Spectrum Sensing Algorithms for Cognitive Radio Networks · Spectrum Sensing Algorithms for Cognitive Radio Networks Francisco de Castro Paisana Nº 63097 Dissertation Submitted for

Spectrum Sensing Algorithms for Cognitive Radio Networks

Francisco de Castro Paisana

Nº 63097

Dissertation Submitted for obtaining the degree of

Master in Electrical and Computer Engineering

Jury Members

President: Prof. Fernando Duarte Nunes (IST)

Supervisor: Prof. António José Castelo Branco Rodrigues (IST)

Co-Supervisor: Prof. Neeli Rashmi Prasad (AAU)

Member: Prof. Francisco António Bucho Cercas (IST)

September 2012

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Acknowledgments

I would, first, like to express my gratitude to everyone involved in the supervision of this

thesis, namely Prof. Neeli R. Prasad and Prof. Albena Mihovska from AAU and Prof. António

Rodrigues from IST. It was a privilege to work under their wing and to have their valuable

guidance throughout my studies.

This work was performed in the Real Network module of the S-Cogito Testbed at the Center

for TeleInFrastruktur (CTIF) in Aalborg University. I am thankful to the CTIF staff for the

facilities provided for making the experimental study of the several spectrum sensing methods

described in this dissertation.

I would also like to give a special thanks to my lab partners Alexandros Fragkopoulos, Bayu

Anggorojati, Nuno Monteiro, Renaud Garigues, Simão Eduardo, Stefano Giuliana and Yasamin

Mustamandi, not only for their useful advises, but also for being such a great company during

my stay in Aalborg. Without them, the experience wouldn’t be the same!

Finally, I want to thank my parents and sister for their unbounded love, encouragement and

support. This thesis is dedicated to them.

To everyone,

Um muito obrigado/Thank you.

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Abstract

The high data rate demands of modern wireless applications have led to a problem of

scarcity of spectrum [1]. According to the Federal Communication Commission (FCC), the

current static frequency allocation schemes leave approximately 70% of the allocated

spectrum underutilized [2]. In order to increase the spectrum usage efficiency, new policies

have emerged that suggest the coexistence and share of resources between primary users

(PUs) and secondary users (SUs).

Cognitive Radio (CR) was the proposed technology to make the coexistence between PUs

and SUs a possible reality. A CR is an intelligent wireless communication system capable of

obtaining information from its surrounding environment and, by adjusting its radio operating

parameters, increasing the communication channel reliability and accessing dynamically the

unused resources, leading to a more efficient utilization of the radio spectrum [3].

Spectrum sensing (SS) is one of the possible techniques to find the unused parts of the

spectrum, called white spaces (WS). Despite not being necessarily a new area of research, it

has been lately subject to fundamental innovations due to the increasing interest on the

cognitive radio technology. However, there are still several SS algorithms that require an

experimental study of their performance and feasibility.

The focus of this work is the implementation and testing of SS schemes, namely the time-

domain cyclostationary detector, the adaptive threshold energy detector and the CP-based

Sliding Window detector, using USRP2 boards as RF front-ends and the GNU Radio framework

for the baseband digital processing. New schemes are also proposed for their benefits in terms

of performance and lower hardware requirements. The empirical results are, then, utilized to

corroborate the theoretical analysis made for these detectors.

Keywords: Cognitive Radio, Spectrum Sensing, GNU Radio, Cyclostationary Detection,

Adaptive Threshold Energy Detection, CP-based Detection.

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Resumo

Os elevados débitos exigidos pelas aplicações sem fios modernas têm agravado o problema

de escassez de espectro electromagnético [1]. De acordo com a Federal Communication

Commussion (FCC), os esquemas estáticos de alocação de frequência actuais deixam

aproximadamente 70% do espectro alocado subutilizado [2]. Com vista a resolver este

problema, novas políticas surgiram sugerindo a coexistência e partilha de recursos entre

utilizadores primários (PUs) e utilizadores secundários (SUs).

Rádio Cognitivo (CR) foi a tecnologia proposta para concretizar esta coexistência entre PUs

e SUs. Um CR é um sistema inteligente de comunicações sem fios capaz de obter informação

do seu meio envolvente e, através do ajuste dos seus parâmetros de operação rádio, aumentar

a qualidade do canal de transmissão e aceder dinamicamente aos recursos não utilizados,

levando a uma mais eficiente utilização do espectro rádio [3].

Spectrum Sensing (SS) é uma das técnicas utilizadas na procura dos espaços não ocupados

do espectro, chamados espaços brancos (WS). Embora não seja uma área de investigação

recente, nos últimos anos tem sofrido inovações fundamentais devido ao crescente interesse

na tecnologia de Rádio Cognitivo. Ainda existem, contudo, diversos algoritmos SS que exigem

um estudo experimental mais aprofundado da sua performance e exiquibilidade.

Este trabalho foca-se no teste e implementação de esquemas SS, nomeadamente o

detector cicloestacionário no domínio do tempo, o detector de energia com threshold

adaptativo e o detector baseado no prefixo cíclico com janela flutuante, usando placas USRP2

como RF front-ends e o software GNU Radio para processamento digital na banda de base.

Novos esquemas são também propostos, com vantagens ao nível da performance e menor

complexidade. Os resultados experimentais são, depois, usados para corroborar a análise

teórica feita para estes detectores.

Palavras-chave: Rádio Cognitivo, Spectrum Sensing, GNU Radio, Detecção ciclostationária,

Detecção de energia com Threshold Adaptativo, Deteçcão baseada no Prefixo Cíclico.

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Contents

Acknowledgments .............................................................................................................. iii

Abstract .............................................................................................................................. v

Resumo ............................................................................................................................. vii

Contents ............................................................................................................................ ix

List of Figures ................................................................................................................... xiii

List of Tables ................................................................................................................... xvii

List of Abbreviations ......................................................................................................... xix

Chapter 1 Introduction .................................................................................................. 1

1.1 Introduction .................................................................................................................. 1

1.2 Motivation and Goals .................................................................................................... 1

1.3 Scope ............................................................................................................................. 2

1.4 Publications ................................................................................................................... 2

Chapter 2 Background ................................................................................................... 3

2.1 Introduction .................................................................................................................. 3

2.2 Physical Architecture of a Cognitive Radio .................................................................... 3

2.3 Non-Cooperative Spectrum Sensing ............................................................................. 4

2.3.1 Hypotheses Testing ............................................................................................... 5

2.3.2 Energy Detection ................................................................................................... 6

2.3.3 Matched Filtering .................................................................................................. 7

2.3.4 Cyclostationary Detection ..................................................................................... 8

2.3.5 Cyclic Prefix Based Detection ................................................................................ 9

2.4 Cooperative Sensing .................................................................................................... 10

Chapter 3 Cyclostationary Detection ............................................................................ 13

3.1 Introduction ................................................................................................................ 13

3.2 Cyclostationary Features of OFDM signals .................................................................. 13

3.3 Traditional Time Domain Cyclostationary Detector .................................................... 15

3.4 Alternative Time Domain Cyclostationary Implementation ....................................... 19

3.5 Sensitivity to frequency offset .................................................................................... 21

3.6 Sensitivity to Cyclic Prefix Size .................................................................................... 22

3.7 Detection of DSSS signals ............................................................................................ 23

Chapter 4 Energy Detection ......................................................................................... 27

4.1 Introduction ................................................................................................................ 27

x

4.2 Fixed Threshold Energy Detection .............................................................................. 27

4.3 Adaptive Threshold Energy Detection ........................................................................ 29

4.3.1 FCME Algorithm .................................................................................................. 30

4.3.2 Alternative adaptive threshold estimation algorithm ......................................... 31

4.3.3 Localization Algorithm Based on Double-thresholding ....................................... 35

Chapter 5 OFDM CP-based Detection ........................................................................... 39

5.1 Introduction ................................................................................................................ 39

5.2 CP-based Sliding Window ............................................................................................ 39

5.3 Second order statistics based detection (GLRT) ......................................................... 39

5.4 Correlation coefficients based detection algorithm (CCE) .......................................... 40

5.5 Nonparametric autocorrelation based detection algorithm (NAC) ............................ 40

5.6 Alternative Second order statistics GLRT based detection (GLRT2) ........................... 41

5.7 Sensitivity to frequency offset .................................................................................... 42

5.8 Sensitivity to Cyclic Prefix Size .................................................................................... 43

Chapter 6 Cyclostationary Implementation and Measurements .................................... 45

6.1 Introduction ................................................................................................................ 45

6.2 Test bed and transmitter’s description ....................................................................... 45

6.3 Detector Implementation ........................................................................................... 45

6.4 Measurements ............................................................................................................ 48

6.5 Sensitivity to Frequency Offset ................................................................................... 51

Chapter 7 Energy Detection Implementation and Measurements ................................. 53

7.1 Introduction ................................................................................................................ 53


7.3 Detector Implementation ........................................................................................... 53

7.4 First Scenario – One Zigbee Transmitter ..................................................................... 55

7.5 Second Scenario – One WLAN Transmitter ................................................................. 60

Chapter 8 OFDM CP based detection implementation and measurements .................... 63

8.1 Introduction ................................................................................................................ 63


8.3 Detector Implementation and Testing ........................................................................ 63

8.4 Measurements ............................................................................................................ 64

8.5 Sensitivity to Frequency Offset ................................................................................... 66

Chapter 9 Hybrid Detector Implementation ................................................................. 69

9.1 Introduction ................................................................................................................ 69

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9.2 TV Band Detector Implementation ............................................................................. 69

9.3 ISM Band Detector Implementation ........................................................................... 72

Chapter 10 Conclusions ................................................................................................. 75

Appendix A ED number of samples required for detection ................................................ 1

Appendix B AED threshold parameter deduction .............................................................. 3

Appendix C AED and TED performance for a WLAN/OFDM modulated PU signal ............... 9

Appendix D Additional CP-SW empirical and simulated results ........................................ 11

Bibliography ...................................................................................................................... 13

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List of Figures

Figure 2.1: Cognitive Radio Physical Architecture......................................................................... 4

Figure 2.2: OFDM signal’s average sample product R[n] for N=32784. ...................................... 10

Figure 3.1: CAF of OFDM signal. The peaks appear at l=±Nd which corresponds to τ=±3.2 µs for

the given OFDM signal’s structure. ............................................................................................. 14

Figure 3.2: CAF of OFDM signal over the cyclic frequency for a lag parameter l=±Nd which

corresponds to τ=3.2 µs for the given OFDM signal’s structure. ................................................ 14

Figure 3.3: SCF of an OFDM signal. The cyclostationary features are not easily visible for such a

low number of samples. .............................................................................................................. 14

Figure 3.4: Cyclostationary detector’s probability of detection as a function of SNR for different

test statistics. .............................................................................................................................. 16

Figure 3.5: T[l=Nd] for different cyclic frequencies. ................................................................... 16

Figure 3.6: Tα [l=Nd] for different cyclic frequencies with a decimation factor equal to 8 ........ 17

Figure 3.7: Cyclostationary detector’s probability of detection as a function of SNR for different

decimation factors. ..................................................................................................................... 18

Figure 3.8: Flow graph of a traditional time-domain cyclostationary detector .......................... 18

Figure 3.9: Flow graph of the proposed cyclostationary detector. ............................................. 20

Figure 3.10: IIR filter structure used for measuring a DFT for the cyclic frequency k using the

Goertzel Algorithm. ..................................................................................................................... 21

Figure 3.11: Variation of cyclostationary detector test statistic with frequency offset. ............ 22

Figure 3.12: Cyclostationary detector’s simulated probability of detection as a function of SNR

for various cyclic prefix sizes. ...................................................................................................... 23

Figure 3.13: Cyclic Autocorrelation Function of a 802.11b signal. .............................................. 24

Figure 3.14: Cyclic Autocorrelation Function of a 802.11b signal for l=0. .................................. 24

Figure 3.15: ACD2’s probability of detection as a function of SNR when using 5 cyclic

frequencies. ................................................................................................................................. 25

Figure 4.1: Flowgraph of the proposed energy detector ............................................................ 32

Figure 4.2: TED, AEC and FCME’s probability of detection as a function of SNR for a received

signal with 60% of its bandwidth occupied by a WLAN/OFDM signal ........................................ 33

Figure 4.3: TED, AEC and FCME’s probability of detection as a function of SNR for a received

signal with 12% of its bandwidth occupied by a Zigbee signal ................................................... 33

Figure 4.4: Probability of detection variation with SNR for the TED, AED and FCME ................. 34

Figure 4.5: TED, AED and FCME algorithms’ probability of detection as a function of SNR when

the received signal is a white Gaussian random signal. .............................................................. 35

Figure 4.6: Spectrum of a NB signal. The upper and lower thresholds are represented by green

and red dash lines respectively. .................................................................................................. 36

Figure 4.7: Probability of detection as a function of SNR for the TED, AED and FCME with and

without LAD. ................................................................................................................................ 36

Figure 4.8: Probability of detection as a function of SNR for the TED, AED and FCME with and

without LAD when clusters separated by an interval equal to 1 channel are joined. ................ 37

Figure 4.9: Bandwidth estimation error as a function of SNR for the FCME, AED, TED algorithms

with and without LAD and LAD2. ................................................................................................ 38

Figure 5.1: Autocorrelation Methods’ simulated probability of detection as a function of SNR.

