . 614.17 Detection Performance Comparison for ∆ = 2dB . . . . . . . . . . . . 614.18 Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 2dB . . . 624.19 Mean Detection Time Comparison for Pr(H0) = 0.8 and ∆ = 2dB . . . 62

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Introduction 1In this thesis we consider some spectrum sensing issues for cognitive radio applica-

tions. The purpose of this chapter is to introduce the problems addressed in thethesis, motivate the need for a new approach, and describe our main contributions

and the organization of the thesis.

1.1 Motivation

Over the last decade, wireless technologies have grown rapidly and more and more spec-trum resources are needed to support numerous emerging wireless services. The Na-tional Telecommunication and Information Administration’s (NTIA) chart of spectrumfrequency allocations in Figure 1.1, shows that within the current spectrum regulatoryframework, all of the frequency bands are exclusively allocated to specific services andaccording to the Federal Communication Commission (FCC) regulations no violationfrom unlicensed users is allowed. Therefore, the issue of spectrum scarcity becomesmore obvious and worries the wireless system designers and telecommunications policymakers. Furthermore, a recent survey of the spectrum utilization made by the FederalCommunications Commission (FCC) has indicated that the actual licensed spectrumis largely under-utilized in vast temporal and geographical dimensions [1].

While the current spectrum allocation leaves no available bandwidth for future wire-less systems, actual measurements of the spectrum utilization show that many assignedbands are not being used at every location and time. Figure 1.2 shows the spectrumutilization in the frequency range 0...6 GHz measured by the Berkeley Wireless Re-search Center (BWRC) at downtown Berkeley. We can see in the chart that for thefrequency ranges 2..3 GHz and 5...6 GHz, the spectrum utilization is less than 10%,while for 3...5 Ghz, it is even worse and is less than 1%.

Measurements taken over 10 minutes in the same location in Berkeley (Figure 1.3),show that there are also temporal gaps in the spectrum usage even in the 0 to 2.5 GHzband, which is considered to be very crowded (more than 30%). Such measurementsare also done in other areas in the US and the world with similar results. The results ofthese measurements, seriously question the suitability of the current regulatory regimeand possibly provide the opportunity to solve the spectrum scarcity problem.

In order to solve the conflicts between the spectrum scarcity and spectrum under-utilization, cognitive radio technology was recently proposed [2]. It can improve thespectrum utilization by allowing secondary users to borrow unused radio spectrum fromprimary licensed users. As an intelligent wireless communication system, a cognitiveradio is aware of the radio frequency environment. It selects the communication pa-rameters (such as carrier frequency, bandwidth and transmission power) to optimizethe spectrum usage and adapts its transmission and reception accordingly. One of the

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Figure 1.1: The NTIA’s Frequency Allocation Chart [1]

Figure 1.2: Measurement of Spectrum Utilization (0-6 GHz) in the Downtown Berkeley [25]

most critical components of the cognitive radio technology is spectrum sensing. Byadapting the transmission to the environment, a cognitive radio is able to fill in spec-trum holes and serve its users without causing harmful interference to the licensed user.Hence, spectrum sensing becomes a key function in the cognitive radio. In this thesis,we address two spectrum sensing problems and propose some algorithms to solve these

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issues.

Figure 1.3: Temporal Variation of the Spectrum Utilization (0-2.5 GHz) in the DowntownBerkeley [25]

1.2 Spectrum Sensing Issues

In short, cognitive radios as secondary users of licensed bands have to dynamicallysense the radio-spectrum environment in order to find spectrum holes (empty bands)and rapidly tune their transmitter parameters to efficiently utilize the available spec-trum. The spectrum sensing problem has been studied extensively in literature. Dif-ferent spectrum sensing techniques are categorized such as matched filtering, energydetection and cyclostationary detection [26]. Among them, matched filtering gives thebest performance but requires complete prior knowledge about the primary user signalwhich is not available all the time. Between cyclostationary and energy detection, en-ergy detection is easier to implement and has a smaller computational complexity, whilethe cyclostationary detection needs more computations but has a better performanceparticularly at low signal to noise ratio (SNR).

Furthermore, it has been shown that cooperative spectrum sensing using severalsecondary users performs far better than when only one user participates in spectrumsensing [4]. The reason is that a single user experience shadowing and multipath fadingthat effects its detection capabilities and sometimes due to hidden terminal problem

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a single user is not able to detect the primary user. Therefore, cooperative spectrumsensing can have better detection performance, since different users experience differentshadowing and fading effects. However, increasing the number of users means increasingthe energy consumption, bandwidth and traffic overhead in our system. Therefore, wehave to find an energy efficient approach which uses less energy but performs as wellas unconstrained energy detection techniques which is the subject of our thesis.

There are several energy efficient techniques which have been proposed for eithercognitive radio or sensor networks, among them the censoring and ”on/off” schemesare two major energy efficient techniques in literature [5],[10]. Assuming a distributeddetection system with a fusion center (FC), the idea behind censoring is that each usersends its decision to the FC, only if the decision is considered to be ”informative” [5].In the ”on/off” scheme, each user is randomly turned ”off” with a specific sleepingrate. In this thesis, we combine these schemes and propose a combined censoring and”on/off” technique in the context of energy detection based spectrum sensing. Wewill see that the proposed technique significantly reduces the energy consumption ofcooperative spectrum sensing.

The second problem that we consider in this thesis is the detection of the primaryuser at low SNR for a wide-band frequency range. As we said earlier, energy detectionis simple and able to locate the spectrum occupancy information quickly. However, itssensing capability is vulnerable to noise uncertainty [24].

Meanwhile, the cyclostationary feature detector locates the periodic cyclostationarysignature of a modulated signal by time or frequency domain signal processing. Itsspectrum sensing performance is robust to noise-like signals. However, this methodadds a lot of computational and implementation complexity to the system and consumesmore power than energy detection.

Recently, there have been a few efforts to study the problem of spectrum sensingfor wide-band signals. In this thesis, a two-stage wide-band spectrum sensing schemeis proposed which performs a coarse sensing using energy detection in a multi-channelfrequency band and locates possible spectrum holes. Then in the next stage a cyclo-stationary feature detector is used for fine sensing of the possible empty channels tomake a final decision about the occupancy of each channel.

1.3 Outline and Contributions

Before describing the content of the thesis chapter by chapter, we briefly summarizeour main contributions. The first major contribution is the development of a combinedcensoring and ”on/off” scheme as an energy efficient technique for cognitive radio. Inthis scheme, each user is randomly turned off with a specific sleeping rate. Furthermore,each active user adopts the censoring technique in order to send its decision to the FC.We show that this scheme is more energy efficient than the pure censoring and pure”on/off” schemes.

The second contribution of the thesis is a two-stage spectrum sensing technique forcognitive radio. This technique consists of a coarse and a fine sensing stage. In thecoarse sensing, we want to locate the possible empty channels in a frequency band withan energy detector. If the test statistic related to the energy detector is lower than

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a decision threshold, we go to the fine sensing stage to make sure that the channel isempty. In the fine sensing we use a cyclostationary detector and we compare the newtest statistic with a new threshold to decide whether the channel is confidently emptyor the primary user is present and we missed the primary user detection in the coarsesensing stage.

Chapter 2: Background discussionIn this chapter, first, we present a literature review of some specific energy efficient

techniques, namely, the censoring and ”on/off” schemes. For each scheme, we derive thedetection performance based on energy detection. The combination of these techniquesforms our first contribution of this work which is presented in Chapter 3.

Then, we present two different versions of two-stage spectrum sensing which areavailable in recent literature.

Chapter 3: Combined Censoring and ”On/Off” SchemeThis chapter contains the first contribution of the thesis. First, we present our

scheme and then analyze its detection performance in terms of the probability of falsealarm and detection. In order to express the censoring rate of each user, two situationsare considered: being aware of the probability of the primary user presence (or absence)or not being aware of such a priori knowledge. For each of these situations the relatedequations are derived. Then, we introduce the energy consumption of the spectrumsensing system as the cost function which has to be minimized subject to a specificdetection performance constraint. We continue this chapter by presenting an energyconsumption analysis of the proposed scheme for the IEEE 802.15.4/ZigBee system.Finally, we present an analysis of convexity of the proposed problem in this chapter.

Chapter 4: Two-Stage Spectrum SensingThis chapter contains the second contribution of the thesis. We present a novel two-

stage spectrum sensing technique in order to improve the detection performance at lowSNR. We present the coarse and fine sensing stages and derive their probability of falsealarm and detection. We define our problem as the maximization of the probability ofdetection subject to a false alarm rate constraint. Such a problem is equivalent to theminimization of the interference to the primary user subject to a constraint on missingan opportunity of spectrum utilization. Furthermore, we analyze the mean detectiontime of the proposed technique. Afterward, we present simulation results for differentnoise uncertainties.

Chapter 5: Conclusions and Further workThis chapter summarizes the main ideas of the thesis and gives suggestions for

further research in the area.

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Background discussion 2In our work, we consider two cognitive radio spectrum sensing issues. To account

for detection problems due to the effects such as shadowing, cooperative spectrumsensing among secondary users has been proposed. However, increasing the number

of sensors means increasing the energy consumption of the system. In this thesis,we propose an energy efficient cooperative spectrum sensing scheme which optimallyreduces the energy consumption based on a detection performance constraint.

The other problem which has been considered in our work is the detection of theprimary user at low SNR conditions for a wide-band spectrum sensing scheme.

In this chapter, we present an overview of the current techniques which addressesthe two problems that are discussed in this thesis.

First in section 2.1, we describe the two main energy efficient techniques which areavailable in literature. These two methods are the censoring and ”on/off” schemes[5],[10]. They have been proposed already for wireless sensor networks. In this chapter,we adopt these two techniques in the context of cooperative spectrum sensing. We firstpresent our spectrum sensing system model which is also used in Chapter 3. Then,we analyze the detection performance of different schemes based on the probability ofdetection and false alarm.

Second, in section 2.2, we introduce the available two-stage techniques for wide-bandspectrum sensing. One of the techniques is based on a wavelet transform approach inthe coarse sensing stage followed by an accurate detection technique such as featuredetection in the fine sensing. The other one is based on a wide-band energy detectionin the coarse sensing followed by a narrow-band energy detection in the fine sensing.

2.1 Current Energy Efficient Techniques

2.1.1 System Model

We consider a cooperative spectrum sensing system as shown in Figure 2.1. In thisscheme, there are N users which sense the spectrum and make their decision regardingpresence or absence of a primary user based on their observation Xi, i = 1, 2, ..., N .Each user decides between two hypotheses,

H0 : primary user is absent

H1 : primary user is present

and sends its decision to the fusion center (FC). The FC makes the final decision aboutthe presence of the primary user based on user decisions. So far, matched filtering,cyclostationary feature detection and energy detection have been proposed as spectrum

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Figure 2.1: Cooperative Spectrum Sensing Configuration

sensing techniques for cognitive radio. In this thesis, we employ the energy detectoras presented in [4] for its simple implementation and independency of prior knowledgeabout the primary user signal. For each observation at time k, Xik , two situations arepossible,

Xik =

{nik if H0

sik + nik if H1(2.1)

where the primary user’s signal and the noise are denoted by sik and nik , respectively.The noise is assumed to be an i.i.d random process with zero mean and variance σ2

ni,

while the signal is assumed to be an i.i.d random process with zero mean and varianceσ2

si. The signal to noise ratio (SNR) is defined as

γi =σ2

si

σ2ni

(2.2)

The decision rule which is employed by the energy detector, after normalization ofthe noise variance is

Ei =1

u

u∑

k=1

(X ′ik

)2H1

≷H0

λi :

{Di = 0 if H0

Di = 1 if H1(2.3)

where λi is the decision threshold related to user i and Di is the decision made by useri. Therefore, each user sends one bit per decision to inform the FC about its decisionon presence (”1”) or absence (”0”) of the primary user. The test statistic of the energydetector (Ei) is a chi-square distribution given by

Ei =

{χ2

2u if H0

χ22u(2γi) if H1

(2.4)

where χ22u is a central chi-square distribution with 2u degrees of freedom and χ2

2u(2γi)is a noncentral chi-square distribution with 2u degrees of freedom, and non-centralityparameter 2γi. Further, u = TW is the time-bandwidth product. The probability of

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false alarm for each user is

Pfi= Pr(Ei > λi|H0) =

Γ(u, λi

2)

Γ(u)(2.5)

where Γ(a) is the gamma function and Γ(a, x) is the incomplete gamma function(Γ(a, x) =

∫∞x

ta−1e−tdt). The probability of detection for each user is

Pdi= Pr(Ei > λi|H1) = Qu(

√2γi,

√λi) (2.6)

where Qu(a, x) is the generalized Marcum Q-function (Qu(a, x) =1

au−1

∫∞x

tue−t2+a2

2 Iu−1(at)dt, with Iu−1(.), the modified Bessel function of the first kindand order u− 1).

The system model which we have discussed in this section has a constant energyconsumption irrespective of the detection performance of the system. In current com-munication systems, the energy consumption of the system is a very important factorin network design. In the following sections, we are going to present two energy ef-ficient techniques to relate the cost of cooperative spectrum sensing to the detectionperformance of the system and then try to reduce this cost for a certain detectionperformance.

2.1.2 Energy Efficient Techniques

The energy consumption of cooperative spectrum sensing, which has been presented insection 2.1.1, tends to increase as the number of users increases, while the detectionperformance does not change that much. Therefore, it is necessary to reduce the numberof participating users in spectrum sensing in a way to reduce the energy consumption,while keeping the detection performance of the system at an acceptable level.

In this section we present two energy efficient techniques which have been proposedin recent literature about either wireless sensor networks or cognitive radio. First,we reduce the transmission energy via censoring a number of users, second, we try torandomly turn ”off” the users to reduce both processing and transmission energy ofthe cognitive radio system. In Chapter 3, we see how the combination of these twoapproaches can give the optimal energy efficiency for a cooperative spectrum sensingsystem.

2.1.2.1 Censoring Scheme

The transmission energy is responsible for a major part of the energy sink in everycommunication system. A significant amount of energy has to be consumed for reli-able transmission of an information packet to the destination. In case of distributedspectrum sensing, each user has to spend a significant amount of energy to transmitits decision to the fusion center. The question then is if it is necessary that all theusers transmit their decisions to the FC, all the time, or can they just don’t send their

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decision when it is not necessary. Censoring is an idea which has been proposed forthis case and it has been studied mainly for sensor networks [5],[6].

The idea behind censoring is that each user sends its decision to the FC, only if thisdecision is considered to be ”informative”. In this thesis, we use the censoring schemeof [6]. Without loss of generality, we assume that every user has the same channelcondition and SNR and thus the same decision rule. The censoring rule we consider isgiven by

”send 1” if Ei ≥ λ2

”no decision” if λ1 < Ei < λ2

”send 0” if Ei ≤ λ1

(2.7)

where λ1 and λ2 are lower and upper thresholds, respectively.In such a scenario, we define the probability of false alarm (Pfc), detection (Pdc)

and miss (Pmc) as

Pfc = Pr(Ei ≥ λ2|H0) =Γ(u, λ2

2)

Γ(u)(2.8)

Pdc = Pr(Ei ≥ λ2|H1) = Qu(√

2γ,√

λ2) (2.9)

In this work, we assume that we are not aware of the probability of primary userpresence Pr(H1) (or absence, Pr(H0)) but we assume that Pr(H1) is lower than Pr(H0)which is a good assumption for cognitive radio networks. Therefore, for each user wecan define the censoring rate ρ as

ρ = Pr(λ1 < Ei < λ2|H0)

=Γ(u, λ1

2)

Γ(u)− Γ(u, λ2

2)

Γ(u)(2.10)

Employing the OR rule at the FC and assuming L users have sent their decision tothe FC, the global probability of false alarm (QFc) is

QFc = Pr(DFC = 1, L ≥ 1|H0)

= Pr(DFC = 1|H0, L ≥ 1)Pr(L ≥ 1|H0) (2.11)

where DFC is the final decision at the FC. Since

Pr(L ≥ 1|H0) = 1− Pr(L = 0|H0)

= 1− ρN (2.12)

and

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Pr(DFC = 1|H0, L ≥ 1) =N∑

L=1

(NL

)

×ρN−L(1− ρ)L[1− (1− Pfc)L] (2.13)

we obtain

QFc = (1− ρN)N∑

L=1

(NL

)ρN−L(1− ρ)L[1− (1− Pfc)

L] (2.14)

The global probability of detection for the censoring scheme (QDc) is

QDc = Pr(DFC = 1, L ≥ 1|H1)

= Pr(DFC = 1|H1, L ≥ 1)Pr(L ≥ 1|H1) (2.15)

where

Pr(L ≥ 1|H1) = 1− Pr(L = 0|H1)

= 1− δN (2.16)

with δ = P (λ1 < Ei < λ2|H1) and

Pr(DFC = 1|H1, L ≥ 1) =N∑

L=1

(NL

)

×ρN−L(1− ρ)L[1− (1− Pdc)L] (2.17)

Therefore

QDc = (1− δN)N∑

L=1

(NL

)ρN−L(1− ρ)L[1− (1− Pdc)

L] (2.18)

We assume the average cost of each user (which is related to the energy consumptionof the cognitive radio system) consists of a sensing (observation or processing) cost Csi

and a transmission cost Cti . Such a cost model can be used easily as the energy modelof each user. Therefore, the total cost of the system considering a censoring rate ρ is

Cc =N∑

i=1

[Csi+ Cti(1− ρ)] (2.19)

In this work, we want to maximize the lifetime of a cooperative spectrum sensingtechnique for a certain detection performance. In other words, we like to minimize thecost subject to a false alarm and detection rate constraint.

11

The reason behind such a constraint is that in a cognitive radio system, we wantto exploit spectrum holes, opportunistically, while we also want to keep the level ofinterference to a primary user signal bellow a threshold. In statistical signal processingterms, the probability of false alarm presents the probability of loosing the opportunityof spectrum utilization by a secondary user and the probability of detection representsthe probability of not interfering with a primary user. In a cognitive radio network, itis desirable to have a high probability of detection and a low probability of false alarm.

Figures 2.2 to 2.4 show the probability of detection versus the probability of falsealarm or receiver operating characteristic (ROC) for different censoring rates and num-ber of users (N = 2, N = 5, N = 10, respectively) and SNR γ = 10 dB. We see that forthe same probability of detection and false alarm, increasing the number of users meansincreasing the censoring rate. Furthermore, as we expected, increasing the censoringrate leads to a decreasing detection performance, but this reduction is not significant,particularly when the number of cooperating users is high. However, as we can see inthese graphs, there is a tradeoff between having a high probability of detection and lowprobability of false alarm. As we said earlier, our problem is

min(λ1,λ2)

Cc

s.t. QFc ≤ α, QDc ≥ β(2.20)

where α and β are the detection performance constraints for the probability of falsealarm and probability of detection, respectively, and Cc is the total system cost for thecensoring scheme as defined in (2.20).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.4

0.5

0.6

0.7

0.8

0.9

1

QFc

QD

c

N=2, SNR=10dB

ρ=0

ρ=0.1

ρ=0.15

ρ=0.2

Figure 2.2: ROC for N=2

12

0 0.2 0.4 0.6 0.8 10.75

0.8

0.85

0.9

0.95

1

QFc

QD

c

N=5, SNR=10dB

ρ=0

ρ=0.1

ρ=0.2

ρ=0.4


0 0.2 0.4 0.6 0.8 10.86

0.88

0.9

0.92

0.94

0.96

0.98

1

QFc

QD

c

N=10, SNR=10dB

ρ=0

ρ=0.2

ρ=0.4

ρ=0.6


13

As an example, to solve (2.21), we look at Figure 2.5. In this figure, our constraintsare α = 0.2 and β = 0.99 for a cooperative spectrum sensing scheme consisting ofN = 10 users and SNR γ = 10 dB. The grey area in Figure 2.5 is our desired areawhere we want to minimize the cost. For the censoring scheme, minimization of thecost in (2.20) means maximization of the censoring rate, ρ. As it is also apparent inFigure 2.5, for the considered detection performance constraints, ρ is maximized whenQFc = 0.2 and QDc = 0.99. In other words, for a certain detection performance, ρis maximized for QFc = α and QDc = β. The reason is that when we increase ρ, wedecrease the mean number of cooperating users, which in an OR rule based distributeddetection leads to a reduction in the probability of detection for a certain probabilityof false alarm.

0 0.2 0.4 0.6 0.8 10.86

0.88

0.9

0.92

0.94

0.96

0.98

1

QFc

QD

c

N=10, SNR=10dB

ρ=0

ρ=0.2

ρ=0.4

ρ=0.6

QDc

=0.99Q

Fc=0.2

Figure 2.5: Feasible set of the problem (2.21)

2.1.2.2 On/Off Scheme

When increasing the number of users, we spend a lot of energy on observation, pro-cessing and transmission, while increasing the number of users does not improve thedetection performance of the system linearly. Hence, it is not necessary to exploit allthe users all the time for spectrum sensing.

The energy consumption of a cognitive radio system mainly depends on two factors:the processing energy, transmission energy. The processing energy is the amount ofenergy that a cognitive radio consumes during the detection time to sense the spectrumand to make its decision about the presence or absence of the primary user as well as

14

the energy consumption due to signal shaping, modulation, coding, memory access andother signal processing efforts before transmission [9]. The transmission energy is theenergy to send the decisions reliably to the FC at an acceptable SNR.

In 2.1.2.1, the transmission energy of the system is reduced by reducing the numberof transmissions to the FC. Although, the transmission is a major energy consumer ofthe whole system, in case of short range radio communications, the processing energybecomes very important and sometimes even dominant to the transmission energy[23]. Therefore, it seems to be valuable to propose a scheme which reduces both thetransmission and processing energy. The idea presented in this section is to let usersrandomly turn their radio ”off” or ”on” at the beginning of a detection slot. Such an”on/off” scheme has already been suggested for sensor networks [10], but the effect ofthis sleeping scheme has not yet been analyzed for energy detection based spectrumsensing.