..................................................................................................................................................... 42

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Figure 5.2: Variation of the CP-based detectors’ test statistics with frequency offset .............. 43

Figure 5.3: CP-based and cyclostationary detectors’ simulated probability of detection as a

function of SNR for several guard interval sizes. ........................................................................ 44

Figure 6.1: OFDM signal’s test statistic T[l=Nd] as a function of α. .......................................... 47

Figure 6.2: Flow graph of a traditional time-domain cyclostationary detector .......................... 47

Figure 6.3: Flow graph of the proposed cyclostationary detector ACD1/ACD2 ......................... 47

Figure 6.4: TCD, ACD1 and ACD2’s empirical and theoretical CDFs under H0............................. 48

Figure 6.5: TCD’s empirical and theoretical CDFs for several SNR values ................................... 49

Figure 6.6: TCD, ACD1 and ACD2’s empirical and theoretical CDFs for a SNR=-7.7 dB .............. 50

Figure 6.7: Relative error of ACD1 and ACD2’s approximations as a function of SNR. ............... 50

Figure 6.8: TCD, ACD1 and ACD2’s empirical and simulated probability of detection as a

function of SNR. .......................................................................................................................... 51

Figure 6.9: Empirical variation of the ACD1 and ACD2’s normalized test statistics with

frequency offset for a SNR=-2 dB. ............................................................................................... 52

Figure 7.1: 1.25 MHz (25 MHz) Sub-band of the emulated ISM band ........................................ 54

Figure 7.2: Flowgraph of the implementation of the Energy Detector ...................................... 54

Figure 7.3: Frequency response of the received signal, whitening filter and the resulting image

..................................................................................................................................................... 54

Figure 7.4: PSD of a Zigbee signal with bandwidth scaled down by 95%. .................................. 56

Figure 7.5: Conventional and proposed energy detector architectures’ empirical and

theoretical CDFs under H0. .......................................................................................................... 56

Figure 7.6: Proposed energy detector’s empirical and simulated CDFs for different SNRs. The

simulated results are represented by a dash line. ...................................................................... 57

Figure 7.7: Empirical variation of the probability of detection with SNR for the traditional and

proposed energy detectors using Me=1310 as the number of spectral averages and σn2= σu

2. . 58


proposed energy detectors using Me=1310 as the number of spectral averages and σn2= ρσu

2 .

..................................................................................................................................................... 58


proposed energy detectors using Me=1310 as the number of spectral averages and σn2= σu

2/ρ.

..................................................................................................................................................... 59

Figure 7.10: AED’s empirical probability of detection as a function of the SNR of the 10th

channel for each output channel, using Me=1310 as the number of spectral averages and σn2=

σu2. ............................................................................................................................................... 59

Figure 7.11: PSD of a WLAN/OFDM signal with bandwidth scaled down by 95%. ..................... 60


proposed energy detectors using Me=1310 as the number of spectral averages and σn2= ρσu

2.61

Figure 8.1: Flowgraph of the implementation of the Energy Detector ...................................... 63

Figure 8.2: CDF of the probability of false alarm of the CP-based SW detector. ........................ 64

Figure 8.3: CDF of the probability of detection of the CP- SW(real) detector. ........................... 65

Figure 8.4: Variation of CP-SW performance with SNR. ............................................................. 65

Figure 8.5: Empirical performance comparison between several OFDM detectors. .................. 66

Figure 8.6: CP-SW sensitivity to frequency offset. ...................................................................... 67

Figure 9.1: TV Band Hybrid detector flowgraph. ........................................................................ 70

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Figure 9.2: CP-based GLRT’s probability of detection as a function of SNR for a DVB-T signal

with Rg=1/32. ............................................................................................................................... 71

Figure 9.3: CP-based GLRT and AED’s probability of detection as a function of SNR for a WM

signal. .......................................................................................................................................... 72

Figure 9.4: ISM Band Hybrid detector flowgraph. ...................................................................... 72

Figure 9.5: Bluetooth, Zigbee and WLAN channels in one of the three 25 MHz wide ISM sub-

bands. .......................................................................................................................................... 73

Figure 9.6: Fractional 4/5 decimator structure with FIR filter of N taps where N=4k, k=1,2,… .. 74

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List of Tables

Table 6.1: TCD Hardware Requirements ..................................................................................... 46

Table 6.2: ACD1/ACD2 Hardware Requirements ........................................................................ 46

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List of Abbreviations

ADC Analog to Digital Converter

ACD Alternative Cyclostationary Detector

AED Alternative Energy Detector

AWGN Additive White Gaussian Noise

BCME Backward Consecutive Mean Excision

CAF Cyclic Autocorrelation Function

CD Cyclostationary Detector

CDF Cumulative Distribution Function

CFAR Constant False Alarm Rate

CP Cyclic Prefix

CP-SW CP-based Sliding Window detector

CR Cognitive Radio

CS Cyclic Spectrum

DFT Discrete Fourier Transform

DSA Dynamic Spectrum Access

DSP Digital Signal Processor

ED Energy Detector

FC Fusion Center

FCME Forward Consecutive Mean Excision

FD Feature Detector

FFT Fast Fourier Transform

FO Frequency Offset

FPGA Field Programmable Gate Array

GA Goertzel Algorithm

GLRT Generalized Likelihood Ratio Test

GPP General Purpose Processor

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ICI Inter-Channel Interference

IIR Infinite Impulse Response

MF Matched Filter

OFDM Orthogonal Frequency Division Multiplexing

PDF Probability Density Function

PU Primary User

SDR Software Defined Radio

SCF Spectral Correlation Function

SU Secondary User

SS Spectrum Sensing

TCD Traditional Cyclostationary Detector

TED Traditional Energy Detector

WS White Space

1

Chapter 1 Introduction

1.1 Introduction

Spectrum scarcity is becoming one of the main and most challenging obstacles to the

development of new wireless communication technologies. In conformity with the traditional

spectrum allocation policies, different wireless networks should operate in separate bands, so

interference doesn’t become an issue. However, studies have shown that this approach is

leaving a great percentage of the spectrum underutilized [2]. To solve this problem, Dynamic

spectrum access (DSA) was one of the proposed solutions. It consists in a new spectrum

sharing paradigm that allows unlicensed secondary users (SU) to access the spectrum holes or

white spaces (WS) opportunistically in the licensed bands that were, traditionally, just

occupied by primary users (PU).

DSA is one of the main applications of Cognitive Radio (CR). A CR is an intelligent wireless

communication system capable of obtaining information from its surrounding environment

and, by adjusting its radio operating parameters, increasing the communication channel

reliability and accessing dynamically the unused resources, leading to a more efficient

utilization of the radio spectrum [3].

In order to adapt to different situations, a CR must be able to transmit and receive in

different bands and to use different coding and modulation schemes. Such flexibility is only

possible if the CR is based on the Software Defined Radio (SDR) philosophy. It consists in

implementing the baseband processing, including the coding and modulation, in software by

using programmable hardware such as Field Programmable Gate Array (FPGA), Digital Signal

Processors (DSP) or General Purpose Processors (GPP).

Spectrum sensing (SS) is one of the possible techniques used by a CR to locate the white

spaces (WS). It simply requires the processing of the received signal in order to make a

decision on the presence or not of a PU in a certain band. SS has low infrastructure

requirements; however, it implies that CRs must be able to detect signals at very low SNRs in a

limited amount of time, so they won’t cause any harmful interference to the PUs.

1.2 Motivation and Goals

There are several spectrum sensing techniques suggested in the literature being Energy

Detection (ED), Matched Filtering (MF) and Feature detection (FD) the most popular ones.

Their performance is evaluated not only in terms of probability of detection and false alarm,

but also in terms of complexity and flexibility. For instance, energy detection is one of the most

basic and effective schemes of detection. However, its performance degrades dramatically

when the noise power isn’t perfectly known a priori. It is also unable to identify and distinguish

2

different types of signals. On the other hand, feature detection has usually better performance

than ED but it is more complex and requires previous knowledge of the signal features.

Despite not being necessarily a new area of research, SS has been lately subject to

fundamental innovations due to the increasing interest on the cognitive radio technology to

solve the problem of scarcity of spectrum. Thus, there are several sensing schemes proposed

in the literature that demand an experimental study on their performance and applicability.

In this work, the author aims to implement and test the time-domain cyclostationary

detector, the adaptive threshold energy detector and the CP-based Sliding Window detector.

There is a concern in testing these sensing schemes for signals whose features are similar to

those from technologies resident in the ISM Band, in particular, Zigbee and 802.11.

1.3 Scope

The main topics covered in this thesis can be summarized as follows: In Chapter 2, an

overview of the main spectrum sensing algorithms is given. In Chapter 3, a theoretical analysis

is made for the time domain cyclostationary detector and a new scheme is proposed. In

Chapter 4, the conventional energy detector and the Forward Consecutive Mean Excision

(FCME) method which uses an adaptive threshold are described. Once again, a new adaptive

threshold scheme is proposed and compared to the other two energy detection schemes. In

Chapter 5, the CP-based methods, used to detect OFDM modulated signals, are explained. In

Chapter 6, Chapter 7 and Chapter 8 the experimental study of the previously described

detectors is finally made. Their probability of detection and false alarm are analyzed for

different threshold values and SNRs and compared to the theoretical/simulated results. In

addition, a study of the behavior of these detectors when in presence of noise uncertainty and

frequency offset is also made. In Chapter 9, hybrid architectures for the TV and ISM Bands are

suggested. Finally, in Chapter 10, the dissertation is concluded and some future work is

proposed.

1.4 Publications

An article was submitted by the author of this thesis to the 15th International Symposium

on Wireless Personal Multimedia Communications and accepted for publication [4]. The title of

this article was: “An Alternative Implementation of a Cyclostationary Detector”.

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Chapter 2 Background

2.1 Introduction

Cognitive Radio, proposed by Joseph Mitola in 1999 [5], is defined as an intelligent wireless

communication system that is aware of the radio environment and able to adapt to its

changing parameters. It was suggested as a way to increase radio spectrum utilization

efficiency and to increase the communication reliability of modern wireless technologies.

According to Haykin [3], the CR three basic units are:

• White Space detection unit;

• Channel identification unit. It deals with channel parameters estimation, in

particular, the channel capacity;

• Dynamic spectrum management unit. Its main purpose is to develop strategies to

use the spectrum resources in an efficient and effective way.

There are several white space identification methods proposed in the literature such as

spectrum sensing, geo-location with database lookup and beacon detection.

In the geo-location method, the CR estimates its position and queries a database for

information of the nearby licensed channel usage. This method has several disadvantages such

as the fact the CRs have to use a geo-location scheme and a database which limits their

independence of the network. Furthermore, geo-location requires changes in the legacy

systems so the centralized database can be updated autonomously.

In the beacon detection method, the CR gets information of the radio environment from

the beacons transmitted by the PUs. Like the geo-location method, this requires changing the

legacy systems.

Spectrum sensing (SS), on the other hand, only requires detecting PUs transmissions during

their normal operation. However, the CR has to able to detect these signals at very low SNRs in

a limited amount of time so it doesn’t create any harmful interference. One of the main

challenges to SS is to overcome the hidden terminal problem.

2.2 Physical Architecture of a Cognitive Radio

In order to adapt to the physical environment, the CR has to transmit and receive at

different bands using different modulations, coding schemes and other radio operating

parameters. Since conventional dedicated hardware doesn’t grant such flexibility, digital

processing operations are implemented in software. This idea is in full accord with the

philosophy of Software Defined Radio (SDR) which consists in bringing the software as close as

possible to the antenna.

4

The typical cognitive radio architecture is displayed in Figure 2.1. It can be divided into 3

sub-systems: Digital Transceiver, Channel Monitoring and Spectrum Sensing module and

Communication Management and Control unit. The digital transceiver, in turn, can be

subdivided into the RF front-end and the baseband processing unit [6].

Figure 2.1: Cognitive Radio Physical Architecture

The RF front-end module corresponds to the hardware part of the CR whose function is the

reception, down conversion, amplification, mixing, filtering and analogue to digital conversion

of the signal of interest. The RF front-end of a CR must be able to sense a wideband spectrum

which imposes severe requirements in the hardware components namely in the antenna,

power amplifier and adaptive filter.

The baseband processing unit, implemented in software, is responsible for all the necessary

digital processing of the signal, such as, the modulation and coding. It is usually implemented

over a Field Programmable Gate Arrays (FPGA), Digital Signal Processor (DSP) or General

Purpose Processors (GPP).

The channel monitoring and spectrum sensing module is capable of obtaining information

from the radio environment, through spectrum sensing or other white space identification

techniques and sending its feedback to the communication management sub-system so, the

CR can adjust its operation parameters in the RF front-end and baseband processing unit.

The communication management and control subsystem role is to manage all CR

operations, namely switching mode decisions and spectrum sensing scanning based on values

provided by performance metrics.

2.3 Non-Cooperative Spectrum Sensing

There are several spectrum sensing techniques suggested in the literature, such as, Energy

Detection (ED), Matched Filter (MF) and Cyclostationary detection (CD).

5

The choice between one sensing method over another depends greatly on the context and

the CR system requirements. Prior knowledge of the PU signal features, computational and

hardware cost and detection time limitations are some of the factors that influence this

choice.

2.3.1 Hypotheses Testing

The signal detection problem is solved by the decision between the two hypotheses:

�H:primaryusernotpresentH�:primaryuserpresent (2.1)

The signal under each hypothesis takes the form:

�H:y�� = w��, n = 1,… , NH�:y�� = x�� + w��, n = 1,… , N (2.2)

where y[n] is a two dimensional vector with the I and Q components of the received signal,

w[n] is a zero mean Additive White Gaussian Noise (AWGN) with variance σ!" , i.e. #$�%~'$0, σ!"%, and x[n] the signal sent by the primary user after attenuation and distortion

from the channel. N is the number of samples of the received signal used in the spectrum

sensing process.

The decision between the two hypotheses is made by comparing a test statistic T with a

threshold). The detector performance is mainly characterized by two metrics: probability of

detection and probability of false alarm. Low probability of detection increases the

interference inflicted on primary users, whereas high probability of false alarm increases the

amount of missed spectral opportunities in the secondary network. The probability of false

alarm and detection are given by the equations (2.3) and (2.4).

*+, = *$T > γ|1% (2.3)

*2 = *$T > γ|1�% (2.4)

According to Neymann-Pearson's theorem, for a fixed probability of false alarm*+,234, the

test statistic that maximizes the probability of detection is the likelihood ratio test (LRT) and

can be expressed as:

T567 = Λ$9% = :$9|1�%:$9|1% ≷ γ (2.5)

where :<9|1=> is the probability density function (PDF) of y under hypothesis 1= and γ the

threshold chosen so that *+,234 = *$T > γ|1%. Throughout this work, unless told

otherwise, the value chosen for the probability of false alarm (*+,234% was 5%.

In order to use the LRT, perfect knowledge of the :<9|1=> parameters, such as, the noise

and source signal distributions as well as the channels characteristics, is usually required.

6

However, in cognitive radio scenarios, this information is sometimes unavailable. In such cases,

other approaches like the Bayesian method and the Generalized Likelihood Ratio test (GLRT)

are more adequate.

In the Bayesian method, the likelihood functions are estimated by marginalization, that is,

:<9|1=> = ?:<9|1=, Θ=> :<Θ=|1=>AΘ= (2.6)

where Θ=defines the possible values for the unknown parameters under 1=. TheΘ=are

treated as random variables with a priori known distribution :<Θ=|1=>. The drawbacks of this

method are the fact that the marginalization operand in (2.6) is not easily computed and the

distribution assigned to the unknown parameters affects dramatically the performance results.

In the GLRT method, the maximum likelihood estimation (ML) is used to estimate the value

of the unknown parameters which are, in turn, used in a normal LRT test. It has the following

expression:

TB567 = argmaxDE :$9|1�, Θ�%argmaxDF :$9|1, Θ% (2.7)

There is no guarantee that the GLRT tends to optimality when the number of samples goes

to infinity since Θ=estimation depends on the statistical models used for the signal and noise.

2.3.2 Energy Detection

Energy Detection (ED) is one of the most basic sensing schemes. It is optimal if both the

signal and the noise are Gaussian, and the noise variance is perfectly known. However, its

performance degrades rapidly when there is uncertainty in the noise power value and is also

incapable to differentiate between signals from different systems and between these signals

and noise. Its advantage lies in its simplicity and not requiring prior knowledge of the PU’s

signal making it best suited for fast and coarse spectrum scanning.

The energy detection process can be made in time domain or frequency domain through a

FFT block. The advantage of the frequency domain testing lies in the flexibility the FFT can

provide by trading temporal resolution for frequency resolution. This means that a

narrowband signal’s bandwidth and central frequency can be estimated without requiring a

very flexible pre-filter.

The ED test statistic can be defined as follows,

TGH = 1'I 9��"JK�LM = 1'I I NO$P%"

JQQRK�OM

5K�SM ≷ ) (2.8)

where '++T is the size of the FFT employed using FFT-based detection and U the number of

samples used in the average of each FFT output bin (' = U.'++T). Since 9��" has a central

7

Chi-square distribution under H0 and non-central Chi-square distribution under H1, the

probabilities of false alarm and detection become [7],

*+, = *<TWGH > γ|1> = Γ Y', )2σ!"[Γ$'% = * \', )2σ!"] (2.9)

*2 = *<TWGH > γ|1�> = ^5 _` aσ!" , ` )σ!"b (2.10)

where Γ$. , . % is the lower incomplete gamma function, Γ$. % the complete gamma function,

P(.,.) the regularized gamma function and ^5(.) is the generalized Marcum-Q function. From

(2.9), it can be inferred that defining a threshold based on the probability of false alarm

requires perfect knowledge of the noise power (σ!").

Considering the central limit theorem, for a desired*2 and*+,, the number of required

samples can be approximated by the equation [8]:

' = 2c^K�<*+,> − ^K�$*2%$1 + e'f%g"e'fK" (2.11)

2.3.3 Matched Filtering

Matched filtering (MF) is a coherent detection technique that employs a correlator

matched to the signal of interest or certain parts of it, such as pilots, preambles, spreading

codes and training sequences. It shows optimal performance results making it a good choice

for applications where the transmitted signal is known a priori like radar signal processing.

However, its performance degrades dramatically with synchronization errors and multipath

fading. Furthermore, taking into account that distinct matched filter implementations are

required for each different type of primary signal, its usage can increase the CR’s complexity

dramatically.

If we assume that the noise is Gaussian and x[n] is deterministic and known by the receiver,

the variable y[n] has the distribution:

9��~ �'$0, hL"%, i�Ajk1'$l��,hL"%,i�Ajk1� (2.12)

By simple deduction, based on the LRT, the test statistic of the matched filter is deduced:

Tmn = I l��9��JK�LM ≷ ) (2.13)

Thus, the probabilities of false alarm and detection are:

*+, = ^ \ )hL√p] (2.14)

8

*H = ^ \) − phL√p] (2.15)

where Q(.) is the Gaussian complementary distribution function, p = �J∑ l��"JK�LM and )

the defined threshold for a *+,234 probability of false alarm. Unlike the energy detector, the

probabilities of false alarm and detection of the matched filter don’t depend on the power of

the noise but its square root, turning it less sensitive to noise uncertainty than the ED.

From equations (2.14) and (2.15), for a specific SNR, the number of samples needed to

meet the required *+, and *2 is:

' = <^$*+,%K� − ^$*2%K�>"e'f (2.16)

The last equation shows that the number of samples N increases with O(SNR⁻¹) in the

matched filter which is an improvement compared to the energy detector case where it

increases with O(SNR⁻²).

2.3.4 Cyclostationary Detection

Any communication signals exhibit underlying periodicities in their signal structures added

by modulation, preambles, pilots or cyclic prefixes for synchronization and signaling purposes.

As a result, these signals can be modeled as cyclostationary processes since their mean and

autocorrelation are periodic. Such inherent cyclic features can be used for distinguishing

primary user signals from AWGN which, by definition, is a stationary process.

The cyclostationary detection has better performance than the energy detection under low

SNRs, doesn’t require information of the noise level but, as a drawback, its complexity and

sensing time can sometimes become prohibitive.

By definition, a zero-mean continuous signal x[n] is considered second order cyclostationary

if its time varying autocorrelation function, defined as

Rss�n, l� = Eux�n�. x∗�n + l�w = 1NI x�n�. x∗�n + l�xK�!M (2.17)

is periodic in time n for a lag parameter l (l=±1, ±2, …). So it can be represented as a Fourier

series

Rss�n, l� = I Rssyz�l�e{"|!}x~�

}MK� (2.18)

where the sum is taken over integer multiples of fundamental cyclic frequency αk (for k

=0,±1,±2, · · ·). The “harmonics” of the Fourier series define the cyclic autocorrelation function

(CAF) [9],

9

Rssyz�l� = 1NI x�n�. x∗�n + l�xK�!M eK{"|!}x (2.19)

The Fourier transform of Rssyz�l� is called the cyclic spectrum (CS) or spectral correlation

function (SCF) which is defined as

Sssyz�f� = 1NIRssyz�l��K��M eK{"|�� (2.20)

Whenα = 0, CS takes the form of the power spectral density Sss�f� (PSD) and the CAF takes

the form of the autocorrelation function Rss�n, l�. For an AWGN signal, Sssy �f� = 0 for any α ≠ 0 and Rssy �l� = 0 for any α ≠ 0 and l ≠ 0. The

reason for this phenomenon is the fact that AWGN is a stationary process (without

cyclostationary features) and its samples are independent.

On the other hand, in the case of a presence of a primary signal x[n], Rssyz�l� ≠ 0 for the

cyclic frequencies αk of x[n]. However, if αk isn’t a cyclic frequency of x[n], Rssyz�l� ≠ 0 since it is

computed using a finite number of samples N. Therefore, it is necessary to determine a

statistical test for the presence of cyclostationarity.

2.3.5 Cyclic Prefix Based Detection

The repetition of data in the cyclic prefix (CP) adds some correlation between the samples

of an OFDM symbol. There are several detectors that exploit this feature of OFDM signals, such

as correlation coefficient-based (CCE), nonparametric autocorrelation (NAC) [10], second-order

statistics based, and CP-based sliding window detectors [11]. In this thesis, the method that

will be implemented in GNU Radio is the CP-based sliding window which, according to the

literature [11], has the best detection results.

CP autocorrelation methods base their analysis on the sample value product, which for a

lag parameter ofN�, where N� is the size of the FFT employed in the OFDM modulation, is

defined as follows:

r�n, N�� = r�n� = x�n�∗. x�n + N��, n = 0,… , N − N� − 1 (2.21)

For n belonging to the CP, due to repetition of data,Eur�n�w ≠ 0 and, for the remaining

cases,Eur�n�w = 0. This correlation feature is periodic with period equal toN� + N�, where N�

represents the number of samples that form the guard interval; that is, ifEur�n�w ≠ 0,

thenEurcn + i$N� + N�%gw ≠ 0. In order to exploit this periodic feature, the average sample

product defined as

R�n� = 1KI rcn + i$N� + N�%g, n = 0,… ,�K��M N� + N� − 1 (2.22)

10

whereK = � xKx�x�~x�� is the number of OFDM symbols contained in N samples, can be used

instead. For a received OFDM signal with N� = 16 and N� = 64, the real part of the respective

average sample product R�n� is shown in Figure 2.2. There is a significant increase of R[n] for n

belonging to the CP as was predicted by the theoretical analysis.

Figure 2.2: OFDM signal’s average sample product R[n] for N=32784.

2.4 Cooperative Sensing

In practice, several factors such as multipath fading, shadowing and, consequently, the

hidden terminal problem may affect the detector’s performance. These factors could be,

however, mitigated if the CR users shared their sensing results with the other CRs. This

mechanism is called cooperative spectrum sensing [12].

The enhancement brought by cooperative sensing results from the exploitation of the

spatial diversity between the observations made by different CR users at different positions.

The shared sensing information is then turned into a combined decision whose performance

improvement compared to individual decisions is called cooperative gain. However,

cooperative sensing also adds some overhead to CRs by increasing delay or spending extra

energy or other resources in the cooperative operations. Furthermore, it usually implies the

usage of a control channel where the share of sensing information is made which results in

more wasted bandwidth to the system.

There are three different cooperative sensing categories based on how CRs share data in

the network: centralized, distributed and relay-assisted. In the centralized category, an entity

called fusion center (FC) controls all the cooperative sensing process by selecting the

frequency band of interest, asking, through a control channel, for the individual sensing results

of other CRs and receiving and combining those sensing results to make a decision on the

11

presence or absence of a PU. Then, the unified decision is broadcasted to the neighbor CRs. In

the case of distributed cooperative sensing, no FC is defined and the CRs communicate among

themselves and converge to a unified solution by iterations. The relay-assisted considers that

the sensing and reporting channels in the cooperative sensing network are not perfect. If a CR1

has a weak sensing channel and a strong report channel to the FC and a CR2 the opposite, they

can complement each other by sending the CR2 sensing results through the path CR2-CR1-FC.

The relay-assisted method can be centralized or distributed depending on the existence of a FC

or not.

A key part of a cooperative sensing model design is the data fusion. The reported sensing

results can be of different forms, types or sizes, depending on the control channel bandwidth

requirement. There are three main ways of combining the sensing results: soft combining;

quantized soft combining and hard combining.

In soft combining the CR users transmit the entire local sensing samples or their test

statistics to the FC or other CRs. The shared data is then combined using diversity techniques

such as equal or maximum gain combining. Soft combining brings the best sensing

performances since there is more information to process by the FC, however, it also incurs in

the greatest overhead to the control channel in terms of required bandwidth.

In the quantized soft combining, the information transmitted by the CRs is a quantized form

of the information sent in normal soft combining methods in order to reduce the overhead to

the control channel. The shared data is used in a weighted linear combination and, then,

turned into a unified decision.

The hard combining is the method that incurs less overhead to the system. Each CR makes a

local individual decision and sends it as a one bit message to the FC or other CRs. The FC, then,

combines the shared information using linear fusion rules such as OR, AND and majority, i.e.,

M out of N rules. In the AND rule, the channel is considered occupied if all CRs have considered

it occupied. In the OR rule, the channel is considered occupied if at least one CR have decided

so. The M out of N is a middle term of the last two. Advanced fusion rules can also be used

such as linear-quadratic method that considers the correlation between CR users.

12

13

Chapter 3 Cyclostationary Detection

3.1 Introduction

Much of the recent work in CR has been focused on the detection of Orthogonal Frequency

Division Multiplexing (OFDM) signals [13] which is a key technology in modern communication

systems such as DVB-T, WLAN, WiMAX and LTE. The cyclic prefix provides important periodic

features to OFDM signals that can be used by cyclostationary detectors. Thus, this chapter will

be mainly centered on the detection of this type of modulation.

In this project, a time-domain cyclostationary detector will be implemented in GNU Radio

and tested. This implementation was chosen over the frequency-domain implementation since

it has clear advantages in terms of performance and reduced complexity at detecting OFDM

modulated signals.

This chapter will start by an analysis of the cyclostationary features present in OFDM

signals. Then, the time-domain cyclostationary detector in [14] will be revised and an

alternative implementation will be proposed. Finally, some comparisons in terms of complexity

and performance between both implementations will be made.

3.2 Cyclostationary Features of OFDM signals

A complex baseband OFDM signal x[n] can be represented as follows [15]:

x�n� = I p�n − u$N� +N�%�~��MK� _I c�u, i�e{"|�K$x�K�%/"x� !x�K�

�M b (3.1)

where N� and N� are the numbers of occupied subcarriers and FFT size, respectively. N�represents the number of samples of the cyclic prefix and N�+N� is the total number of

samples of an OFDM symbol. c[u,i] is the coefficient value of the ith subcarrier in the uth symbol

and p[n] is a rectangular shaped pulse with a duration of N� + N� samples.

The autocorrelation function can be written as:

Rss�n, l� = σ�"A�l�I p�n − u$N� + N�%�. p�n − u$N� + N�% + l�xK�!M (3.2)

where σ�" = Euc�u, i�c∗�u, i�w and A�l� is expressed as

A�l� = sin$πlN�/N�%sin$πN�/N�% . (3.3)

It is clear that the autocorrelation function is periodic with a period of N� + N� at

lagl = N�. Thus the OFDM signal is cyclostationary with cyclic frequencies

14

� = �α} = k$N� + N�%T , k = 0,±1,±2,···�. (3.4)

The CAF of x[n], Rssyz�l�, can be calculated by Fourier series expansion of Rss�n, l� as follows,

Rssyz�l� = �σ�"A�l� sin πα} ¡<N� + N�> − |l|¢£πk , for|l| ≤ N� + N�0,otherwise (3.5)

Therefore, it can be concluded that Rssyz�l� has the maximum value for l = ±N� considering

lag parameters different than 0. Also, Rssyz�l = N�� = 0 if N� = 0 because in this case the

cyclostationary features created by the CP disappear. These cyclic features can be seen in

Figure 3.1 and Figure 3.2 where the CAF of a WLAN/OFDM signal is illustrated. The cyclic

spectrum of the same signal is also illustrated in Figure 3.3.

Figure 3.1: CAF of OFDM signal. The peaks appear at

l=±Nd which corresponds to τ=±3.2 µs for the given

OFDM signal’s structure.

Figure 3.2: CAF of OFDM signal over the cyclic

frequency for a lag parameter l=±Nd which

corresponds to τ=3.2 µs for the given OFDM

signal’s structure.