In this work, we assume that every user is ”off” with a sleeping rate µ 6= 0 during adetection slot. We define the total cost of the system using the ”on/off” scheme withsleeping rate µ as

Co = (1− µ)N∑

i=1

(Csi+ Cti) (2.21)

Without loss of generality, we assume in this work that the probability of false alarmand probability of detection for each user are the same (every user experiences the sameSNR and employs the same decision rule).

In this scheme, each active user at a specific detection slot decides about presence orabsence of the primary user and sends the decision to the FC. In the ”on/off” scheme,the FC again chooses an OR rule to make the final decision. Therefore, the globalprobability of false alarm (QFo), for this scheme, assuming the number of active usersis denoted as K, is

QFo = Pr(DFC = 1, K ≥ 1|H0)

= Pr(DFC = 1|H0, K ≥ 1)Pr(K ≥ 1|H0) (2.22)

where

Pr(K ≥ 1|H0) = 1− Pr(K = 0|H0)

= 1− µN (2.23)

and

Pr(DFC = 1|H0, K ≥ 1) =N∑

K=1

(NK

)

×µN−K(1− µ)K [1− (1− Pf )K ] (2.24)

15

with Pf derived in (2.5). Therefore, we obtain

QFo = (1− µN)N∑

K=1

(NK

)µN−K(1− µ)K [1− (1− Pf )

K ] (2.25)

The global probability of detection (QDo), can be derived in a similar way as follows

QDo = Pr(DFC = 1, K ≥ 1|H1)

= Pr(DFC = 1|H1, K ≥ 1)Pr(K ≥ 1|H1) (2.26)

where

Pr(K ≥ 1|H1) = 1− Pr(K = 0|H1)

= 1− µN (2.27)

and

Pr(DFC = 1|H1, K ≥ 1) =N∑

K=1

(NK

)

×µN−K(1− µ)K [1− (1− Pd)K ] (2.28)

with Pd derived in (2.6). Therefore, we obtain

QDo = (1− µN)N∑

K=1

(NK

)µN−K(1− µ)K [1− (1− Pd)

K ] (2.29)

Figures 2.6 to 2.8 show the probability of detection versus the probability of falsealarm for different sleeping rates and number of users (N = 2, N = 5, N = 10,respectively) and SNR γ = 10 dB. We see that as for the censoring scheme, for the sameprobability of detection and false alarm, increasing the number of users means increasingthe sleeping rate. Furthermore, as expected, increasing the sleeping rate, leads to adecreasing detection performance, but this reduction is not significant, particularlywhen the number of cooperating users is high. However, as we can see in these graphs,there is a tradeoff between having a high probability of detection and low probabilityof false alarm. As for the censoring case, for the ”on/off” scheme, our problem is

min(µ,λ)

Co

s.t. QFo ≤ α, QDo ≥ β(2.30)

where α and β are the detection performance constraints for the probability of falsealarm and the probability of detection, respectively, and Co is the total system cost forthe ”on/off” scheme as defined in (2.22).

As an example, to solve the problem (2.31), we look at Figure 2.9. In this figure,our constraints are α = 0.1 and β = 0.98 for a cooperative spectrum sensing scheme

16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

QFo

QD

o

N=2, SNR=10dB

µ=0

µ=0.1

µ=0.15

µ=0.2


0 0.2 0.4 0.6 0.8 10.75

0.8

0.85

0.9

0.95

1

QFo

QD

o

N=5, SNR=10dB

µ=0

µ=0.1

µ=0.2

µ=0.4


17

0 0.2 0.4 0.6 0.8 10.86

0.88

0.9

0.92

0.94

0.96

0.98

1

QFo

QD

o

N=10, SNR=10dB

µ=0

µ=0.2

µ=0.4

µ=0.6


consisting of N = 10 users and SNR γ = 10 dB. The dashed area in Figure 2.9is the desired area where we want to minimize the cost. For the ”on/off” scheme,minimization of the cost in (2.31) means maximization of the sleeping rate µ. Aswe can see in Figure 2.9, for the considered detection performance constraints, µ ismaximized when QFo = 0.1 and QDo = 0.98. In other words, as for the censoring case,for a certain detection performance, µ is maximized for QFo = α and QDo = β.

2.2 Two-Stage Spectrum Sensing

As we said earlier in Chapter 1, spectrum sensing is the most critical part in the imple-mentation of a cognitive radio. When a cognitive radio is activated in an environment,it has to search for an empty band. Upon detection of an empty band, the cognitiveradio can label it as a spectrum hole and can exploit it until a primary user signalappears. Therefore, it is important to enable the cognitive radio to sense a spectrumthat is as wide as possible. Furthermore, the modulation of the secondary users needsa wide bandwidth to operate such as OFDM signal modulation.

So far, there have been few works in the area of wide-band spectrum sensing. Amongthem the two-stage sensing attracted some attention in literature. These ideas arebriefly summarized in the following.

Y. Hur, et al. [21]: The architecture of the proposed cognitive radio access system isshown in Figure 2.10. The idea is that at the beginning of the spectrum sensing process,a coarse sensing is performed over the entire frequency range with a wide bandwidth.

18

0 0.2 0.4 0.6 0.8 10.86

0.88

0.9

0.92

0.94

0.96

0.98

1

QFo

QD

o

N=10, SNR=10dB

µ=0

µ=0.2

µ=0.4

µ=0.6

QFo

=0.1Q

Do=0.98

Figure 2.9: Feasible set of the problem (2.31)

Through this step, pre-occupied spectrum bands, where the energy level is over thethreshold level and possible spectrum holes for secondary users are identified. Thiscourse sensing result is reported to the medium access control (MAC). Then, for thesepossible empty bands, the fine sensing detects the unique features of the modulatedsignals. If the spectrum band is confirmed to be unoccupied through the fine sensing,the MAC assigns this spectrum hole for the secondary users. For the coarse sensingstage, a wavelet transform approach is used to reconstruct the power spectral densityof the signal. From comparing the derived power spectral density in each band withthe threshold level, we can determine whether the spectrum band is possibly empty ornot.

L. Luo and S. Roy [20]: In this scheme as, it is shown in Figure 2.11, the authorsassume a total bandwidth B, which is divided into N channels with bandwidth Bc.They assume that L empty channels are randomly distributed among the total Nchannels and furthermore, L/N << 1. First the total bandwidth is divided into βequal-size coarse sensing blocks (CSBs). Each CSB has α channels: α = N/β.

In the coarse sensing stage, one of the CSBs is randomly selected and checked for thepossibility of having at least one empty channel. An energy detector with bandwidthBsense = αBc is used as the detection technique. This random search continues untilone block with at least one empty channel is determined.

Upon detection of one possibly empty block, in the fine sensing stage, a serial search(one by one channel sensing in a row) is done until one empty channel is determined.In this stage, the same energy detector with bandwidth Bsense = Bc is used.

19

Figure 2.10: Block diagram of the cognitive radio proposed by Y. Hur et al [21]

Figure 2.11: Two-stage sensing scheme of [20]

20

2.3 Conclusions

In this chapter, we have first introduced an energy detection based cooperative spectrumsensing scheme in section 2.1. Then, we have discussed two major energy efficienttechniques which are available in literature. These two techniques are the censoringand ”on/off” schemes. Furthermore, we have analyzed their detection performance interms of the probability of false alarm and detection. The introduced system modeland energy efficient techniques in section 2.1 will be used in Chapter 3 to develop acombined censoring and ”on/off” scheme which is our first contribution in this thesis.

In section 2.2, we have discussed available two-stage sensing techniques. In thesetechniques the detection performance is not analyzed. In Chapter 4, we will introducea novel two-stage sensing technique as well as its detection performance analysis whichis our second contribution of this work.

21

Combined Censoring and”On/Off” Scheme 3In this chapter, we address the problem of energy efficiency for a cooperative spectrum

sensing scheme.

To account for spectrum sensing sensitivity to multipath fading and shadowing,it has been shown that cooperative spectrum sensing using several secondary users,performs far better than single user detection [3]. However, increasing the number ofusers means increasing the energy consumption, bandwidth and traffic overhead in oursystem. In this chapter, we present an energy efficient technique that optimally reducesthe energy consumption of the system for a certain detection performance. The pro-posed technique, which is called combined censoring and ”on/off” scheme, combines theadvantages of existing pure censoring and pure ”on/off” schemes presented in Chapter2. Afterwards, we analyze the energy consumption of the proposed method for a specialcase of IEEE 802.15.4/ZigBee which is designed as a low rate energy efficient protocolfor sensor networks and works in the 2.4 GHz ISM frequency band [8].

3.1 Combined Censoring and ”On/Off” Scheme

The energy consumption (cost) of the basic cooperative spectrum sensing scheme whichhas been presented in section 2.1.1, tends to increase, as the number of users increases,while the detection performance does not change that much. Therefore, it is necessaryto reduce the number of users participating in the spectrum sensing in order to reducethe energy consumption, while keeping the detection performance of the system at anacceptable level.

So far, different energy efficient techniques have been proposed for wireless sensornetworks, which we can apply for cognitive radio. As we discussed in Chapter 2, thesetechniques either try to reduce the number of decision transmissions to the FC in thecensoring scheme [5]-[6], or try to turn the sensors randomly ”off” in the ”on/off” scheme[10]. In this work, we want to combine these two techniques in order to minimize theenergy consumption of the system for a certain detection performance constraint.

In the combined censoring and ”on/off” scheme, the decision rule of a participatinguser is defined as

”send 1” if Ei ≥ λ2

”no decision” if λ1 < Ei < λ2

”send 0” if Ei ≤ λ1

(3.1)

Based on this decision rule, the probability of detection (Pdc) and false alarm (Pfc)

23

for a participating user are

Pfc = Pr(Ei ≥ λ2|H0) =Γ(u, λ2

2)

Γ(u)(3.2)

Pdc = Pr(Ei ≥ λ2|H1) = Qu(√

2γ,√

λ2) (3.3)

Assuming a sleeping rate µ 6= 0 and a censoring rate ρ 6= 0, we define the total costof the system (Coc) as

Coc = (1− µ)N∑

i=1

(Csi+ Cti(1− ρ)) (3.4)

where Csiand Cti are the sensing and transmission cost of each user, respectively.

Assuming Pr(H1) is lower than Pr(H0), ρ can be expressed as

ρ = Pr(λ1 < Ei < λ2|H0)

=Γ(u, λ1

2)

Γ(u)− Γ(u, λ2

2)

Γ(u)(3.5)

In case we are aware of the prior probability of the target presence (or absence), wecan express the censoring rate of each user as

ρ = π0Pr(λ1 < Ei < λ2|H0) + π1Pr(λ1 < Ei < λ2|H1)

= π0δ0 + π1δ1 (3.6)

where π0 = Pr(H0) and π1 = Pr(H1).In this scheme, each active user at a specific detection slot decides about the presence

or absence of the primary user based on the decision rule in (3.1) and if it comes upwith a decision, it sends the decision result to the FC. The FC employs the OR ruleto make the final decision. In sections 3.1.1 and 3.1.2, we will analyze the detectionperformance of the combined censoring and ”on/off” scheme in terms of probability offalse alarm and detection.

3.1.1 Detection Performance without Prior Knowledge

In this section, we want to analyze the detection performance of the combined censoringand ”on/off” scheme, for the case we are not aware of π0 and π1. In section 3.1.2 we willanalyze the detection performance of the system for the case we have prior knowledgeabout π0 and π1.

The global probability of false alarm (QFoc), assuming the number of active usersto be K, and L users out of K active users send their decision to the FC, is

24

QFoc = Pr(DFC = 1, L ≥ 1, K ≥ 1|H0)

= Pr(DFC = 1|H0, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1, K ≥ 1|H0)

= Pr(DFC = 1|H0, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1|K ≥ 1, H0)Pr(K ≥ 1|H0) (3.7)

where Pr(K ≥ 1|H0) and Pr(L ≥ 1|K ≥ 1, H0) are

Pr(K ≥ 1|H0) = 1− Pr(K = 0|H0)

= 1− µN (3.8)

Pr(L ≥ 1|K ≥ 1, H0) = 1− Pr(L = 0|K ≥ 1, H0)

= 1− ρK (3.9)

and

Pr(DFC = 1|H0, L ≥ 1, K ≥ 1) =N∑

K=1

{ (NK

)

×µN−K(1− µ)K

[K∑

L=1

(KL

)

×ρK−L(1− ρ)L[1− (1− Pfc)L]

]}(3.10)

with Pfc derived in (3.2). Therefore, we obtain

QFoc = (1− µN)

{N∑

K=1

(NK

)µN−K(1− µ)K(1− ρK)

×[

K∑L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pfc)

L]

]}(3.11)

The global probability of detection (QDoc) can be derived in a similar way as follows

QDoc = Pr(DFC = 1, L ≥ 1, K ≥ 1|H1)

= Pr(DFC = 1|H1, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1, K ≥ 1|H1)

= Pr(DFC = 1|H1, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1|K ≥ 1, H1)Pr(K ≥ 1|H1) (3.12)

25


Pr(K ≥ 1|H1) = 1− Pr(K = 0|H1)

= 1− µN (3.13)

Pr(L ≥ 1|K ≥ 1, H1) = 1− Pr(L = 0|K ≥ 1, H1)

= 1− δK (3.14)

with δ = P (λ1 < Ei < λ2|H1), and

Pr(DFC = 1|H1, L ≥ 1, K ≥ 1) =N∑

K=1

{ (NK

)

×µN−K(1− µ)K

[K∑

L=1

(KL

)

×ρK−L(1− ρ)L[1− (1− Pdc)L]

]}(3.15)

with Pdc derived in (3.3). Therefore, we obtain

QDoc = (1− µN)

{N∑

K=1

(NK

)µN−K(1− µ)K(1− δK)

×[

K∑L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pdc)

L]

]}(3.16)

3.1.2 Detection Performance with Prior Knowledge

In section 3.1.1, we considered the case where we are not aware of the prior knowledgeabout the primary user, which is true in most situations. However, in order to completeour discussion, we also analyze the detection performance of the scheme, for the case wehave prior knowledge about the probability of the primary user presence (or absence).

In this case, the global probability of false alarm (QFoc) is

QFoc = Pr(DFC = 1, L ≥ 1, K ≥ 1|H0)

= Pr(DFC = 1|H0, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1, K ≥ 1|H0)

= Pr(DFC = 1|H0, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1|K ≥ 1, H0)Pr(K ≥ 1|H0) (3.17)

26


Pr(K ≥ 1|H0) = 1− Pr(K = 0|H0)

= 1− µN (3.18)

Pr(L ≥ 1|K ≥ 1, H0) = 1− Pr(L = 0|K ≥ 1, H0)

= 1− δK0 (3.19)

and

Pr(DFC = 1|H0, L ≥ 1, K ≥ 1) =N∑

K=1

{ (NK

)

×µN−K(1− µ)K

[K∑

L=1

(KL

)

×ρK−L(1− ρ)L[1− (1− Pfc)L]

]}(3.20)

with Pfc derived in (3.2). Therefore, we obtain

QFoc = (1− µN)

{N∑

K=1

(NK

)µN−K(1− µ)K(1− δK

0 )

×[

K∑L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pfc)

L]

]}(3.21)

The global probability of detection (QDoc) can be derived in a similar way as follows

QDoc = Pr(DFC = 1, L ≥ 1, K ≥ 1|H1)

= Pr(DFC = 1|H1, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1, K ≥ 1|H1)

= Pr(DFC = 1|H1, L ≥ 1, K ≥ 1)

× Pr(L ≥ 1|K ≥ 1, H1)Pr(K ≥ 1|H1) (3.22)


Pr(K ≥ 1|H1) = 1− Pr(K = 0|H1)

= 1− µN (3.23)

27

Pr(L ≥ 1|K ≥ 1, H1) = 1− Pr(L = 0|K ≥ 1, H1)

= 1− δK1 (3.24)

and

Pr(DFC = 1|H1, L ≥ 1, K ≥ 1) =N∑

K=1

{ (NK

)

×µN−K(1− µ)K

[K∑

L=1

(KL

)

×ρK−L(1− ρ)L[1− (1− Pdc)L]

]}(3.25)

with Pdc derived in (3.3). Therefore, we obtain

QDoc = (1− µN)

{N∑

K=1

(NK

)µN−K(1− µ)K(1− δK

1 )

×[

K∑L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pdc)

L]

]}(3.26)

3.1.3 Analysis and Problem Definition

We define our problem as the minimization of the cost in (3.4) for a certain detectionperformance as follows

min(µ,λ1,λ2)

Coc

s.t. QFoc ≤ α, QDoc ≥ β(3.27)

where α and β are the detection performance constraints for the probability of falsealarm and the probability of detection, respectively and Coc is the total system cost forthe censoring and ”on/off” scheme as defined in (3.4).

The optimization problem (3.27) is a highly non-linear optimization problem whichis very difficult to solve analytically. Therefore we look for a suboptimal approach.Before we discuss how we are going to solve this problem, it is interesting to explorethe inherent trade off between the sleeping and censoring rate in this scheme. At firstwe analyze the problem without prior knowledge as presented in section 3.1.3.1 andthen with prior knowledge as discussed in section 3.1.3.2.

3.1.3.1 Problem Analysis without Prior Knowledge

At this point, looking at the problem (3.27), we know that for ρ → 0 we reduceour scheme to a pure ”on/off” one, while for µ → 0 we have a pure censoring scheme.

28

Figures 3.1 to 3.4 show how the sleeping rate changes with respect to the censoring ratefor different numbers of cooperating users and detection performance constraints. In allscenarios, we put the false alarm rate constraint to QFoc ≤ 0.1 and the SNR is set to beγ = 10 dB. In these figures, the detection rate constraint is QDoc ≥ 0.7, 0.8, 0.9, 0.99,respectively. In each figure, we can see how the sleeping rate changes with the censoringrate for a certain detection performance constraint and different numbers of users (N =2, 5, 10). As we can see, there is an inherent tradeoff between the sleeping rate andthe censoring rate in the combined censoring and ”on/off” scheme, which is not a linearrelation. Therefore, the choice of the sleeping and censoring rate in order to minimizethe average cost, depends on the sensing cost (Csi

) and the transmission cost (Cti) ofeach user. We also know that the transmission cost by itself depends on the distanceof the users to the FC and hence on the network topology. Thus, for the combinedcensoring and ”on/off” scheme, our assumptions about the sensing and transmissioncost affects the optimal sleeping and censoring rate. In section 3.2, we will discussabout the optimal sleeping and censoring rate for a 2.4 GHz IEEE 802.15.4/ZigBeesystem and a WLAN 802.11g system.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Censoring Rate

Sle

epin

g R

ate

QF<=0.1, QD>=0.7, SNR=10dB

N=2N=5N=10

Figure 3.1: Feasible µ and ρ for QFoc ≤ 0.1 and QDoc ≥ 0.7

3.1.3.2 Problem Analysis with Prior Knowledge

Figures 3.5 and 3.6 show how the censoring rate changes with the sleeping rate for thecase that we are aware of the prior knowledge about the probability of the primaryuser presence π1 = Pr(H1) (or absence π0 = Pr(H0)). In both figures we assume theSNR is γ = 10 dB, the number of users is N = 5 and the probability of false alarm

29

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8QF<=0.1, QD>=0.8, SNR=10dB

Censoring Rate

Sle

epin

g R

ate

N=2N=5N=10


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Censoring Rate

Sle

epin

g R

ate

QF<=0.1, QD>=0.9, SNR=10dB

N=2N=5N=10


30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Censoring Rate

Sle

epin

g R

ate

QF<=0.1, QD>=0.99, SNR=10dB

N=2N=5N=10


constraint is QFoc ≤ 0.1.

In Figure 3.5, we assume the probability of primary user absence is Pr(H0) = 0.8which is larger than Pr(H1). As we can see, the curves for different detection rateconstraints are almost the same as the curves for the case we have no prior knowledgebut we assumed that Pr(H1) < Pr(H0). Hence, Figure 3.5 confirms our censoring ratedefinition in (3.5) for the case without prior knowledge.

However, in Figure 3.6, the curves are not similar to the curves for the case withoutprior knowledge. As we can see, the possible region for the censoring rate is reducedcompared to Figure 3.5. The reason is that if the probability of primary user presenceis higher, then the probability of each sensor sending its results to the FC, would behigher as well, and thus the censoring rate reduces.

3.2 Energy Consumption Analysis

In this section, we want to analyze the energy consumption of the combined censoringand ”on/off” scheme and discuss how to derive the optimal censoring and sleeping rates,for a certain detection performance. We consider a 2.4 GHz IEEE 802.15.4/ZigBeesystem as well as a WLAN 802.11g system. In the following sections we first give anintroduction to the considered system, then we present the channel and radio modelwhich are used in our analysis and finally we analyze the energy consumption of thepresented scheme.

31

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8P(H0)=0.8, SNR=10dB, N=5, QF<=0.1

Sleeping Rate(µ)

Cen

sorin

g R

ate(

ρ)

QD>=0.7QD>=0.8QD>=0.9QD>=0.99

Figure 3.5: Feasible µ and ρ for QFoc ≤ 0.1 with Pr(H0) = 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7P(H0)=0.2, SNR=10dB, N=5, QF<=0.1

Sleeping Rate(µ)

Cen

sorin

g R

ate(

ρ)

QD>=0.7QD>=0.8QD>=0.9QD>=0.99

Figure 3.6: Feasible µ and ρ for QFoc ≤ 0.1 with Pr(H0) = 0.2

32

3.2.1 IEEE 802.15.4/ZigBee

The IEEE 802.15.4 is designed for low data rate wireless personal area networks(WPANs) to provide low-complexity, low-cost and low-power wireless connectivityamong inexpensive devices. The IEEE 802.15.4/ZigBee is a special type of this proto-col and can be used in the 2.4 GHz Industrial, Scientific and Medical (ISM) frequencyband with a maximum data rate of 250 kbps in the range of 10 to 70 m [8]. In thisthesis we use a Chipcon CC2420 which is designed as a 2.4 GHz IEEE 802.15.4/ZigBeeRF transceiver. CC2420 includes a digital direct sequence spread spectrum basebandmodem providing a spreading gain of 9 dB and an effective data rate of 250 kbps. TheCC2420 is a low-cost, highly integrated solution for robust wireless communications inthe 2.4 GHz unlicensed ISM band [8].