Figure 3.3: SCF of an OFDM signal. The cyclostationary features

are not easily visible for such a low number of samples.

The advantage of the time-domain cyclostationary detector over the frequency domain is in

the fact that, for OFDM signals, the cyclic frequencies αO ∈ � only exist for the lag parameter

l=N�. Not needing to compute the CAF for several lag parameters can greatly enhance the

15

speed of the detector and reduce its complexity. In the case of the ISM Band and TV Band,

there is no need to use cyclostationary detection for more than 1 and 2 lag parameters,

respectively, because the FFT size N� is the same for 802.11g and 802.11a (N� = 64) and, for

DVB-T, there are only 2 modes with different FFT sizes available (N� = 2048 and N� = 8192).

3.3 Traditional Time Domain Cyclostationary Detector

The hypotheses test of the traditional time domain cyclostationary detector (TCD) is

defined as follows,

� H:∀α ∈ �, Rªssy �l� = ϵ$α%H�:∃α ∈ �, Rªssy �l� = Rssy �l� + ϵ$α% (3.6)

where ϵ$α% is the CAF of the noise for the cyclic frequency α. It is considered that there is

prior knowledge of the N� and N� of the OFDM signal, so the peaks of the Rssy �l� can be more

easily found. First, the cyclic autocorrelation function Rssyz�l� is obtained for a P = N�. Then,

since the peaks appear for αO ∈ � (see equation (3.4)) only these values are used in the

statistical test.

The test statistic used to detect the presence of cyclostationarity, based on GLRT, was

proposed by Dandawaté [9] and is expressed as follows

Tyz�l� = rssyz . Σssyz . rssyz° (3.7)

where rssyz�l� = cRe±Rªssyz�l�², Im±Rªssyz�l�²g and Σýz is the estimation of the covariance matrix.

For low SNRs, Rªssyz�l� = ϵ$α% which is an asymptotically normal distributed zero mean complex

random variable. The covariance matrix Σýz, according to [14], can then be estimated as

follows

Σssyz = µC�� C�"C�" C""· (3.8)

where

C�� = 1N++T I Re±Rªssyz²"xQQRK�}M (3.9)

C"" = 1N++T I Im±Rªssyz²"xQQRK�}M (3.10)

C�" = 1N++T I Re±Rªssyz². Im±Rªssyz²xQQRK�}M (3.11)

The expression (3.7) can be rewritten as

16

Tyz�l� = r"C�� + ¸"C"" − 2k¸C�"C��C"" − ¹�"" (3.12)

where �r, i� = rssyz�l� = cRe±Rªssyz�l�², Im±Rªssyz�l�²g. To improve the detection performance, in [15], test statistics that use several cyclic

frequencies were proposed. Two that stood out for their simplicity and good results were

T �º = I Tyzyz»� (3.13)

Tº¼s = maxyz»� Tyz (3.14)

Under H0, having rýz�l� a zero mean Gaussian distribution, the test statistic Tyz�l� follows a χ"" distribution. T �º, being a sum of approximately independent χ"" distribution variables, has,

in turn, a χ"x¾" distribution, where Nα is the number of cyclic frequencies used in the test

(3.13). In the case of Tº¼s, it follows approximately a FÀÁÁ$T% EÂ¾ distribution.

The threshold used, for each test, for a specific false alarm probabilityP�¼, is derived as

follows:

FÀÁÂ¾Á $γ´�º% > 1 − P�¼ (3.15)

FÀÁÁ$γº¼s% > $1 − P�¼%x¾ (3.16)

The T �º gives slightly better results than Tº¼s as it is shown in Figure 3.4. This simulation

was done using a FFT with size 2048 and for the cyclic frequencies α}ϵ� with k=0,±1,±2. In

Figure 3.5, it is displayed the variation of Ty�l = N�� with α for the OFDM signal.

Figure 3.4: Cyclostationary detector’s probability of

detection as a function of SNR for different test

statistics.

Figure 3.5: T�l=N�l=N�l=N�l=Ndddd�� for different cyclic frequencies.

17

It can be seen in Figure 3.5 that the cyclic frequencies of the OFDM signal are much lower

than the range of α for which the CAF was measured. In [14], the author proposes the usage of

decimation before the calculation of the DFT of the CAF. The main purposes are to control the

detection time without altering the size of the FFT employed and to reduce the power

consumption by decreasing the sampling rate. A good estimate of the necessary time for the

TCD to detect the presence of a signal for each lag parameter would be:

ΔtÅ´Æ = Ç \È'++TÉ23ÊWË'2 +'Ì Í <'2 +'Ì> + '2] ≈ T$N��ÆM�Å��º + N�% (3.17)

where 1/T is the sampling frequency, N��Æ the size of the FFT and M�Å��º the decimation

factor. For a M�Å��º = 8, Ty�l = N�� is shown on Figure 3.6.

Figure 3.6: Tα [l=Nd] for different cyclic frequencies with a decimation factor equal to 8

In Figure 3.7, the performance of the cyclostationary detector is illustrated for different

decimation factors. By examining it, we can conclude that the performance of the

cyclostationary detector increases by approximately 2 dB for an increase of a power of 2 in the

decimation factor.

18

Figure 3.7: Cyclostationary detector’s probability of detection as a function of SNR for different decimation

factors.

The flow graph for this CD is displayed in Figure 3.8. The autocorrelation block measures

the product x[n].x*[n+l] for a specified lag l from the set ℒ. This requires a RAM memory with

size equal to the highest lag value in ℒ which can go from 64 in WLAN up to 8192 in the case of

DVB-T signals, for example. The decimation factor É23ÊWË of the decimator block is adjusted

according to the time available for detection. In order to obtain a CAF with enough spectral

resolution, a FFT block of large size (Nfft) is needed. However, this will also dramatically

increase the memory requirements of the detector. The test statistic block only involves the

measurement of the elements of the covariance matrix Σssyz, the test statistics for each αk Tyz�l� and their sum T �º.

Figure 3.8: Flow graph of a traditional time-domain cyclostationary detector

This detector shows great robustness to noise uncertainty, since it uses a Constant False

Alarm Rate (CFAR) algorithm, and to frequency offset. However, it requires previous

knowledge of the lag parameters and cyclic frequencies of the PU signals to be able to detect

them in real time. In the case of OFDM signals this corresponds to knowing the Ng and Nd

values. If the test statistic is made for several lag parameters (for example for detecting 2k and

8k DVB-T signal modes), in order not to increase significantly the detection time, the block

diagram from Figure 3.8 must be replicated for each different P ∈ ℒ. Such drawback

emphasizes the importance of reducing Figure 3.8 flowgraph hardware requirements.

19

3.4 Alternative Time Domain Cyclostationary Implementation

With this alternative cyclostationary detector (ACD) architecture, it is intended to overcome

the limitations of the TCD described before by reducing its hardware requirements.

Improvements in detection performance can be also obtained as long as the CAF is measured

using a DFT size which is a multiple of the cyclic frequencies of interest. This last requirement

isn’t difficult to be met since the new ACD architecture uses separate single frequency DFT

blocks instead of a power of two FFT algorithm. The FFT already incorporated in the wireless

communication devices that use OFDM will, then, remain available for other operations such

as the modulation/demodulation of the transmitted/received signals or for other detection

algorithms like ED to run in parallel.

Considering the independence between the real and imaginary parts of the noise, for a SNR

lower than zero, the element C12 of the covariance matrix in (3.8) is much smaller than the

diagonal elements and can be approximated to zero. The test statistic then becomes

T �º = 1C"" fÑ" + 1C��fW" (3.18)

where cRÒ"R�"g = ∑ Re±Rªssyz�l�²", Im±Rªssyz�l�²"£yz»Ó . The last equation shows an existing

sensitivity of the CD to a phase shift between Im±Rªssyz�l�² and Re±Rªssyz�l�² components.

Considering very low SNR cases again, the received signal is mainly composed by noise and the

second approximation can be made

C�� ≈ C"" ≈ �"x∑ ÔRªssyzÔ"xQQRK�}M = CÕ . (3.19)

According to Parseval’s theorem,

CÕ = �"x∑ ÔRªssyzÔ"xQQRK�}M = �"∑ |x[n]. x∗[n + l]|"xQQRK�!M . (3.20)

Thus, CÕ can be measured in time domain, and the Rªssyz[l] for ÖO ∈ �, can be measured

using the Goertzel Algorithm which is more efficient computationally and in terms of memory

usage than the FFT for a small number of frequencies tested Nα. The resulting test statistic can,

then, be written as follows,

T �º = ∑ �×Ø ¡Re±Rªssyz[l]²" + Im±Rªssyz[l]²"¢yz»� = �

×Ø ∑ ÔRªssyz[l]Ô"yz»� . (3.21)

Some information was, however, lost about the difference between the elements C11 and

C22 of the covariance matrix which is different than zero as SNR increases. This information can

be gathered from the DFTs we measured for Rªssyz[l], ÖO ∈ �. In fact, in absence of noise, Rssyz[l] = 0, ÖO ∉ � and Rssyz[l] ≠ 0, α}ϵA. As a result, the difference between C11 and C22 (∆)

can be estimated using the equation

∆= C�� − C"" ≈ �xQQR <fÑ" − fW">. (3.22)

20

The elements C12 of the covariance matrix can also be approximated by (3.16) using only

the cyclic frequencies ÖO ∈ �,

CÕ�" = �x ∑ Re±Rªssyz². Im±Rªssyz²ÛÜ∈� . (3.23)

The resulting covariance matrix becomes

Σssyz = ÝCÕ + ∆ 2Þ CÕ�"CÕ�" CÕ − ∆ 2Þ ß. (3.24)

The approximation in (3.21) is usually sufficient but both (3.21) (ACD) and (3.24) (ACD2)

performances will be tested later.

The flow graph of this alternative cyclostationary detector is shown in Figure 3.9. The main

novelty compared to the TCD is the complete removal of the FFT and insertion of an IIR filter

bank, formed by Nα elementary Goertzel filters to measure the CAF for each α} ∈ �, and a

<|.|2> block to measure the CÕ parameter. Another, also relevant, difference was the removal

of the variable M decimator block and insertion of a fixed low order M CIC filter. There are two

main reasons for this switch. The first is that the Goertzel Algorithm (GA) provides total

freedom in the choice of the DFT size, so it can now be used to adjust the detection time

instead of the variable M decimator block as in the TCD case. Second, the GA complexity is

equal or lower than a FIR filter so, the usage of a high order decimator, which would include

FIR filters with a high number of taps, wouldn’t reduce the power consumption of the sensing

device. The ACD1 or ACD2 test statistics measurement blocks didn’t suffer any relevant change

in complexity when compared with the TCD. This architecture is only heavier computationally

than the TCD if the number of cyclic frequencies Nα analyzed is high enough which doesn’t

happen very often.

Figure 3.9: Flow graph of the proposed cyclostationary detector.

The several Goertzel IIR filters that form the IIR Filter bank have the structure shown in

Figure 3.10, each one corresponding to a differentα} ∈ �. The feedback part only involves

sums and one real/complex multiplication whereas the forward part only needs to be

computed for the last cycle. For the special caseα} = 0, the complexity decreases even more

since no multipliers are required. The number of multiplications, compared to the generic FFT,

is reduced if 'Û < 5log"<'++T>/6. However, the greatest advantage of the GA results from

21

the low memory it requires due to the fact it doesn’t use approximately '++T shift registers to

store variables in intermediate steps and doesn’t require a large table of pre-computed sines

and cosines. Another advantage of the GA is the fact it can be used for a '++T number which is

not a power of 2. If the '++T used is a multiple of the cyclic frequency bins analyzedα} ∈ �,

the scalloping loss effect of the DFT can be dramatically reduced increasing, consequently, the

performance of the detector.

z-1

++

z-1

x[n] Xk

-Wk

NAk

-1

Figure 3.10: IIR filter structure used for measuring a DFT for the cyclic frequency k using the Goertzel Algorithm.

3.5 Sensitivity to frequency offset

In real scenarios, hardware components add some frequency offset to the received signal.

This phenomenon can degrade the performance of feature detectors and, sometimes, even

make detection impossible, unless some prior frequency synchronization is made.

For a frequency offset of â+, the received signal without the noise component becomes

l�� = l��j="ãäQL°F (3.25)

Rªssyz�l� suffers, then, a phase shift as it can be shown by the following deduction:

Rªssyz�l� = 1NI l��j="ãäQL°F . x∗�n + l�jK="ãäQ$L~S%°FxK�

!M eK{"|!}x

= Rssyz�l�jK="ãäQS°F

(3.26)

This phase shift remains constant over time and doesn’t alterRssyz�l�’s amplitude. The

simulation of the variation of the test statistics (3.12), (3.21) and (3.24) with â+ are shown in

Figure 3.11.

22

Figure 3.11: Variation of cyclostationary detector test statistic with frequency offset.

As expected, the ACD1 test statistic (3.21), which only depends on the Rssyz�l�’s amplitude,

remains constant with the frequency offset variation. It can also be concluded that the

cyclostationary detector TCD presented in [14], as well as the proposed approximation ACD2

sensitivity to frequency offset isn’t relevant, so no prior synchronization device is necessary.

3.6 Sensitivity to Cyclic Prefix Size

As shown before, cyclostationary detection of OFDM signals is based on the correlation

generated by the cyclic prefix of each symbol. Thus, it is evident that the guard interval

duration (Tg) –useful symbol duration (Td) ratio fÌ = 7å7æ will affect this detector performance.

In Figure 3.12, a simulation of the variation of the ACD performance with the ratio fÌ is

shown. The PU signal used is equivalent to the 2k mode DVB-T signal which can have four

different fÌ values. As expected, decreasing the guard interval size reduces the probability of

detection.

Decreasing the guard interval relative size also means that the sinc-like CAF of the OFDM

signal, illustrated in Figure 3.2, is widened, and the signal’s cyclostationary features will be

spread over higher cyclic frequencies. Thus, to achieve higher performance, more cyclic

frequencies have to be read which, in turn, will increase the CD complexity. In Figure 3.12, this

phenomenon was proved by showing a significantly higher performance of the ACD for fÌ = 1/32 when using 51 cyclic frequencies than when using 5.

23

Figure 3.12: Cyclostationary detector’s simulated probability of detection as a function of SNR for various cyclic

prefix sizes.

3.7 Detection of DSSS signals

Every modulated signal contains hidden periodicities that can be detected by a

cyclostationary detector. Throughout this Chapter, the hidden periodicity that has been

analyzed is the cyclic prefix of OFDM symbols. However, cyclostationary detectors can also find

other features such as the spreading code of direct spread spectrum (DSSS) signals.

Take, for instance, the WLAN IEEE 802.11b signal which has a DSSS modulation with a

symbol rate of 1 Mbps and a chip rate of 11 Mcps. The CAF of this signal is displayed at the

sampling rate 25 MS/s in Figure 3.13 and for the special case P = 0 in Figure 3.14. The

spreading code and modulation schemes used for the transmitter were the Barker Code with

length 11 and DBPSK, respectively. As can be seen in Figure 3.13, the 802.11b has more cyclic

frequencies than normal OFDM signals, making its detection easier.

The chip and symbol rate of DSSS signals can be estimated by the cyclostationary detector

as shown in Figure 3.14. At P = 0, the main peak of the CAF matches with the chip rate of the

system. The symbol rate is, in turn, revealed by the distance between the main and secondary

peaks.

24

Figure 3.13: Cyclic Autocorrelation Function of a 802.11b signal.

Figure 3.14: Cyclic Autocorrelation Function of a 802.11b signal for l=0.

In Figure 3.15, a simulation of the ACD performance was made using N=32768 samples and

the set of cyclic frequencies and lag parameters:

$�, ℒ% = u$±11É1è, 0%, $±1É1è, 0.28aé%, $±2É1è, 0.36aé%w. (3.27)

which correspond to the 6 highest peaks of the received signal’s CAF. This detector

performance could be further improved if more cyclic frequencies were taken into account in

the final test statistic, however, at the expense of more complexity to the system.

25

Figure 3.15: ACD2’s probability of detection as a function of SNR when using 5 cyclic frequencies.

In this example, the advantage of the ACD over the TCD in terms of complexity is, once

more, evident. With the ACD, only the 6 fêÛ�P�’s of interest were estimated. On the other hand,

if the TCD was employed, the total number of DFTs computed would be a much higher – 3'++T.

26

27

Chapter 4 Energy Detection

4.1 Introduction

This chapter is dedicated to the study of the frequency domain energy detector (ED), also

called channelized radiometer. First, the conventional fixed threshold energy detector (TED)

architecture, performance and its advantages/disadvantages will be briefly discussed.

Afterwards, the analysis will take a main focus on EDs with adaptive threshold whose

sensitivity to noise uncertainty is very low compared to the TED.

A low complexity adaptive threshold estimation algorithm will be proposed and its

comparison with other existing algorithms in the literature, such as the FCME, will be made.

4.2 Fixed Threshold Energy Detection

The fixed threshold Energy Detection is the most basic sensing method. Unlike feature

detection, it is incapable of distinguishing between different types of signals and between

them and noise. It requires perfect knowledge of the noise variance which is a requirement

usually difficult to be met by CRs if no online noise estimation schemes are used.

Considering flat-fading channels and independence between the samples x[n] of the source

signal, the PDF distributions of the received signal can be represented as,

:<ë|1=> =ì:<9��|1=>JK�LM . (4.1)

Assuming that the noise and source signal are both random processes with Gaussian

distribution,

9��~ �'$0, hL"%, i�Ajk1'$0, hê" +hL"%,i�Ajk1� (4.2)

where hê" and hL" are the source signal power and noise power respectively. By simple

deduction, the LRT test becomes the following energy detector test statistic,

TGH = 1'I 9��"JK�LM = 1'I I NO$P%"

JQQRK�OM

5K�SM ≷ ). (4.3)

where '++T is the size of the FFT used,U = JJQQR the number of FFT operations employed for

each frequency, NO the FFT output of y[n] for the frequency k and ) is the threshold which was

pre-established taking into account the noise power. Therefore, it can be concluded that the

28

energy detector is based on LRT, i.e., optimal, when the received samples are independent and

show Gaussian distribution.

If the detection is made for a channel i formed by í ∈ ¹W FFT output frequencies where #¹W = ï = JQQRJðñ < '++T, the test statistic becomes

TWGH = 1ïUI I NO$P%"O∈òó5K�SM ≷ ). (4.4)

where 'Êô is the number of channels considered and í ∈ ¹W are the FFT bins that form the

channel i. Under 1, being TWGH obtained from a sum of É3 = ïU squares of zero-mean

Gaussian variables õO$P%, it has a ö" distribution with 2É3 degrees of freedom. Under1�, TWGH

has a non-central ö" distribution with 2É3 degrees of freedom with a non-linearity parameter

of a = ∑ ∑ ÷O$P%"O∈òó5K�SM . Then, according to [7], the probability of false alarm becomes

*+, = *<TWGH > γ|1> = Γ YÉ3 , )2σ!"[Γ$É3% = * \É3 , )2σ!"] (4.5)

where Γ$É3 , x% is the lower incomplete gamma function, Γ$É3% the complete gamma

function and P(É3,x) the regularized gamma function. The probability of detection can be

deduced as

*2 = *<TWGH > γ|1�> = ^5 _` aσ!" , ` )σ!"b (4.6)

where ^5(.) is the generalized Marcum-Q function [7]. From (4.5), it can be inferred that

defining a threshold based on the probability of false alarm requires perfect knowledge of the

noise power.

Considering the central limit theorem, for a desired *2 and *+,, the number of required

samples can be approximated by the equation

' = 2c^K�<*+,> − ^K�$*H%$1 + e'f%g"e'fK" (4.7)

where Q(.) is the standard Gaussian complementary CDF. The deduction is presented in

Appendix A. This shows that, without noise uncertainty, the signals could be detected for an

arbitrarily low SNR, and the number of samples N, or the sensing time, is proportional to e'fK".

In the case of existence of uncertainty of x dB, the estimated noise power varies between

σ!" ∈ Ýσ�" øÞ , øσ�"ß where ø = 10ê �⁄ > 1 and σ�" the center of the variation interval. In the

worst case scenario, the *2 and *+, will be:

29

*2 = minúûÁ∈µúüÁ ýÞ ,ýúüÁ·^5 _àσ!" , ` )σ!"b = ^5 _`øaσ�" , `ø)σ�"b (4.8)

*+, = maxúûÁ∈µúüÁ ýÞ ,ýúüÁ·* \É3 , )2σ!"] = * YÉ3 , )2øσ�"[ (4.9)

In the cases of low SNR, e'f + 1 ≈ 1 and the number of required samples to meet the *+,

and *2 requirements is approximately:

' = 2 µø^K�<*+,> − ^K�$*H% Y1ø + e'f[·" þe'f − Yø − 1ø[�K" (4.10)

As an example, for a noise uncertainty of x=0.5 dB, ø ≈ 1.122 and ¡ø − �ý¢ = 0.231. As a

result, for a SNR=0.231=-6.368 dB, the number of samples N required goes to +∞. This limit

on the detector’s performance is called “SNR Wall” and is defined by the expression

e'f�,SS = ø" − 1ø = 10"ê �⁄ − 110ê �⁄ . (4.11)

For SNR values below or equal to e'f�,SS, the detector can’t meet the required *+, and *2

using a finite number of samples.

4.3 Adaptive Threshold Energy Detection

In the literature, there are already several architectures that use a dynamic threshold to

reduce the sensitivity of energy detection to noise uncertainty. Some of the most popular are

constant false alarm rate (CFAR) schemes such as cell averaging (CA-CFAR) and ordered

statistics (OS-CFAR) [16]. The CA-CFAR sets the threshold adaptively by estimating the mean

level in a window of N range unoccupied cells. The OS-CFAR scheme obtains the noise estimate

from the kth largest cell in an N size window. These methods, however, assume that the cells

used for the noise level estimation are not corrupted, i.e., free of interference which might not

be the case in real CR scenarios. To address this issue, before making the actual detection, an

additional stage called censoring, which consists in the removal of the corrupted cells from the

reference set, has to be added. In [17], the author suggests, as censoring schemes, the CA

scaling factor based method, the forward consecutive mean excision (FCME) or the backward

consecutive mean excision (BCME). In [18], a slightly different approach based on Bayesian

Estimation is suggested. This detector bases its decision on the estimation of the number of

available cells, not using iterative methods like the previous ones.

In this work, a low complexity frequency domain adaptive threshold algorithm (AED) is

proposed and compared with the FCME algorithm. Both detectors use the unoccupied

channels of the spectrum to make an estimate of the threshold. This implies that the received

signal is sparse in frequency domain, which is usually true, if the bandwidth analyzed is wide

enough.

30

Like the TED, the AED and FCME start by computing the FFT of the received signal and

grouping the several FFT bins into different channels. The result is the traditional TED test

statistic:

SW = 1É3I I NO$P%"O∈òó5K�SM ,¸ = 0,… ,'Êô (4.12)

where É3 = ïU is the number of spectral averages, NO$P%" the magnitude square of the

FFT bin k that belongs to the channel i, and 'Êô the number of channels analyzed. It’s in the

next stage that the three methods differ.

4.3.1 FCME Algorithm

The FCME is an automated method that separates the data into two sets: the clean set

made by noise-only samples/channels SW, i.e., channels free of interference and outliers set

formed by channels occupied by PUs. The threshold that separates these two sets is calculated

iteratively.

The samples SW are first ordered in an ascending order becoming:

÷$W% = sortW $eW% , ¸ = 1,… ,'Êô . (4.13)

Then, the FCME assumes a clean set formed by the first ^$% ÷$W% samples where ^$% ≈ 0.1'Êô. Then it performs the following test recursively:

÷$�~�% > ÇòmG÷�� (4.14)

where ÇòmG is the threshold parameter and ÷�� is the average of the current clean set

formed by the first ^$% ÷$W% samples. If the test result is false, ÷$�~�% is added to the clean set, ^$% is incremented (becoming ^$�%), ÷�� is recalculated and the (4.14) test is repeated. If

(4.14) test returns true, the algorithm stops and the channels ÷$�~�%, … , ÷$Jðñ% are considered

occupied. The threshold parameter ÇòmG is obtained from,

*+,234 = jK7��m I 1!mK�ËM $ÇòmGÉ3%Ë (4.15)

which is the Poisson CDF function �$l| % for a = ÇòmGÉ3 and l = É3. *+,234 defines the

clean sample rejection rate of the test. According to [19], the (4.15) estimation isn’t precise

enough for high *+,234, so an empirical adjustment might have to be done.

The added complexity by the FCME scheme to the ED is greater than other BCME schemes

but also shows better results [20]. It requires sorting 'Êô samples which has O(N2) complexity,

Q comparison tests and Q add and division operations which have linear complexity.

31

Considering the cases where there are less than ^$% vacant channels for noise estimation,

the initial set is corrupted and, as result, the probability of false alarm will be lower and the

theoretical upper limit for the probability of detection will be:

*2Ë,ê = 'Êô − ^$%'�Ê (4.16)

where '�Ê represents the number of occupied channels. For example, if all 'Êô = 25

channels are occupied and ^$% = 1, *2Ë,ê = 0.96.

4.3.2 Alternative adaptive threshold estimation algorithm

The proposed threshold estimation algorithm, called alternative energy detector (AED),

starts by searching for the minimum value of SW: SËWL = minWM�,…,Jðñ SW. (4.17)

Afterwards, a rough estimation of the number of unoccupied channels ^ of the received

signal is made. There are several ways to make this estimation. In this work, a very low

complexity method is used which consists in counting the number of eW samples below )7GH,

where )7GH is the fixed threshold of the conventional ED. Thus, the estimation can be

expressed as follows,

^ = countWM�,…,JðñuSW < )7GHw (4.18)

where )7GH is obtained offline through the expression,

)7GH = 2øσ!"*K�<É3 , *+,234>. (4.19)

If ^ = 0, all channels are considered occupied and no further calculations are needed. On

the other hand, when ^ ≠ 0, the following test statistic is used,

Ç�GH = eW ≶ )�� SËWL (4.20)

where )�� is the threshold parameter for a clean set of ^ samples.

Without loss of generality, considering a clean set Θ of ^ out of 'Êô unoccupied channels

and considering that the remaining channels have an infinitely large SNR, the probability of

false alarm is,

*+, = *<eW > )�� SËWLÔ¸ ∈ Θ>. (4.21)

The threshold parameter )�� only depends onQ, É3 and*+,234 so, by fixing a priori theÉ3

and*+,234 values, it can be computed offline for each ^ and stored in an array of size'Êô.

In Appendix B, the solution to (4.21) is deduced. It is proven that puSËWLw = ï�hL" and ��kuSËWLw = ï"hL� where ï� and ï" are variables whose value depends only on Q and É3.

32

The equation (4.21) solved for the variable )�� can then be approximated by a quadratic

function with solution,

)�� = ï� − �� 1É3 <ï�" − �"ï"> + ï"ï�" − �"ï" (4.22)

where � = jk�K�<2*+,234 − 1>√2.

Since a fixed threshold )7GH is used to estimate the number of occupied channels, some

sensitivity to noise power is expected from this detector. Another alternative would be to use SËWL to get an estimate of ^. However, tests showed that using )7GH gives good enough

results and can cope better with the cases where there is no sparsity in the spectrum of the

received signal. In fact, by using )7GH, if there aren’t any free channels, (4.18) will return 0

which is the correct result.

The flowgraph of the proposed energy detection is displayed in Figure 4.1. In comparison to

the TED, 3 blocks and one multiplication were added. “Estimate ^” and “Min” require 'Êô

tests, so they have O('Êô) complexity. “Estimate )�� ” has �$1% complexity since it only

requires accessing to the position ^ of a 'Êô size array. Therefore, it can be inferred that, for a

low 'Êô, the complexity added to the AED in comparison to the TED is negligible.

Figure 4.1: Flowgraph of the proposed energy detector

In Figure 4.2, the variation of the probability of detection of the three EDs with the SNR is

shown for a signal with approximately 40% of its spectrum free and for a noise uncertainty of 1

dB. The number of spectral averages and channels used were É3 = 500 and 'Êô = 50, so the

total number of samples read was N=25000. The FCME performance is completely

independent of the noise power since its detection curves for the hL" = øh�" and hL" = �ýh�"

cases are overlapping. The fact that the AED uses both a fixed threshold )7GH and an adaptive

threshold makes it more sensitive to noise uncertainty than the FCME. However, this feature

could be easily eliminated if an adaptive threshold was used instead to measure the number of

unoccupied channels Q. The TED, on the other hand, only uses a fixed threshold, turning it into

the one with the most unstable behavior when the noise is not perfectly known a priori.