3.2.2 Channel and Radio Model

In this work, we use the channel and radio model that is used in [7] for the energy con-sumption analysis. In a wireless channel, electromagnetic propagation can be modeledas an attenuation following a power law function of the distance between the transmitterand receiver. Due to the short range communication between the different users a sim-ple free space path loss model (d2 reduction) is assumed for the IEEE 802.15.4/ZigBeesystem [7].

The processing energy for each decision consists of two parts: the energy consump-tion of sensing and making the decision and the energy consumption of the signalprocessing part for modulation, signal shaping, etc, [9]. The sensing energy of thisscheme depends on the number of samples taken during the detection time. Since thebandwidth of each channel in ZigBee is 5 MHz, if we take 5 samples, then the detectiontime is T = 1 µs. The typical circuit power consumption of ZigBee is approximately40 mW . Therefore, the sensing energy of each user is approximately 40 nJ . The pro-cessing energy related to the signal processing part in the transmit mode for a datarate of 250 kbps and a voltage-current couple of (2.1 V, 17.4 mA) is approximately150 nJ/bit. Since we use one bit per decision, the processing energy of each user isCs = 190 nJ .

In the considered model the transmitter dissipates the energy to run the radioelectronics and the power amplifier. As discussed earlier, the power attenuation dependson the distance between the transmitter and receiver. The power control can be usedto invert this loss by setting the power amplifier to ensure a certain power threshold(−90 dBm in the worst case for CC2420) at the receiver. Therefore, to transmit onebit over a distance d, the radio spends:

Cti(d) = Ct−elec + Ct−amp(d) (3.28)

= Ct−elec + eampd2 (3.29)

where Ct−elec is the transmitter electronics energy. Assuming a data rate of 250 kbpsand a transmit power of 20 mW , [11], Ct−elec = 80 nJ/bit. The eamp to satisfy a receiversensitivity of −90 dBm for SNR= 10 dB is 40.4 pJ/bit/m2.

33

3.2.3 Optimal Sleeping and Censoring Rate

In Section 3.1, we discussed the combined censoring and ”on/off” scheme and intro-duced the problem (3.27) in order to find the optimal censoring and sleeping rate forthis scheme, subject to a detection performance constraint. As we mentioned earlier,the problem (3.27) is highly non-linear and difficult to solve. Here, we propose a subop-timal approach to find the sleeping rate and censoring rate to minimize the cost whichis defined as the energy consumption of the system.

In order to illustrate our approach, we use the 2.4 GHz IEEE 802.15.4/ZigBee asthe communication technology for our secondary users which have to cooperate witheach other to sense the spectrum. For the numerical analysis, we consider our networkto be a square field with a length of 100 m, where the users are uniformly distributedand the FC is located in the center. Every numerical result in this section is averagedover 1000 runs.

3.2.3.1 Energy Consumption of the System without Prior Knowledge

Our approach is to see how the energy consumption of the system changes with thesleeping rate (µ) and the censoring rate (ρ) and to find the sleeping and censoring ratethat minimize the energy consumption. Figure 3.7 shows the energy consumption of thesystem with respect to the censoring and sleeping rate for N = 10 users and differentdetection rate constraints but the same false alarm rate constraint(QFoc ≤ 0.1). Wecan see that for the case of a 2.4 GHz IEEE 802.15.4/ZigBee system, the sleepingscheme is completely dominant over the censoring scheme, because in every case, theoptimal sleeping rate for this system is located where the censoring rate is equal to zero(ρ = 0). The reason behind such a result for this radio model is that the sensing energyis dominant over the transmission energy for this short range range radio model.

At this point, it is interesting to compare the energy consumption of the combinedcensoring and ”on/off” scheme with existing techniques. Figure 3.8 shows the energyconsumption of the pure censoring, the pure ”on/off”, the combined censoring and”on/off” and the no censoring/no ”on/off” schemes with respect to the probabilityof detection for N = 10 users, SNR= 10 dB and QF ≤ 0.1. We can see that forthe case of ZigBee, the sleeping scheme is optimal as its energy consumption is equalto the case of the combined censoring and ”on/off” scheme, which always gives theoptimal energy efficiency with respect to the pure censoring or pure ”on/off” scheme.This analysis shows that for low-rate, short-range radios such as ZigBee, the sleepingscheme is a promising approach to optimally reduce the energy consumption of thespectrum sensing system while keeping the detection performance of the system at anacceptable level.

As an example of a system where the transmission energy is higher than the sensingenergy, in Figure 3.9, we show the energy consumption of a WLAN 802.11g system at1 Mbps data rate. For calculation of the sensing and transmission energy we used thesingle chip 802.11/g transceiver in [12]. The outdoor range of WLAN at 1 Mbps is about300 m and its receiver sensitivity is −94 dB. For the sensing energy we obtain Cs =41 nJ , the transmitter electronic energy is Ct−elec = 165 nJ and eamp = 4.8 pJ/bit/m2.As we can see in Figure 3.9, in this case, the ”on/off” scheme is not always dominant

34

00.5

1 0 0.2 0.4 0.6 0.8 1

0

500

1000

1500

2000

2500 N=10, SNR=10dB, QF<=0.1

Sleeping RateCensoring Rate

Ene

rgy[

nJ]

QD>=0.7QD>=0.8QD>=0.9QD>=0.99

Figure 3.7: Energy Consumption of ZigBee for QFoc ≤ 0.1

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1500

1000

1500

2000

2500

3000

3500

Probability of Detection

Ene

rgy[

nJ]

N=10, SNR=10dB, QF<=0.1

no censoring/no on/offcensoringon/offcensoring & on/off

Figure 3.8: Energy Consumption Comparison for ZigBee

to the censoring scheme, but still the combined censoring and ”on/off” scheme givesthe smallest energy consumption for the system.

35

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1400

600

800

1000

1200

1400

1600

1800N=5, SNR=10dB, QF<=0.1


Ene

rgy[

nJ]

no censoring/ no on/offcensoringon/offcensoring & on/off

Figure 3.9: Energy Consumption Comparison for WLAN 802.11/g at 1 Mbps

3.2.3.2 Energy Consumption of the System with Prior Knowledge

Here, we want to analyze the energy consumption of a system consisting of N = 5secondary users for two different cases. Figure 3.10 shows how the energy consump-tion changes for different detection rate constraints while the false alarm rate con-straint is fixed at QFoc ≤ 0.1. In this case Pr(H0) = 0.8 which means that thecurves are very close to the ones for the case where no prior knowledge is assumedbut Pr(H0) > Pr(H1). Figure 3.11 compares the energy consumption of the opti-mal combined censoring and ”on/off” scheme with the pure censoring and the pure”on/off” schemes. As for the case without prior knowledge, the ”on/off” scheme is themost energy efficient technique for a ZigBee system.

Figure 3.12 shows the energy consumption of the same system but with Pr(H0) =0.2. We observe that the pure censoring scheme performs even worse compared tothe previous case, because the censoring rate reduces due to the high probability ofthe primary user presence. Figure 3.13 also shows that the ”on/off” scheme is theoptimal solution for ZigBee in this case. Comparing Figures 3.11 and 3.13 we seethat the optimal solution is not different for different prior knowledge, but the energyconsumption of the system in the pure censoring scheme is higher for a higher Pr(H1).

3.3 Convex Analysis of the Problem

The constraints in the problem (3.27) are not convex nor concave with respect to λ1,thus it is not possible to use a convex optimization algorithm to solve the problem.

36

00.20.40.60.8

0

0.5

1

500

600

700

800

900

1000

1100

1200

1300

1400

1500

Censoring Rate

P(H0)=0.8, N=5, SNR=10dB, QF=0.1

Sleeping Rate

Ene

rgy[

nJ]

QD>=0.7QD>=0.8QD>=0.9QD>=0.99

Figure 3.10: Energy Consumption of ZigBee for QFoc ≤ 0.1 and Pr(H0)=0.8

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1400

600

800

1000

1200

1400

1600

1800P(H0)=0.8, N=5, SNR=10dB, QF<=0.1


Ene

rgy[

nJ]

no censoring/ no on/offcensoringon/offcensoring & on/off

Figure 3.11: Energy Consumption Comparison for ZigBee and Pr(H0) = 0.8

37

00.20.40.60.8

0

0.5

1

500

600

700

800

900

1000

1100

1200

1300

1400

1500 P(H0)=0.2, N=5, SNR=10dB, QF<=0.1

Censoring RateSleeping Rate

Ene

rgy[

nJ]

QD>=0.7QD>=0.8QD>=0.9QD>=0.99

Figure 3.12: Energy Consumption of ZigBee for QFoc ≤ 0.1 and Pr(H0)=0.2

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1400

600

800

1000

1200

1400

1600

1800


Ene

rgy[

nJ]

no censoring/ no on/offcensoringon/offcensoring and on/off

Figure 3.13: Energy Consumption Comparison for ZigBee and Pr(H0) = 0.8

38

However, with a little modification of the arguments of the problem (3.27), we attain alog-concave problem, which is solvable by a convex optimization algorithm such as theinterior-point algorithm.

Theorem 1 : The following problem is log-concave with respect to µ, ρ and λ2:

min(µ,ρ,λ2)

Coc

s.t. QFoc ≤ α, QDoc ≥ β(3.30)

Proof : It is obvious that the objective function is log-concave respect to µ and ρand λ2, because it is a linear function with respect to each of the variables.

Before going to prove the log-concavity of the constraints, we present the followinglemma, which will be used in the proof.

Lemma 1 : Let t(x) = ax + b, where a may be either positive or negative. Then if

h(x) = h(t(x)) for all x, then h is log-concave if and only if h is log-concave.

Proof of Lemma 1 : For the (ln(h))′′ we have

(ln(h))′′ = a2(ln(h(x))′′ (3.31)

Since (ln(h(x))′′ ≤ 0 so is the (ln(h))′′, hence h is log-concave. ¤Furthermore, the following propositions which are proved in [15] and [33] are used

in the proof.

Proposition 1 : Let ai, i = 1, .., n be a log-concave sequence (a2i ≥ ai−1.ai+1) and k

be a positive integer, then ck = a1 + ...ak is also a log-concave sequence [15].

Proposition 2 : if f is a log-concave multivariate function, then all marginal functionsare also log-concave [33].

Looking at the probability of false alarm, QFoc , we can rewrite it as the followingfunction of µ

QFoc = (1− µN)N∑

K=1

fK(µ)BK (3.32)

fK(µ) =

(NK

)µN−K(1− µ)K (3.33)

BK = (1− ρK)K∑

L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pfc)

L] (3.34)

We know that the product of two log-concave functions is a log-concave function

[14]. Furthermore, ∂2 log (1−µN )∂µ2 ≤ 0, so we only have to prove that

∑NK=1 fK(µ)BK is

log-concave.

First, we look at fK(µ) (which is log-concave with respect to µ, because ∂2ln fK(µ)∂µ2 ≤

0) and verify whether f 2K ≥ fK+1.fK−1 is correct or not.

39

{ (NK

)µN−K(1− µ)K

}2

≥(

NK + 1

)µN−K−1(1− µ)K+1

×(

NK − 1

)µN−K+1(1− µ)K−1

After simplification, we obtain

1

K(N −K)≥ 1

(K + 1)(N −K + 1)(3.35)

which is a true statement. Hence fK is a log-concave sequence.Second, we have to prove the log-concavity of BK . Before going through the proof,

we rewrite BK as follows

BK = (1− ρK)K∑

L=1

gL(ρ)EL (3.36)

gL(ρ) =

(KL

)ρK−L(1− ρ)L (3.37)

EL = 1− (1− Pfc)L (3.38)

First, we check the log-concavity of EL. Suppose that

[1− (1− Pfc)L]2 ≥ [1− (1− Pfc)

L+1] (3.39)

×[1− (1− Pfc)L−1] (3.40)


2 ≤ 1− Pfc +1

1− Pfc

(3.41)

We know that 0 < Pfc < 1. Assuming 0 < x = 1 − Pfc < 1, and the fact thatx + 1

x≥ 2, (3.41) is a true statement.

Similar to fK , we can prove that gL is also a log-concave sequence. Since, the productof two log-concave sequences still is a log-concave sequence, gL EL forms a log-concavesequence. Therefore, according to the proposition 1,

∑KL=1 gL(ρ)EL is log-concave with

respect to K.At this point, we just have to prove the log-concavity of (1 − ρK) to prove the

log-concavity of BK . Since, all the concave sequences are log-concave as well [15], wecheck the concavity of (1− ρK) instead of its log-concavity. A sequence ai, i = 1, ..., nis concave if 2ai ≥ ai+1 + ai−1 [15], thus for (1− ρK), we obtain

2(1− ρK) ≥ (1− ρK+1) + (1− ρK−1) (3.42)

40


2 ≤ ρ +1

ρ, 0 < ρ < 1 (3.43)

which is a true statement. Since the product of two log-concave sequences is also log-concave, BK is log-concave. Therefore, fK(µ)BK is also a log-concave sequence. Let us

assume DN(µ) =∑N

K=1 fK(µ)BK . Looking at DN(µ), we see it is a marginal functionof fK(µ)BK that is marginalized with respect to K. Thus, according to proposition 2,DN(µ) is also log-concave with respect to µ and so is QFoc .

For the probability of detection, we can write

QDoc = (1− µN)N∑

K=1

fK(µ)CK (3.44)

CK = (1− δK)K∑

L=1

(KL

)ρK−L(1− ρ)L[1− (1− Pdc)

L] (3.45)

We can see that the structure of QDoc is similar to that of QFoc and so in the sameway, QDoc is also log-concave with respect to µ.

Again, we can write QFoc as follows


K=1

fK(µ)(1− ρK)K∑

L=1

gL(ρ)EL (3.46)

We proved above that EL and gL are log-concave. Hence, in a similar way as weproved for µ, the following function is also log-concave with respect to ρ

BK(ρ) = (1− ρK)K∑

L=1

gL(ρ)EL (3.47)

Therefore, we would have


K=1

fK(µ)BK(ρ) (3.48)

Since, the product preserves the log-concavity, fK(µ)gK(ρ) is log-concave. Again,

according to proposition 2,∑N

K=1 fK(µ)gK(ρ) is log-concave with respect to ρ and soQFoc is log-concave with respect to ρ.

For the probability of detection we can also write

QDoc = (1− µN)N∑

K=1

fK(µ)(1− δK)K∑

L=1

gL(ρ)FL (3.49)

FL = 1− (1− Pdc)L (3.50)

which has the same structure as QFoc and so it is log-concave with respect to ρ.

41

Before going to prove the log-concavity of QFoc and QDoc with respect to λ2, wepresent the following lemma

Lemma 2 : Let t be a positive monotonically decreasing function, defined on the realinterval (a, b); and let h be a function with domain (t(a), t(b)). Define the function h

on (a, b) so that h(x) = h(t(x)) for all x ∈ (a, b). If t is log-concave on (a, b) and h is

log-concave on (t(a), t(b)), then h is log-concave on (a, b).

Proof of Lemma 2 : (ln(h))′′ is of the same sign as h(x)′′h(x)′ − h(x)′

h(x)and (ln(t))′′ is

of the same sign as t(x)′′t(x)′ − t(x)′

t(x)[13]. Furthermore, (ln(h))′′ is of the same sign as

h(x)′′h(x)′ − h(x)′

h(x)+ t(x)′′

t(x)′ , [13]. We have

h(x)′′h(x)′ −

h(x)′h(x)

+t(x)′′t(x)′ ≤

t(x)′t(x)

(3.51)

Since, t(x) is positive and monotonically decreasing function, t(x)′t(x)

≤ 0. So h(x)′′h(x)′ −

h(x)′h(x)

+ t(x)′′t(x)′ ≤ 0, which proves that h is log-concave. ¤

Now we have to prove that QFoc and QDoc are log-concave with respect to λ2. Wecan write QFoc as


K=1

fK(µ)(1− ρK)K∑

L=1

gL(ρ)[1− (1− Pfc)L] (3.52)

Since∂2[1−(1−Pfc)

L]

∂Pfc2 ≤ 0, [1 − (1 − Pfc)

L] is concave with respect to Pfc and so

it is also log-concave. We also proved above that [1 − (1 − Pfc)L] is a log-concave

sequence in L. Because, the product of two log-concave sequences still is log-concave,gL(ρ)[1−(1−Pfc)

L] is also log-concave in L and the application of proposition 2 ensures

the log-concavity of QFoc with respect to Pfc. On the other hand, Pfc =Γ(u,

λ22

)

Γ(u), which

means that Pfc is log-concave with respect to λ2, since u ≥ 1 [13]. Since Pfc is a positiveand monotonically decreasing function of λ2, according to lemma 2, QFoc is log-concavewith respect to λ2.

For the probability of detection, we can follow a similar approach and prove thatQDoc is log-concave with respect to Pdc. We know that Pdc = Qu(

√2γ,

√λ2). Since Pdc

is log-concave with respect to λ2 [13], according to the lemma 2, QDoc is log-concavewith respect to λ2. ¤

We proved that QFoc and QDoc are log-concave with respect to (µ, ρ, λ2). Using thefollowing theorem we can define a convex optimization problem in order to solve (3.27)systematically.

Theorem 2 : The following problem is convex with respect to µ, ρ and λ2:

min(µ,ρ,λ2)

Coc

s.t. (1−QFoc)−1 ≤ (1− α)−1

Q−1Doc

≤ β−1

(3.53)

Proof : Coc is convex with respect to ρ and µ and λ2. Since QFoc and QDoc are log-concave with respect to (µ, ρ, λ2), (1 − QFoc)

−1 and Q−1Doc

are log-convex with respect

42

to (µ, ρ, λ2) (according to lemma 1 which says linear transformation preserves the log-concavity, 1 − QFoc is log-concave). Since all the log-convex functions are also convex[14], (1 − QFoc)

−1 and Q−1Doc

are convex with respect to (µ, ρ, λ2) and we can apply anon-equality constraint convex optimization algorithm to solve the problem. ¤

3.4 Conclusion

In this chapter, we presented a combined censoring and ”on/off” scheme based on thecooperative spectrum sensing scheme which is introduced in 2.1. We derived the prob-ability of false alarm and detection for two different situations: with prior knowledgeabout π0 and π1 and without prior knowledge. Defining an average cost function, weformulated our problem as the minimization of the cost subject to a detection perfor-mance constraint. Energy consumption analysis show that our proposed scheme is themost energy efficient technique compared to the censoring and ”on/off” schemes. Fur-thermore, we modified the problem (3.27) to a convex optimization problem in orderto solve it systematically.

43

Two-Stage Spectrum Sensing 4In this chapter, we address the problem of primary user detection in a cognitive radio

system at low SNR for a wide-band frequency range.The role of spectrum sensing in cognitive radio (CR) system is to locate unoccupied

spectrum segments as quickly and accurately as possible. Inaccurate and delayed sens-ing results can either result in interference to the primary user or a missed opportunityof using the spectrum holes.

Spectrum sensing for a single narrow band radio spectrum has been thoroughlystudied during the past few years based on energy detection or cyclostationary detec-tion. Energy detection is simple and able to locate the spectrum occupancy informationquickly. However, its sensing capability is vulnerable to the noise [24].

Meanwhile, the cyclostationary detector locates the periodic cyclostationary signa-ture of a modulated signal by time or frequency domain signal processing [17]. Itsspectrum sensing performance is robust to noise-like signals. However, this methodadds a lot of computational and implementation complexity to the system and con-sumes more power than energy detection.

Recently, there have been a few efforts to study the problem of spectrum sensingfor wide-band signals. In this chapter, a two-stage wide-band spectrum sensing schemeis proposed which performs a coarse sensing using energy detection in a multi-channelfrequency band and locates possible spectrum holes. Then in the next stage a cyclo-stationary feature detector is used for fine sensing of the possible empty channels tomake a final decision about the occupancy of each channel.

4.1 Two-Stage Spectrum Sensing

We propose a two-stage wide-band spectrum sensing technique which consists of acoarse and a fine sensing stage. In coarse sensing, we want to locate the possible emptychannels among L channels in a frequency band by comparing their test statistics with athreshold, λi. If the test statistic is lower than the threshold, we go to the fine sensingstage to make sure that the channel is empty. In the fine sensing, we compare thenew test statistic with a threshold, say γi to decide whether the channel is confidentlyempty or the primary user is present and we missed the primary user detection inthe coarse sensing stage. For the coarse sensing, we use a simple detector such asthe energy detector and then we use a more complex and accurate detector such asthe cyclostationary detector for the fine sensing. The reason behind this scheme isthat simple detectors such as the energy detector, are very sensitive to the noise level,shadowing effects and noise uncertainty [24]. Furthermore, for special types of signalssuch as spread spectrum signals, the energy detector is not applicable. In the following,we discuss our two-stage spectrum sensing technique for each stage and explain the

45

details of the coarse and fine sensing.

4.1.1 Coarse Sensing

In the coarse sensing stage, we use an energy detector which serially searches everychannel within the band. The energy detector accumulates energy of u samples andthen compares it with a threshold λi to decide whether the primary user is present orthere is a possible empty channel and so we have to go to the fine sensing. Thus, wedefine our hypothesis testing as

H0c : possible empty band

H1c : primary user is present (4.1)

The energy detector makes its decision based on the observation Xik , i =1, ..., L, k = 1, .., u which is defined as

Xik =

{nik if H0c

sik + nik if H1c(4.2)

with the primary user’s signal and noise denoted by sik and nik , respectively. The noiseis assumed to be an i.i.d random process of zero mean and variance σ2

ni, while the signal

is assumed to be an i.i.d random process of zero mean and variance σ2si.