33

Figure 4.2: TED, AEC and FCME’s probability of detection as a function of SNR for a received signal with 60% of its

bandwidth occupied by a WLAN/OFDM signal

In Figure 4.3, the same simulation of Figure 4.2 was made but, in this case, for a signal with

only 12% of its spectrum occupied. Both the FCME and AED probabilities of detection

increased as a result of a larger number of noise-only channels existent in the received signal.

From this plot, it can also be concluded that the FCME only has (slightly) better performance

than the AED for the case of very sparse signals. The explanation for this phenomenon is the

fact that, for dense signals, there is a higher chance that the FCME’s clean set gets corrupted

by occupied channels.

Figure 4.3: TED, AEC and FCME’s probability of detection as a function of SNR for a received signal with 12% of its

bandwidth occupied by a Zigbee signal

34

In Figure 4.4, it is illustrated the variation of the probability of false alarm with the SNR for

the FCME and the proposed AED algorithm. In spite of being considered a constant false alarm

rate (CFAR) scheme, the FCME probability of false alarm for the empty channels goes over 5%

for high SNRs. On the other hand, the AED can keep its probability of false alarm below or

approximately at 5%.

Figure 4.4: Probability of detection variation with SNR for the TED, AED and FCME

If there is no sparsity in the received signal, the initial clean sets of both algorithms will be

corrupted and the probability of detection and false alarm will drop. As shown before, for the

FCME algorithm, the probability of detection will have a theoretical upper limit *2Ë,ê < 1 even

for a ^$% = 1. However, this limit might be too optimistic. Considering the hypothetical case

where the received signal power is approximately constant over all channels, the *2 → *+,234

and, practically, no detection will be possible. This phenomenon can be seen in Figure 4.5. The

AED, on the other hand, since it uses a fixed threshold to estimate the number of available

channels, will tend to the fixed threshold energy detector. The insensitivity to noise

uncertainty will be, however, completely lost.

35

Figure 4.5: TED, AED and FCME algorithms’ probability of detection as a function of SNR when the received signal

is a white Gaussian random signal.

4.3.3 Localization Algorithm Based on Double-thresholding

The type of modulation scheme employed severely affects the spectrum shape of

transmitted signals. Even after long periods of averaging, this shape can be very irregular

which may affect the ability of the energy detection schemes, described in the previous

section, to correctly estimate the received signals’ bandwidth.

In Figure 4.6, the spectrum of a generic signal is displayed. It is well known that a low

threshold increases the probability of false alarm. However, it can also be seen from this figure

that if the threshold is too large, the original signal may be separated into several signals. In

order to solve this issue, the localization algorithm based on double-thresholding (LAD), which

uses two thresholds instead of one, is suggested in this section. This algorithm uses one upper

threshold whose purpose is to decrease the false alarm probability rate and one lower

threshold which is used to avoid the segmentation of the original signal. The LAD can increase

the detector’s performance and estimate the signal bandwidth more efficiently without

requiring a priori knowledge of the transmitter signal and without great computational costs.

36

Figure 4.6: Spectrum of a NB signal. The upper and lower thresholds are represented by green and red dash lines

respectively.

The LAD starts by grouping adjacent samples above the lower threshold into clusters. Then,

the largest element of each cluster is compared with the upper threshold. If it’s higher, all

elements of the cluster are considered occupied. If it is lower, all samples are considered free.

For an OFDM signal that occupies 60% of the spectrum analyzed, the probability of

detection for the FCME and AED algorithms, using a É3 = 500, 'Êô = 50 is displayed in Figure

4.7. Using an upper and lower threshold equivalent to the probabilities of false alarm 4% and

10%, a total probability of false alarm of approximately 5% was obtained for the LAD. As

expected, there is an increase in performance of the AED and FCME algorithms when

combined with LAD.

Figure 4.7: Probability of detection as a function of SNR for the TED, AED and FCME with and without LAD.

Taking into account the wideband nature of the signal that is being detected (only 40% of

the spectrum is free) another enhancement to the traditional LAD algorithm can be made,

which consists in joining clusters when the interval between them is narrow enough. With this

37

change, it is intended to increase the probability of detection of the energy detector and,

consequently, decrease the usage of channels/bands where the interference caused by signals

present in neighbor channels might still be relevant.

In Figure 4.8, under the same conditions as in Figure 4.7, the performance of the LAD when

clusters separated by just 1 channel are joined (LAD2) is shown. With this minor change, the

probability of detection of the AED and FCME performance can reach or even surpass the

traditional energy detector optimal performance while maintaining a probability of false alarm

of 5%.

Figure 4.8: Probability of detection as a function of SNR for the TED, AED and FCME with and without LAD when

clusters separated by an interval equal to 1 channel are joined.

In Figure 4.9, it is shown the relative error incurred by the AED and FCME algorithms, with

and without the usage of LAD and LAD2, in the estimation of the signal’s bandwidth. Overall,

double-thresholding algorithms have the best results. It can also be concluded that the AED

relative error is lower than the FCME for SNR values below -8 dB which is in accord with the

probability of detection curves illustrated in Figure 4.8 for both methods.

It can also be seen from Figure 4.9, that the FCME+LAD2 curve starts to rise at -4 dB. The

main cause for this phenomenon is the fact that this algorithm is more sensitive than the

others to the power leaked to the stopbands as a result of the non-ideal OFDM modulation.

38

Figure 4.9: Bandwidth estimation error as a function of SNR for the FCME, AED, TED algorithms with and without

LAD and LAD2.

39

Chapter 5 OFDM CP-based Detection

5.1 Introduction

In this chapter, it is intended to make a brief study of some of the state-of-the-art

autocorrelation detection algorithms for OFDM signals, such as, the CP-based second-order

GLRT (GLRT 2nd), the CP-based sliding window (CP-SW) [10], the correlation coefficient-based

(CCE) and the nonparametric autocorrelation (NAC) [11]. These feature detectors’ behavior

will also be analyzed when subject to noise uncertainty and carrier frequency offset.

5.2 CP-based Sliding Window

The CP-based sliding window (CP-SW) test statistic measures the absolute value of a N� size

cyclic moving average of R[n] (explained in page 9) as is shown in the next equation,

Ç��$,�4% = max� I f��L!�" (5.1)

where S# = ±θ, … , <θ+ N� − 1>mod<N� + N�>², 0 ≤ θ ≤ N� +N� − 1 corresponds to

the set of R�n� samples selected by the sliding window [11]. In [21], the author suggests,

instead of the absolute value, using the real part of the moving average of R[n] as shown in the

following equation,

Ç��$Ñ3,S% = max� fj � I f��L!�"%. (5.2)

Although, this change gives better results than (5.1), it also turns the detector more

sensitive to frequency offset as it will be shown later. According to [11], this detector has the

best performance results of all CP-based detectors. However, it requires previous knowledge

of the noise power, so it is expected a drop in performance when in presence of noise

uncertainty. Since there are no expressions for measuring the probability of detection and

false alarm, the threshold has to be measured empirically.

5.3 Second order statistics based detection (GLRT)

The test statistic of this method purposed in [11] is based on the GLRT and consists in the

division of the energy of R[n] in the case of existence of a PU signal (H1) by the same variable in

the case of absence of a PU signal (H0). The energy of R[n] under H0 can be estimated a priori

or based on the samples of the received signal. The latter has clear advantages since it isn’t

sensitive to noise uncertainty.

40

In order to make the estimation of R[n]’s energy under H0, the values ofReuR�n�w, nϵS#

where θ corresponds to the first index of the CP are averaged and subtracted toR�n�, nϵS#.

The purpose is to eliminate the correlation created by the CP. The next equation illustrates the

test statistics explained before:

ÇB567 = max�∑ |f��|"Jæ~JåK�LM∑ &f�í� − 1'Ì ∑ fjuf�¸�wW!�" &"O!�" + ∑ |f�'�|"=∉�"

. (5.3)

In spite of not needing a priori knowledge of the noise power, its performance is slightly

worse and requires more calculations than the CP-SW in (5.2). There isn’t any expression for its

false alarm probability so its threshold has to be measured empirically.

5.4 Correlation coefficients based detection algorithm (CCE)

This method, proposed in [10], makes use of the autocorrelation function of OFDM signals

and its known distribution. The estimated autocorrelation of the received signal is expressed

as follows:

fê�P� = 1'I l��∗. l�� + P� =JK�LM

1'I k��, P�JK�LM . (5.4)

For a sufficiently large N, according to the central limit theorem,Rªs�l� has approximately a

Gaussian distribution with mean Rs�l� and variancevar±Rªs�l�² = úû)x .

For a sufficiently large N, Rªs�0� ≈ Rs�0� and the relation √Nρs�l� = √N +ª,��+ª,�� = √N +ª,��úûÁ has

a N$√Nρs�l�, 1% distribution. If we define a test statistics as follows:

ÇòòG = '$øê�P��" + ⋯+ øê�P5�"% (5.5)

where L is the number of lag parameters that need to be evaluated, its distribution, under

H0, is a chi-square with 2L degrees of freedom. Given a false alarm probability, the threshold

can be defined the same way as other statistics with known distribution:

FÀÁ.Á $γ××/% > 1 − P�¼. (5.6)

Since the γ××/ only depends on L andP�¼, this method is nonparametric and immune to

noise uncertainty.

5.5 Nonparametric autocorrelation based detection algorithm (NAC)

This method, also proposed in [10], has a test statistic which is basically equal to the time-

domain cyclostationary detector explained before with the exception that the statistic is only

measured forα = 0. So we have:

41

T�l� = kêê. Σêê. kêê° (5.7)

where kêê�P� = cRe±fêê�l�², Im±fêê�l�²g and Σêê is the estimation of the covariance matrix.

If more than one lag parameter is used in the test statistic,

TJ�ò =IÇ�PW�5W (5.8)

where L is the number of lag parameters used in the estimation. The threshold is also

defined the same way as the cyclostationary detector:

FÀÁ.Á $γxÓ×% > 1 − P�¼. (5.9)

This method is nonparametric and immune to noise uncertainty and, in spite of involving

more calculations than CCE has the advantage, also shared by the cyclostationary detector, of

its analysis not being based on the assumption that the noise is Gaussian.

5.6 Alternative Second order statistics GLRT based detection (GLRT2)

In order to mitigate the GLRT method, described in [11], sensitivity to frequency offset, a

simple change in (5.3) test statistic is suggested:

ÇB567 = max�∑ |f��|"Jæ~JåK�LM∑ &f�í� − 1'Ì ∑ f�¸�W!�" &"O!�" + ∑ |f�'�|"=∉�"

(5.10)

This time, the correlation created by the CP is eliminated by subtracting not only the real

part of the f�í� inside the CP but also the imaginary which, in theory and in perfect

synchronization, has 0 mean. This change might, however, slightly reduce this GLRT2 detector

performance.

For a R�n� of K=409 averages, approximately the same number of samples used during the

cyclostationary detector analysis with decimation factor equal to 16 (N=32864), the

performance of these detectors was simulated in Matlab and is illustrated in Figure 5.1. The

sliding window shows the best performance results, as expected, when the noise is completely

known and there is no frequency offset. The GLRT 2nd, however, seems more interesting since

it is a CFAR method and its performance is very close to the CP-SW.

42

Figure 5.1: Autocorrelation Methods’ simulated probability of detection as a function of SNR.

5.7 Sensitivity to frequency offset

Frequency offset added by hardware components can degrade feature detectors

performance if no synchronization device is employed. As it was shown in Chapter 3, for a

frequency offset of â+, the received signal without the noise component becomes

l�� = l��j="ãäQL°F (5.11)

r�n� suffers, then, a phase shift as it can be shown by the following deduction:

r�n� = x�n�∗jK="ãäQL°F . x�n + N��j="ãäQ$L~x�%°F = r�n�j="ãäQx�°F (5.12)

Considering no variation of the frequency offset over time, R[n] also suffers the same phase

shiftj="ãäQx�°F. As a result, test statistics of detectors such as (5.2) and (5.3) which base their

analysis on the real part of R[n] instead of its absolute value will be affected.

The variation of the test statistics described before with â+ are shown in Figure 5.2,

simulated in Matlab. It can be concluded that, as predicted, (5.2) and (5.3) are sensitive to

frequency offset while (5.1) and (5.10), which don’t depend entirely on the real part of R[n],

aren’t.

43

Figure 5.2: Variation of the CP-based detectors’ test statistics with frequency offset

5.8 Sensitivity to Cyclic Prefix Size

Similarly to the cyclostationary detector described in Chapter 3, CP-based detection is

based on the correlation generated by the cyclic prefix of each OFDM symbol. Thus, its

performance varies with the guard interval duration (Tg) –useful symbol duration (Td) ratio fÌ = 7å7æ as illustrated in Figure 5.3. For comparison purposes, the ACD algorithm, using a

constant number of cyclic frequencies in its test statistic (5 peaks), was also simulated and

added to this plot. As can be seen, the CP-based methods show less sensitivity than the ACD to

the variation of the ratio fÌ, making them more advisable for detecting OFDM signals with low

guard interval duration such as DVB-T signals whose fÌ can be as low as 1/32.

44

Figure 5.3: CP-based and cyclostationary detectors’ simulated probability of detection as a function of SNR for

several guard interval sizes.

45

Chapter 6 Cyclostationary Implementation and

Measurements

6.1 Introduction

In this chapter, the implementation on GNU Radio and an experimental study will be made

for the cyclostationary detector architectures proposed in the literature [14] and in this work

(see equations (3.21) and (3.24)).

Their performance will be evaluated in the presence of an OFDM PU signal and displayed in

the form of *2 vs SNR, *+, vs γ and *2 vs γ plots. A comparison will be made with theoretical

and Matlab simulated models.

6.2 Test bed and transmitter’s description

The detector’s performance was tested in an indoor space with both the URSP2 transmitter

and receiver in line of sight. A center frequency and sampling frequency of 5.5 GHz and 1 MS/s

respectively were used for both boards.

The transmitter’s signal was an OFDM/BPSK modulated pseudorandom sequence of bits

with a bandwidth of 500 kHz in the baseband. A numerical amplifier was used to test the signal

detection for different SNR values. The OFDM FFT size was '2 = 64 with 52 occupied

subcarriers and the guard interval was composed by '2 = 16 samples at 1 MS/s.

6.3 Detector Implementation

Unless told otherwise, for both the ACD and TCD, during the experimental study, the lag

parameter used was l = N� = 64 and the DFT/FFT bins analyzed were

� = �α} = kM�Å��º$N� + N�% , k = 0, ±1,±2�. (6.1)

For the TCD, a decimation factor of Mdecim=16 and a FFT size of 2048 were employed.

Therefore, the resulting number of samples per test statistic was N=32832. In the case of the

ACD, the CIC decimation factor was Mdecim=2 and two different DFT sizes were tested. The first

DFT size was Ndft=16384 which allowed the comparison of the ACD with the TCD when the

number of samples per test statistic is the same (N=32832). The second DFT size was, on the

other hand, Ndft=16360. The purpose of using this value was to show the ACD superior

performance when the DFT size is a multiple of the bins analyzed$α} ∈ �% even for a lower

number of samples read N. In Table 6.1 and Table 6.2, the hardware requirements of both the

TCD, implemented in [14], and the ACD1/ACD2 are shown. As it can be seen, the proposed

architecture has clear advantages, especially in terms of (real) memory usage. The number of

real multipliers and real adders were also significantly reduced because the ACD controls the

detection time by altering the DFT size and not through a high order variable M decimator as

in the TCD case.

46

Stages Operations

Multipliers Adders Memory Dividers

Auto-corr. 4 2 2N� = 128 0

Decimator 40 80 80 0

FFT 4$1log�N��Æ2− 1%= 20

101log�N��Æ2− 2 = 58

2$N��Æ − 1%= 4094

0

Σssy Estimation 3 3 3 0

T �º 6 9 3 1

Total 73 152 4308 1

Table 6.1: TCD Hardware Requirements

Stages Operations

Multipliers Adders Memory Dividers

Auto-corr. 4 2 2N� = 128 0

CIC Decimator 0 12 12 0

IIR Filter Bank 6$Ny − 1%= 24

6$Ny − 1% + 2= 34 4$Ny − 1% + 2= 18

0

< |. |" > 2 1 1 0

T �º 1/6 1/9 1/3 1

Total 31/36 50/59 160/163 1/1

Table 6.2: ACD1/ACD2 Hardware Requirements

For the considerations previously described, the TCD resulting test statistic TÛ�l = N��, obtained from the received OFDM signal, is displayed in Figure 6.1. The attenuation at the

borders is caused by the filtering during the decimation process and dictates an adjustment in

the threshold obtained from equation (3.16) for a certain *+,234. The equation used to obtain

the desired threshold γ´�º* from the theoretical one γ´�º (3.16) was

γ´�º∗ = fM�Å��ºf��4�5� γ´�º (6.2)

where f��6�5� is the cutoff frequency at -3 dB of the filter and �, the sampling rate. It still

should be noted that the adjustment is made a priori so it doesn’t require any estimation of

any parameter such as the noise level.

47

Figure 6.1: OFDM signal’s test statistic T�l=N�l=N�l=N�l=Ndddd] ] ] ] as a function of α.

The flowgraphs of the traditional and alternative cyclostationary detectors (TCD) and

(ACD1/ACD2) used during the testing are displayed in Figure 6.2 and Figure 6.3.

Figure 6.2: Flow graph of a traditional time-domain cyclostationary detector

Figure 6.3: Flow graph of the proposed cyclostationary detector ACD1/ACD2

For 12 different SNR values whose range goes approximately from -22 to -4 dB, 2500 test

statistics of each detector were stored into files using the “File Sink” block from GNU Radio.

The rest of the signal processing, such as measuring the probabilities of detection and false

alarm from those test statistics were done in Matlab.

48

6.4 Measurements

In Figure 6.4, the cumulative function distribution (CDF) of the traditional (TCD) and the

proposed (ACD and ACD2) cyclostationary detectors, in the case of absence of a primary signal

(1), is displayed. The experimental CDFs are almost identical to the theoretical model

obtained from equation (6.2). There isn’t a noticeable difference between the*+,’s of the TCD

and ACDs which proves the analysis made in Chapter 3.

Figure 6.4: TCD, ACD1 and ACD2’s empirical and theoretical CDFs under H0.

In Figure 6.5, due to a lack of a theoretical model for the TCD’s probability of detection of

OFDM signals, its empirical CDF curves are compared to its simulated CDF curves for different

SNR values. For comparison purposes, the threshold represented in the x axis was divided by

the *+,234 = 5% threshold. Unlike the 1 case, the empirical CDFs show greater variance than

the simulated curves. Possible explanations for this phenomenon are the multipath fading that

can reduce the periodicity induced by the insertion of a cyclic prefix in each OFDM symbol, the

existence of sampling clock offset (SCO) in the USRP2 board and the fact the noise isn’t

completely white. The experimental CDF mean value, on the other hand, matches the

simulated mean value.

49

Figure 6.5: TCD’s empirical and theoretical CDFs for several SNR values

In Figure 6.6, the empirical CDFs of the TCD, ACD1 and ACD2 are shown for a SNR of -7.7 dB.

The probabilities of detection for the TCD, ACD1 and ACD2 for a ' = 32832 are practically

identical which shows that no drop in performance was caused by the approximation

suggested in Chapter 3. In fact, the weakest approximation (ACD1) shows slightly better results

than the TCD and ACD2.

In this figure, the ACD1 CDF curve for a' = 32720 is also displayed. The main purpose of

this curve is to show the increased performance of the ACD1 (and ACD2) detector, even for a

lower number of samples read, compared to the TCD. Since the ACD isn’t constrained by the

size of the FFT block, the DFT can be measured for a multiple of the cyclic frequencies tested

(see eq. (6.1)), avoiding, this way, the scalloping loss caused by limited resolution of the FFT.

50

Figure 6.6: TCD, ACD1 and ACD2’s empirical and theoretical CDFs for a SNR=-7.7 dB

Figure 6.7 shows the empirical relative error of the ACD1 (see Eq. (3.21)) and the ACD2 (see

(3.24)) test statistics when compared to the TCD using equation (3.12). The (3.21)

approximation has the largest relative error but its test statistic becomes greater than TCD’s as

the SNR value increases. Thus, its performance is slightly better for high SNRs. The ACD2 is

almost identical to the TCD in the case the cyclic frequencies of the received signal are

completely known. If this requirement can’t be met, its curve will tend to the ACD1’s curve.

The reason for the ACD1 better performance is the fact that (3.21) is independent of the Rªssyz

phase angle which can be altered by frequency offset.

Figure 6.7: Relative error of ACD1 and ACD2’s approximations as a function of SNR.

51

In Figure 6.8, the variation of the probability of detection with SNR is shown. The

experimental curves of the TCD and ACDs are overlapping for the same number of samples N,

so it can be inferred that their performance is roughly the same. The ACD1 curve for N=32784

(Ndft=16360), on the other hand, in spite of using a lower number of samples, shows better

performance since 16360 is a multiple of the bins analyzed (α}ϵ�). In Figure 6.8, it can also be

seen that the theoretical values, represented by dash lines, match the empirical ones.

Figure 6.8: TCD, ACD1 and ACD2’s empirical and simulated probability of detection as a function of SNR.

6.5 Sensitivity to Frequency Offset

In order to test the detectors’ sensitivity to different frequency offset (FO) values, the

transmitter’s amplitude was kept constant and 17 different central frequencies, ranging from -

17,5 kHz to 17,5 kHz in relation to 5,5 GHz, were used. For each FO, 2500 test statistics were

stored into a file using the “File Sink” block. Despite the constant gain of both the transmitter

and receiver, the SNR of the received signal can vary considerably over time. For this reason,

the test statistics were normalized to a SNR=-2 dB considering the SNR measured during their

extraction.

From the theoretical analysis made in Chapter 3, it is not expected for this cyclostationary

detector architecture to show any sensitivity to frequency offset. The theoretical analysis is

proved by the experimental results in Figure 6.9. The threshold, represented by a dash line, is

much lower than the obtained test statistics which shows that there is no risk in miss detection

due to FO.

52

Figure 6.9: Empirical variation of the ACD1 and ACD2’s normalized test statistics with frequency offset for a SNR=-

2 dB.

53

Chapter 7 Energy Detection Implementation and

Measurements

7.1 Introduction

In this chapter, the energy detectors described in Chapter 4, namely the fixed threshold

energy detector (TED) and the proposed adaptive threshold energy detector (AED), will be

implemented and tested in GNU Radio. Since the performance of the AED depends on the

sparsity of the received signal, the experimental study will be made for different types of

transmitters of the ISM band, in particular, for 802.11g/OFDM and Zigbee transmitters.

The *2 vs SNR, *+, vs γ and *2 vs γ curves will be utilized to make the comparison between

the empirical, simulated and theoretical results/models.


The detectors’ performances were tested in an indoor space with both the USRP2

transmitter and receiver in line of sight for the central frequency of 5.5 GHz in order to avoid

interference from WiFi signals inside the University.

In order to test the proposed detectors in more authentic scenarios, the 2.4 GHz ISM Band

was emulated using transmitters with the channel spacing and modulation schemes of

conventional WiFi and Zigbee transmitters.

Due to the limitations imposed by the USRP maximum sampling rate, the signals

bandwidths were scaled down. The scale factor was of 5 %, which means that a traditional 20

MHz WiFi signal (in the conventional ISM Band) will only occupy 1 MHz in the emulated band.

The WiFi transmitter is considered to work in the 1, 6 and 11 channels to avoid overlapping.

It uses an OFDM/BPSK modulation with a FFT size of 64 and a Cyclic Prefix of 16 samples at the

sampling frequency of 1 MHz (20 MHz).

In the case of the Zigbee signal, its occupied band will be 0.25 MHz (5 MHz). The Zigbee

transmitter was implemented in Matlab and the samples were stored into a file and used as a

File Source Block in the GNU Radio. The signal is OQPSK modulated with a chip rate value of

0.1 Mchip/s (2 Mchip/s in the conventional ISM band). The pulse shape filter employed was a

half sine filter.

7.3 Detector Implementation

The implemented energy detectors divide the emulated (real) ISM Band in three main sub-

bands with 1.25 MHz (25 MHz) of bandwidth. Each sub-band can be occupied by several

Zigbee transmitters but only one WLAN transmitter. In Figure 7.1 the 1.25 MHz (25 MHz) sub-

band structure is explained. For the WLAN channel, two colors were used to emphasize the

fact that the 802.11b/g DSSS and OFDM signals have different bandwidth. For the sake of

simplicity, without loss of generality, the tests were only made for one sub-band.

54

Figure 7.1: 1.25 MHz (25 MHz) Sub-band of the emulated ISM band

The proposed energy detector is implemented using a FFT block of size 1024. The FFT

frequency outputs magnitude is squared, averaged and, then, grouped into 'Êô = 25 different

channels so the final frequency resolution obtained is 50 kHz (1 MHz) – the same bandwidth of

a Bluetooth signal. For each channel, 2500 test statistics values were stored into a file using

the “File Sink” block from the GNU Radio Library. The flowgraph employed is the same for the

TED and AED and is displayed in Figure 7.2. A whitening filter was added in order to

compensate the non-flat frequency response caused by the filters employed in the ADC of the

USRP board. The frequency response of the received signal, whitening filter and resulting

image is shown in Figure 7.3.

Figure 7.2: Flowgraph of the implementation of the Energy Detector

Figure 7.3: Frequency response of the received signal, whitening filter and the resulting image

55

Unless told otherwise, the number of spectral averages for each channel wasMÅ = 1310,

so the total number of samples read was N = N�9MÅ = 32750 which is approximately the

same number of samples used for the cyclostationary detector in the last Chapter.

During the experimental study, it was considered the existence of noise uncertainty of 1 dB.

To test the sensitivity of the TED and AED to it, the test statistics stored into files were

multiplied by a factor inside the interval �ý , ø£ altering the noise and signal powers without

changing the SNR of the signal.

Two possible scenarios were considered during the experimental study: (i) one Zigbee

signal present; (ii) One WLAN signal present. For each scenario, for 12 different SNR values

whose range goes approximately from -25 to 0 dB, 2500 test statistics were stored into files

using the “File Sink” block from GNU Radio. The rest of the signal processing, such as

measuring the probabilities of detection and false alarm from those test statistics and the

resulting plots were made using Matlab.

7.4 First Scenario – One Zigbee Transmitter

In Figure 7.4, the spectrum of the received signal is shown for a SNR≈40 dB. In spite of each

Zigbee channel having 250 kHz (5 MHz) of Bandwidth, the signal itself only occupies

approximately 60% of it in order not to cause ICI to other channels. As a result, there are

approximately 22 FFT empty channels of the 'Êô = 25 available that can be used for

estimating the noise power and, consequently the threshold. The channel chosen to make the

detector’s performance analysis was the 10th since it is located near the center frequency of

the received signal.

Some spikes caused by IQ imbalance of the USRP board can be seen in the PSD of the

received signal, in Figure 7.4. These spikes might affect the probability of false alarm for the

channels where they are located.

56

Figure 7.4: PSD of a Zigbee signal with bandwidth scaled down by 95%.

In Figure 7.5, the cumulative function distribution (CDF) of the conventional and proposed

energy detectors, in the case of absence of a primary signal (1), is displayed. In the x axis,

instead of the real ED threshold value, it is shown the coefficient that was multiplied by the

noise power for each detector. The experimental CDFs obtained are almost identical to the

theoretical/simulated curves, represented by dash lines.

Figure 7.5: Conventional and proposed energy detector architectures’ empirical and theoretical CDFs under H0.

In Figure 7.6, due to the lack of a theoretical model for the probability of detection of the

AED, the empirical CDF under 1� is compared to a Matlab simulated curve for different SNRs.

Like the 1 case, the empirical CDFs are very close to the simulated curves.

57

Figure 7.6: Proposed energy detector’s empirical and simulated CDFs for different SNRs. The simulated results are

represented by a dash line.

In Figure 7.7, Figure 7.8 and Figure 7.9, the variation of the probability of detection with the

SNR for the traditional and proposed energy detectors under noise uncertainty is displayed. As

explained in Chapter 4, when in presence of uncertainty, the noise power value is inside the

intervalhL" ∈ �ýh�", øh�"£. Three different noise power scenarios were tested: (i) σ!" = σ�"; (ii)

σ!" = ρσ�"; (iii) σ!" = �: σ�". The SNR Wall, measured using (4.11), is displayed using a vertical

black dashed line. The theoretical curves for the TED and simulated curves for AED are also

displayed using a yellow and green dash line, respectively.