The decision rule used by the energy detector is given by

Ei =u∑

k=1

(Xik)2

H1c

≷H0c

λi (4.3)

where λi is the decision threshold for the coarse sensing related to the band i. The teststatistic Ei for u ≥ 250, can be modeled by a gaussian distribution as follows [16],

Ei =

{ N (Mσ2ni

, 2Mσ4ni

), if H0c

N (M(σ2ni

+ σ2si), 2M(σ2

ni+ σ2

si)2) if H1c

(4.4)

Then, the probability of false alarm and detection for the energy detector in each bandare

Pfic= Q(

λi − uσ2ni√

2uσ4ni

) (4.5)

Pdic= Q(

λi − u(σ2ni

+ σ2si)√

2u(σ2ni

+ σ2si)2

) (4.6)

46

4.1.2 Fine Sensing

After the coarse sensing stage, we have determined the possible empty bands and inthe fine sensing stage we want to make sure that the primary user is confidently absent.Therefore, our binary hypothesis test in this stage is

H0f : primary user is absent

H1f : primary user is present (4.7)

The energy detector presented in section 4.1.1, is very sensitive to the noise leveland noise uncertainty, so there is a signal to noise ratio level under which the energydetector is not able to work [16]. Since the energy detector can not detect the primaryuser under a specific signal to noise ratio level, it is necessary to use a more accuratedetector to be sure about the emptiness of the band. Two candidates for this stageare matched filtering and cyclostationary detection. The matched filtering is optimalbut needs the complete knowledge about the primary user signal which is generally notavailable in a cognitive radio system. Therefore, in our thesis, we use a cyclostationarydetector for the fine sensing stage, which has a better accuracy than the energy detector,particularly for a low signal to noise ratio.

Cyclostationary processes are random processes for which the statistical propertiessuch as the mean and autocorrelation change periodically as functions of time [17].Many of the signals used in wireless communications and radar systems possess thisproperty. The cyclostationarity may be caused by modulation and coding [17], or itmay be intentionally produced to help the channel estimation, equalization or synchro-nization such as the cyclic prefix (CP) in an OFDM signal. [18] In order to exploit thecyclic statistics, the signal must be oversampled with respect to the symbol rate, ormultiple receivers must be used to observe the signal. In our work, we use the secondorder time domain cyclostationary detector presented in [19].

4.1.2.1 Cyclostationarity [19]

A continuous-time random process x(t) is wide-sense second-order cyclostationary ifthere exists a Tc > 0 such that:

µx(t) = µx(t + Tc), ∀t (4.8)

and

Rx(t1, t2) = Rx(t1 + Tc, t2 + Tc), ∀(t1, t2) (4.9)

where µx(t) = E[x(t)] is the mean value of the random process x(t), Rx(t1, t2) =E[x(t1)x

∗(t2)] is the autocorrelation function and Tc is called the cyclic period.Due to the periodicity of the autocorrelation Rx(t1, t2), it has a Fourier-series rep-

resentation. By denoting t1 = t and t2 = τ , we obtain the following expression for theFourier-series [17]:

Rx(t, τ) =∑

α

Rαx(τ)ejαt (4.10)

47

where the Fourier coefficients are

Rαx(τ) =

1

Tc

∫ ∞

−∞Rx(t, τ)e−jαtdt (4.11)

with α called the cyclic frequency and Rαx(τ) called the cyclic autocorrelation function.

If the process is zero mean, then this function can also be called the cyclic autocovari-ance function.

In general, a random process is called cyclostationary if there exists an α 6= 0 suchthat Rα

x(τ) 6= 0 for some value of τ . The following set A is called the set of cyclicfrequencies

A = {α|α 6= 0, Rαx(τ) 6= 0} (4.12)

Typically, the cyclic frequencies are assumed to be known or could be estimated.

4.1.2.2 Time-Domain Test [19]

Here, we want to derive a test for finding the cycles present in the time varying co-variance Rx(t, τ) = E{x(t)x∗(t + τ)}, for a fixed time lag τ . In other words, we wishto detect those α’s for which Rα

x(τ) 6= 0. Then we can say that there is second-ordercyclostationarity present in x(t). Hence, by detecting the cycles of Rx(t, τ) we areessentially testing for the presence of cyclostationarity.

To check if Rαx(τ) is null for a given candidate cycle, consider the following estimator

of Rαx(τ)

Rαx(τ) =

1

T

T−1∑t=0

x(t)x∗(t + τ)e−jαt

= Rαx(τ) + εα

x(τ) (4.13)

where εαx(τ) represents the estimation error which vanishes as T → ∞. Due to the

error εαx(τ), the estimator Rα

x(τ) is seldom exactly zero in practice, even if α is not acyclic frequency. This raises an important issue about deciding whether a given value ofRα

x(τ) is ”zero” or not. To answer this question statistically, we use the decision-makingapproach of [19].

In general, we consider a vector of Rαx(τ) values rather than a single value in order

to check simultaneously for the presence of cycles in a set of lags τ .Let τ1, ..., τN be a fixed set of lags, α be a candidate cycle-frequency, and

Rx =[Re{Rα

x(τ1)}, ..., Re{Rαx(τN)},

Im{Rαx(τ1)}, ..., Im{Rα

x(τN)}] (4.14)

represent a 1×2N row vector consisting of cyclic correlation estimators from (4.13) withRe and Im representing the real and imaginary parts, respectively. If the asymptoticvalue of Rx is given as Rx

48

Rx =[Re{Rα

x(τ1)}, ..., Re{Rαx(τN)},

Im{Rαx(τ1)}, ..., Im{Rα

x(τN)}] (4.15)

then, we can write

Rx = Rx + εx (4.16)

where

εx =[Re{εα

x(τ1)}, ..., Re{εαx(τN)},

Im{εαx(τ1)}, ..., Im{εα

x(τN)}] (4.17)

is the estimation error vector. To check if α is a cyclic frequency or not, we formulatethe following hypothesis testing problem:

H0f : α /∈ A, ∀{τn}Nn=1 ⇒ Rx = εx

H1f : α ∈ A, ∃{τn}Nn=1 ⇒ Rx = Rx + εx (4.18)

Therefore, testing for the presence of a given α in A is equivalent to a binaryclassification problem and requires the knowledge of the distribution of εx for designinga decision strategy.

In [19], the test statistic related to the cyclostationary detection has been derivedas follows

T = T RxΣ−1RH

x (4.19)

where Σ is the estimator of the covariance matrix Σ and is equal to

Σ =

[Re{Q+Q∗

2} Re{Q−Q∗

2}

Im{Q+Q∗2} Im{Q∗−Q

2}

](4.20)

where Q and Q∗ are

Q(m,n) = Sτm,τn(2α; α)

Q∗(m,n) = S∗τm,τn(0;−α) (4.21)

and Sτm,τn(2α; α) and S∗τm,τn(0;−α) are

Sτm,τn(2α; α) =1

T l

(l−1)/2∑

s=−(l−1)/2

W (s)

×FT,τn(α− 2πs

T)FT,τm(α +

2πs

T) (4.22)

49

S∗τm,τn(0;−α) =

1

T l

(l−1)/2∑

s=−(l−1)/2

W (s)

×F ∗T,τn

(α +2πs

T)FT,τm(α +

2πs

T) (4.23)

with W (s) a spectral window of length l (odd) and FT,τ (ω) =∑T−1

t=0 x(t)x∗(t + τ)e−jωt.In [19], it is shown that the test statistic T under hypothesis H0f , asymptotically hasa central chi-squared distribution

limT→∞

T =

{χ2

2N if H0f

N (0, 4RxΣ−1RH

x ) if H1f(4.24)

Having the asymptotic distribution of the test statistics T , we say that if T ≥ γwe can declare α ∈ A for some τ1, ..., τN and therefore the primary user is present.Otherwise we declare α /∈ A, ∀τ1, ..., τN , and thus the primary user is absent, whichmeans that this band is empty and can be used by the cognitive radio. It is worthto mention here that for a large T , we can approximate the distribution of the teststatistic T under the hypothesis H1f as

T ∼ N (T RxΣ−1RH

x , 4T RxΣ−1RH

x ) (4.25)

The probability of detection Pdifand the probability of false alarm Pfif

correspond-ing to the ith band are

Pfif= P (Ti ≥ γi|H0f ) =

Γ(γi/2, N)

Γ(N)(4.26)

Pdif= P (Ti ≥ γi|H1f ) = Q(

γi − T RxΣ−1RH

x√(4T RxΣ−1RH

x )) (4.27)

where Γ(a) is the gamma function and Γ(a, x) is the incomplete gamma function(Γ(a, x) =

∫∞x

ta−1e−tdt).

4.2 Analysis and Problem Formulation

4.2.1 Problem Formulation

The role of spectrum sensing in a cognitive radio system is to locate specific spectrumholes and to detect the primary user. Upon detection of the primary user, the cognitiveradio should rapidly vacate that part of the spectrum. Therefore, in every spectrumsensing scheme for cognitive radios, three conditions should be satisfied: a high spec-trum hole detection probability (low false alarm rate), a low interference to the primaryuser signal (high probability of detection) and the agility. These three conditions areconflicting with each other. If we want to have a high probability of detection fora fixed probability of false alarm (minimizing the interference for a fixed information

50

rate), we have to increase the detection time for each detector; therefore what we loosein such a case is the agility of the spectrum sensing. On the other hand, increasingthe probability of detection for a fixed detection time, means increasing the probabilityof false alarm and so missing the possibility of using a spectrum hole by the cognitiveradio.

In our spectrum sensing scheme we have the following vector with length L for theprobability of detection and the probability of false alarm

Pf = [Pf1 Pf2 ...PfL] (4.28)

Pd = [Pd1 Pd2 ...PdL] (4.29)

where for each Pfiand Pdi

, i = 1, ..., L we have

Pfi= Pfic

+ (1− Pfic)Pfif

(4.30)

Pdi= Pdic

+ (1− Pdic)Pdif

(4.31)

Our goal is to design a decision strategy (determination of λi and γi), in order tomaximize the probability of detection of each band for a false alarm rate constraint(equivalent to minimizing the interference to the primary user for an information rateconstraint). Therefore our problem is given by

max(λi,γi)

Pdi

Pfi≤ β

i = 1, ..., L (4.32)

For a false alarm rate, Pfi, we have the following relation between λi and γi

λi = Q−1(Pfi

− Γ(γi/2,N)Γ(N)

1− Γ(γi/2,N)Γ(N)

)√

2Mσ4ni

+ Mσ2ni

(4.33)

The inequality constraint in the problem (4.32) can be reduced to an equality con-straint by the following theorem.

Theorem 4.1 : The optimal value of the probability of detection in (4.32) is attainedby Pfi

= β.Proof : The first derivative of Pdi

with respect to λi and γi is negative. Hence, themaximum Pdi

is attained for the lowest possible λi and γi. Since, the first derivative ofPfi

with respect to λi and γi is also negative, the optimal Pdiis attained by Pfi

= β. ¤As an example, we find the feasible set of the problem for Pfi

= 0.1, when anenergy detector with M = 9216 samples is used in the coarse sensing stage and acyclostationary detector with one time lag is used in the fine sensing. As we can see inFigure 4.1, there is a tradeoff between γi and λi for a fixed probability of false alarm.

51

4 6 8 10 12 14 169380

9400

9420

9440

9460

9480

9500

9520

9540

9560

9580

CD Threshold(γ)

ED

Thr

esho

ld(λ

)

Pf=0.1

Figure 4.1: Feasible set of (4.32) for Pf = 0.1

4.2.2 Mean Detection Time Analysis

In order to compare the agility of the two-stage sensing with energy and cyclostationarydetection, we need to compare their mean detection time. The mean detection time ofthe two-stage sensing has two terms as follow

Td = Tc + Tf (4.34)

where Tc is the coarse sensing time duration and is equal to LT1, with T1 the sensingtime for each channel for the coarse sensing stage and Tf is the fine sensing stage meandetection time. Tf can be derived as follows

Tf = E[K]T2 (4.35)

where E[K] is the mean number of reported channels for the fine sensing stage and T2

is the sensing time of each channel. K is a random variable which follows a binomialdistribution, with parameters L and Prep. Prep is the probability that each channelwould be reported to the fine sensing stage and assuming the same probability of falsealarm and detection for all channels is

Prep = Pr(H0)(1− Pfc) + Pr(H1)(1− Pdc) (4.36)

Hence, the mean detection time of the fine sensing stage is

Tf = LPrepT2 (4.37)

52

Hence, the total mean detection time is

Td = L(T1 + PrepT2) (4.38)

4.3 Simulation Results

In this section, we want to compare the detection performance of our proposed two-stage sensing with energy and cyclostationary detection. In these simulations we useda DVB OFDM signal with 10 channels. The bandwidth of each channel is 8 MHz.Each OFDM signal has 8192 carriers with a CP of length 1024. In these simulationswe have used an OFDM signal consisting of 18 OFDM symbols. Furthermore, a Kaiserwindow of length 61 is applied in the simulations. We assume that all the channelsexperience the same SNR and have the same probability of false alarm constraint,Pf1 = ... = PfL = Pf , therefore they will have the same probability of detection. Inthe following simulations, the false alarm constraint is assumed to be Pf ≤ 0.1.

Figure 4.2 shows the detection performance versus SNR for a spectrum sensingsystem with a sensing time of T1 = 2 ms for energy detection and T2 = 18 ms forcyclostationary detection with zero noise uncertainty (∆ = 0 dB). As we can see, foran SNR that is less than −12 dB, the two-stage sensing scheme performs better thanenergy detection, at the price of increasing the detection time.

−20 −15 −10 −5 0

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=0dB

Two−Stage SensingCyclostationary DetectorEnergy Detector

Figure 4.2: Detection Performance Comparison for ∆ = 0dB

In order to see how the detection time looks like for the two-stage sensing comparedto energy and cyclostationary detectors, we present the mean detection time of the two-

53

stage sensing for different SNRs. In Figure 4.3 we consider Pr(H0) = 0.2. As we cansee, in the range where the two-stage sensing performs better than energy detection,(SNR less than−12 dB), the two-stage sensing outperforms the cyclostationary detectorin terms of mean detection time as well as detection performance. However, after acertain SNR, we don’t gain any detection performance by the two-stage sensing while weincrease the detection time. However, as we can see in Figure 4.4, where Pr(H0) = 0.8,and thus the Prep is higher, the two-stage sensing does not always have a smaller meandetection time than the cyclostationary detector.

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=0dB


Figure 4.3: Mean Detection Time Comparison for Pr(H0) = 0.2

Figure 4.5 shows the detection performance of the different schemes for the samesystem as used in the previous scenario but with a noise uncertainty, ∆ = 0.05 dB. Insuch a case, the energy detector starts to loose its performance at higher SNRs comparedto the previous scenario. Therefore we see that in the low SNRs e.g., −20 dB, the two-stage sensing performs as good as the cyclostationary detector and it means that wedon’t get any advantage by doing coarse sensing. Figures 4.6 and 4.7 show the effect interms of the mean detection time. We see that below the SNR= −15 dB, the systemspends more time on sensing than the cyclostationary detector. These figures as well asthe Figures 4.8 to 4.19 (for ∆ = 0.1, 0.5, 1, 2 dB) show that the noise uncertainty limitsthe SNR region where the two-stage sensing performs better than both the energy andcyclostationary detector.

54

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=0dB


Figure 4.4: Mean Detection Time Comparison for Pr(H0) = 0.8

−20 −15 −10 −5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=0.05dB


Figure 4.5: Detection Performance Comparison for ∆ = 0.05dB

55

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=0.05dB


Figure 4.6: Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 0.05dB

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=0.05dB



56

−20 −15 −10 −5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=0.1dB



−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=0.1dB



57

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=0.1dB



−20 −15 −10 −5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=0.5dB



58

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=0.5dB



−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=0.5dB



59

−20 −15 −10 −5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=1dB



−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=1dB


Figure 4.15: Mean Detection Time Comparison for Pr(H0) = 0.2 and ∆ = 1dB

60

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=1dB



−20 −15 −10 −5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pro

babi

lity

of D

etec

tion

T1=2ms, T2=18ms, ∆=2dB



61

−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.2, P(H1)=0.8, ∆=2dB



−20 −15 −10 −5 020

40

60

80

100

120

140

160

180

200

SNR

Mea

n D

etec

tion

Tim

e(m

s)

T1=2ms, T2=18ms, P(H0)=0.8, P(H1)=0.2, ∆=2dB



62

4.4 Conclusion

In this chapter, we presented a novel two-stage spectrum sensing technique for a wide-band frequency range. At the first stage called coarse sensing, we used the energydetection with low sensing time to locate the possible empty channels. In the secondstage called fine sensing, we exploited the cyclostationary detection with higher sensingtime to make the final decision about the emptiness of the reported channels from thecoarse sensing stage. We defined our problem as a maximization of the probabilityof detection in each channel subject to a false alarm rate constraint, in order to findthe decision thresholds for the coarse and fine sensing stages. Analysis of the detec-tion performance and mean detection time by simulations show that in the low SNRregion, two-stage sensing technique outperforms the energy and cyclostationary detec-tors. However, we show that increasing the noise uncertainty leads to a decreasing SNRrange which two-stage sensing performs better than the energy and cyclostationary de-tectors.

63

Conclusions and further work 5In this chapter we summarize the work done in the thesis, draw the final conclusions,

and suggest directions for further research.

5.1 Conclusions

In this thesis, we have first presented an overview of two spectrum sensing problemsfor cognitive radio. We discussed a general cooperative spectrum sensing scheme inChapter 2. The energy consumption of such a system increases as long as the numberof secondary users involved in sensing the spectrum increases. We reviewed two energyefficient techniques, censoring and ”on/off” in the context of cognitive radio. Based onexisting observations it is not possible to say which of these approaches is optimal inthe sense of energy efficiency. Furthermore, in Chapter 2, we initiated the discussion ofsome two-stage sensing techniques for wide-band spectrum sensing. We presented twoavailable techniques, wavelet transform and multi-resolution energy detection.

In Chapter 3, we presented a novel combined censoring and ”on/off” scheme as anenergy efficient cooperative spectrum sensing technique. We exploited the advantagesof both pure censoring and pure ”on/off” schemes. We defined a cost function for thisscheme and minimized it for a certain detection performance constraint.

The feasible set of the optimization problem showed that there is an inherent trade-off between the sleeping rate and the censoring rate. Therefore, the optimal solutionis also dependent on the transmission and sensing costs. We analyzed the energy con-sumption of an IEEE 802.15.4/ZigBee technology and found that the optimal solutionfor the combined censoring and ”on/off” scheme is the same as for the pure ”on/off”one. Therefore, we found that for the short range communications, because of thehigher sensing cost with respect to the transmission cost, the ”on/off” scheme is dom-inant over the censoring one, and thus the optimal energy efficient solution is veryclose to the pure ”on/off” solution. However, as we have seen for the case of a WLAN802.11/g system at 1 Mbps, the censoring and ”on/off” schemes give almost the sameresult and thus the combined censoring and ”on/off” technique is not the same as the”on/off” scheme and reduces the energy consumption of the system significantly.

In Chapter 4, we presented a two-stage wide-band spectrum sensing scheme con-sisting of a coarse and a fine sensing stage. In the coarse sensing we used an energydetector with low sensing time while in the fine sensing, we used a cyclostationaryfeature detector with longer sensing time. We maximized the probability of detectionwith respect to a false alarm rate constraint in order to find the detector thresholds foreach stage.

Our simulation results for an OFDM signal showed that at low SNR, where theenergy detector is not reliable, the cyclostationary detector becomes dominant, so the

65

two-stage sensing becomes valuable. However, the price for such an improvement is ahigher mean detection time than the energy detector. Furthermore, we showed thatintroducing a noise uncertainty to the system reduces the detection performance of theenergy detector and hence limits the SNR region where the two-stage sensing schemeperforms better than the energy detector and cyclostationary detectors in terms ofdetection performance or mean detection time.

5.2 Suggestions for further Work

• Different Secondary User ConditionsIn Chapter 3, we assumed the same decision threshold and SNR for all the sec-ondary users. However, in reality, it rarely happens that all the cognitive radiosexperience the same conditions. Furthermore, the idea of cooperative spectrumsensing is based on compensating the effects of shadowing and multipath fading.Therefore, the combined censoring and ”on/off” scheme has to be refined and de-veloped for the general case where secondary users experience different conditions.

• Non Ideal Communication LinksIn the proposed cooperative sensing schemes which have been proposed in Chap-ters 2 and 3, the channel is assumed to be error free. Thus, we assume that allthe communication between cognitive radios and the FC is error free. However,in practical situations, the channel is not error free and possible communicationerrors have to be considered in the scheme.

• Primary User BehaviourIn the problem definition for the combined censoring and ”on/off” scheme, weassumed that we either don’t have any knowledge about the primary user or wejust know the probability of primary user presence (or absence). This is a goodassumption in many situations. However, sometimes we my know something aboutthe primary user behavior such as its temporal ”on/off” statistics. For example,we know that the primary user is periodically ”on” or ”off”. In this case, we canuse a learning algorithm in order to understand the behavior of the primary userand use it for a sleeping policy in the spectrum sensing to make it more energyefficient.

• Cross Layer Energy EfficiencyIn the considered energy efficient techniques, we just looked at the physical layersetup and signal processing level. It is a big advantage to also consider the energyefficiency in upper layers. For example, when we use the OR rule in the FC,if just one user detects the primary user, it is enough for the FC to announcethe primary user presence. Thus, it is not necessary that all the users send theirdecisions to the FC. We can propose an ordered transmission which is controlledby the upper layers to prevent redundancy in sending decisions to the FC.

66

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