Figure 7.7 corresponds to the most common case (i), where the noise power is close to its

expected value. The AED shows much better performance than the TED, while maintaining a

probability of false alarm of 5 %.

For the conventional energy detector, according to (4.6), the probability of detection is

maximal for the case (ii), whereσ!" = ρσ�". In full accord with this analysis, in Figure 7.8, the

TED performance is also greater than in the cases (i) and (iii). The AED performance, however,

doesn’t show a significant variation due to its insensitivity to uncertainty in the noise power.

The maximum probability of false alarm of 5% was respected by both detectors.

Figure 7.9 corresponds to the worse possible scenario for the traditional detector where

the probability of detection is minimal. Once again, the AED performance doesn’t seem to be

dramatically affected by the noise uncertainty, keeping the probability of false alarm equal or

below 5 %. The theoretical model of the SNR Wall matches with the empirical results of the

TED since there is no detection for SNRs below it (the TED curve crosses the SNR Wall for

positive probability of detection between -3.8 dB and -3,3 dB due to the interpolation error).

58

For the three figures, the empirical probability of detection is a slightly lower than the

simulated for the AED. One possible cause for this anomaly is the high error value incurred in

the SNR estimate for low SNRs.

Figure 7.7: Empirical variation of the probability of detection with SNR for the traditional and proposed energy

detectors using Me=1310 as the number of spectral averages and σn2= σu

2.


detectors using Me=1310 as the number of spectral averages and σn2= ρσu

2 .

59


detectors using Me=1310 as the number of spectral averages and σn2= σu

2/ρ.

Figure 7.10 shows the variation of the probability of detection for each AED output channel

with the SNR of the 10th channel. The orange and blue colors represent the highest and lowest

probabilities of detection respectively. It is clear that the probability of false alarm maintains

its value of approximately 5 % (dark blue color) for the channels not affected by the primary

signal as the SNR increases. This means that the AED’s dynamic threshold successfully adapted

to the number of empty channels in the received signal. The 14th channel probability of false

alarm, as expected, was affected by the spike present in the PSD of the received signal (see

Figure 7.4) caused by IQ imbalance.

Figure 7.10: AED’s empirical probability of detection as a function of the SNR of the 10th

channel for each output

channel, using Me=1310 as the number of spectral averages and σn2= σu

2.

60

7.5 Second Scenario – One WLAN Transmitter

In Figure 7.11, the spectrum of the received signal is shown for a SNR=40 dB. There are

approximately 7 empty channels that the AED can use for estimating the noise power and,

consequently the threshold. The detector’s performance analysis was made for the 10th

channel.

Once again, some spikes caused by IQ imbalance of the USRP board can be seen in the PSD

of the received signal. These spikes will affect the probability of false alarm of the channels

where they are located and reduce the number of empty channels that can be used to

estimate the noise power to 4.

Figure 7.11: PSD of a WLAN/OFDM signal with bandwidth scaled down by 95%.

In Figure 7.12, the variation of the probability of detection with SNR for the AED and TED

when σ!" = ρσ�" is shown. The drop in performance of the AED relatively to the optimal TED is

clearer than in Figure 7.8 where there were more empty channels available to make the noise

power estimation. This shows that the proposed detector, in spite of more robust to noise

uncertainty, is also more sensitive to the sparcity of the received signal. The *2 vs SNR curves

for the cases σ!" = σ�" and σ!" = �:σ�" are shown in Appendix.

61


detectors using Me=1310 as the number of spectral averages and σn2= ρσu

2.

62

63

Chapter 8 OFDM CP based detection

implementation and measurements

8.1 Introduction

In this chapter, the main aspects of implementation and testing of the OFDM CP based

detection algorithms, in particular the sliding window scheme (CP-SW), described in Chapter 5

will be discussed. The empirical results will be displayed in the form of *2 vs SNR, *+, vs γ and *2 vs γ curves and compared with the simulated curves.

An analysis of the sensitivity of these detectors to the carrier frequency offset will also be

made to prove the analysis made in Chapter 5.


These detectors were tested in an indoor space with both the USRP2 transmitter and

receiver in line of sight. A center frequency and sampling frequency of 5.5 GHz and 1 MS/s

respectively were used for both boards.

The transmitter’s signal was an OFDM/BPSK modulated pseudorandom sequence of bits

with a bandwidth of 500 kHz in the baseband. A numerical amplifier was used to test the signal

detection for different SNR values. The OFDM FFT size was '2 = 64 with 52 subcarriers and

the guard interval was composed by '2 = 16 samples at 1 MS/s.

8.3 Detector Implementation and Testing

The flowgraph of the CP-based Sliding Window detector is displayed in Figure 8.1. Before

the averaging block used to calculate f�� from k��, a series to parallel block of size '2 +'Ì = 80 is employed. The number of averages made per f�� output is ï = 409 so, the

total number of samples read per test statistic is ' = ï<'2 +'Ì> + '2 = 32784.

Figure 8.1: Flowgraph of the implementation of the Energy Detector

For 12 different SNR values whose range goes approximately from -22 to -4 dB, 2500 test

statistics of the CP-SW detector were stored into files using the “File Sink” block from GNU

Radio. The rest of the signal processing, such as measuring the probabilities of detection and

false alarm from those test statistics were made using Matlab.

64

In order to make a fair comparison between this detector and the cyclostationary detectors

in Chapter 6, the same signal samples were utilized in the calculation of both test statistics.

This was possible by first storing the signal samples received by the USRP for each SNR value

into different data files and, then, by using these files as a “Source” block for the detectors in

GNU Radio.

8.4 Measurements

In Figure 8.2, the cumulative distribution function (CDF) of the CP-based sliding window

detection methods using the real (CP-SW(real)) and absolute (CP-SW(abs)) value of R[n], in the

case of absence of a primary signal (1), is displayed. The threshold represented in the x axis

was normalized by the threshold relative to *+,234 = 5% for each detector so the results would

be clearer and easier to compare. For a ï = 409, the experimental CDFs matches the

simulated curves.

Figure 8.2: CDF of the probability of false alarm of the CP-based SW detector.

In Figure 8.3, the variation of the CDF of the CP-SW(real) with the threshold for different

SNR values is shown. Once again, the x axis corresponds to the normalized threshold. For

SNR=-6.7 dB and SNR=-4.9 dB, the empirical probability of detection is lower than the

simulated one. One possible explanation for this was an error in the SNR estimation caused by

the usage of an outdated value for the noise power. In this plot, it can also be seen that the

empirical curves show higher variance than the simulated. This suggests the influence of other

not necessarily destructive factors such as multipath fading or the fact the noise isn’t exactly

white. The CDF for the probability of detection of the CP-SW(abs) is shown in the Appendix D.

65

Figure 8.3: CDF of the probability of detection of the CP- SW(real) detector.

In Figure 8.4, the empirical and simulated detection performance variation with SNR is

shown for the CP-based sliding window detectors CP-SW(real) and CP-SW(abs) using the real

and absolute value of R[n], respectively. As expected, the CP-SW(real) shows better results

than the absolute value when there is no frequency offset.

Figure 8.4: Variation of CP-SW performance with SNR.

In Figure 8.5, a comparison is made between the CP-SW and the cyclostationary detectors

analyzed in Chapter 6. The CP-SW is slightly better than the cyclostationary detector in cases of

inexistence of DC and frequency offset and when the noise level is perfectly known.

66

Figure 8.5: Empirical performance comparison between several OFDM detectors.

8.5 Sensitivity to Frequency Offset

Like in Chapter 6, in order to test the detectors’ sensitivity to different frequency offset (FO)

values, the transmitter’s amplitude was kept constant and 17 different central frequencies,

ranging from -17,5 kHz to 17,5 kHz in relation to 5,5 GHz, were used. For each FO, 2500 test

statistics were stored into a file using the “File Sink” block. Despite the constant gain of both

the transmitter and receiver, the SNR of the received signal can vary considerably over time.

For this reason, the test statistics were normalized to a SNR=-2 dB considering the SNR

measured during their extraction.

According to the theoretical analysis made in Chapter 5, the CP-SW using the real part of

R[n] is very sensitive to frequency offset. This is proved by the experimental results in Figure

8.6 for a SNR=-2 dB. For some frequency offsets, the threshold, represented by a dash line, is

even higher than the obtained test statistics which shows the need of this detector to use a

pre-synchronization block. The phase shift between the empirical and simulated curves is

caused by the difficulty associated with controlling the frequency offset of the USRP boards.

67

Figure 8.6: CP-SW sensitivity to frequency offset.

68

69

Chapter 9 Hybrid Detector Implementation

9.1 Introduction

Currently, cognitive radio research has mainly been focused on the ISM and TV bands,

which were made available for unlicensed use by FCC. To achieve coexistence and spectrum

sharing among different technologies in these bands, spectrum sensing is a critical preliminary

step.

The diversity of wireless technologies existent in these bands hampers the design of low

complexity detectors able to sense signals with different modulation schemes, bandwidths,

etc.

The TV Band is mainly occupied by digital TV signals which are OFDM modulated and

usually have a bandwidth of 6 or 8 MHz and wireless microphones which are FM modulated

with a max bandwidth of 200 kHz.

The industrial, scientific and medical (ISM) Band was originally reserved internationally for

the use of RF electromagnetic fields for industrial, scientific and medical purposes. However, in

recent years it is also shared with license-free technologies such as WLAN, Bluetooth, Zigbee,

Cordless Phones, etc. WLAN signals have a bandwidth of 20-22 MHz and are OFDM/DSSS

modulated. Bluetooth has a range of approximately 10 meters, 1 MHz of bandwidth and uses a

FHSS modulation scheme. These characteristics make it a technology that should be ignored by

detectors in the search for white spaces. The Zigbee is DSSS modulated with a bandwidth of 5

MHz approximately. In spite of Zigbee, WLAN and Bluetooth being the most commonly used,

there are countless other unlicensed error-tolerant technologies operating in this band.

In this chapter, a hybrid detector architecture, composed by a feature detector for

detecting OFDM signals and an adaptive-threshold energy detector for the remaining signals, is

suggested for its high performance and reasonably low complexity. The feature detector and

the adaptive-threshold energy detector blend perfectly since the first detects OFDM signals,

such as WLAN and DVB-T, which are wideband signals, while the second, whose performance

is greater when the signals’ bandwidth is lower (it requires the existence of sparsity in the

received signal), detects the remaining signals, such as Zigbee, Wireless Microphones and

Cordless Phones. Furthermore, since the feature detector has higher performance, priority is

being given to the detection of the WLAN and DVB-T signals whose range is usually higher and

are more commonly used.

9.2 TV Band Detector Implementation

The IEEE 802.22, the world-wide first CR standard, defined the sensing requirements for the

detection of digital TV signals, analog TV signals and wireless microphones (WM) [22].

However, due to the fact that analog TV is being switched off and replaced by digital TV in

70

most countries, this section will only focus on digital TV namely DVB-T and wireless

microphones.

The IEEE 802.22 originally stipulated the sensitivity requirements of -21 dB and -12 dB for

DTV and wireless microphones respectively for a probability of detection and false alarm of

90% and 10% respectively. Despite the second memorandum [23], that made this standard

turn its attention to geo-location methods for detecting white spaces, these requirements will

still be used to test the hybrid algorithm proposed.

The hybrid detector flowgraph is represented in Figure 9.1. The sampling rate at the input is

equal to the bandwidth of the TV channel analyzed (8 MHz for DVB-T in Europe). The decision

is based both in a feature detector, in this case a CP-based detector, and an adaptive threshold

energy detector. If the feature detector detects an OFDM signal, the whole TV channel is

considered occupied and the output of the energy detector is not taken into account.

Contrarily, in the case where no OFDM signal is detected, the energy detector is used to

identify the subchannels (of the whole TV channel) available for usage by the CR. The energy

detector can work in parallel with the feature detector to reduce the total time required for

detection or in series to reduce the power consumption since it only needs to be activated if

no digital TV signal was detected.

Figure 9.1: TV Band Hybrid detector flowgraph.

The feature detection algorithm chosen was the GLRT CP-based, described in section 5.3,

which showed greater performance, reliability and lower complexity, especially for short cyclic

prefixes (Rg=1/32), when compared to the cyclostationary detector. To reduce its sensitivity to

frequency offset, the alteration proposed in Section 5.6 which consisted in using R[n] instead

of its real part in the test statistic is used. In order to detect, in parallel, the 2k and 8k DVB-T

modes for each different cyclic prefix size, the GLRT architecture has to be replicated 8 times.

To fulfill the IEEE 802.22 requirements for the worst case scenario (Rg=1/32), a number of

samples around 3170048 have to be read, which takes approximately 396.3 ms. However, the

noise figure generated by the device hardware components might demand an increase of this

time interval. The GLRT CP-based performance is shown in Figure 9.2 and Figure 9.3 for the

71

OFDM and WM signals respectively. As expected the GLRT CP-based algorithm is incapable of

detecting any signal that is not OFDM-modulated.

The energy detector is designed to detect WMs and other types of narrowband

interference existent in the TV band. Since each WM signal occupies, at most, 2.5% of a DVB-T

channel, the more adequate energy detector algorithm would be the FCME for its better

performance for very sparse signals. However, its higher complexity imposes a major

challenge, making the AED a more attractive option. The number of channels ('Êô) and FFT

size chosen for the ED is 128, so each channel has a bandwidth of 62.5 kHz. The IEEE 802.22

sensitivity requirements for WM signals are quite low, so a decrease in detection time interval

when compared to OFDM detection is expected. According to simulations, the required

number of samples read is 288000 which takes approximately 36 ms. In Figure 9.3, it is

displayed the detection curve of the AED algorithm emphasizing the detection rate at SNR

equal to -12 dB.

Figure 9.2: CP-based GLRT’s probability of detection as a function of SNR for a DVB-T signal with Rg=1/32.

72

Figure 9.3: CP-based GLRT and AED’s probability of detection as a function of SNR for a WM signal.

9.3 ISM Band Detector Implementation

Due to the large number of technologies existent operating in the ISM Band, it is practically

impossible to create a sensing device made exclusively by feature detection algorithms. For

this reason, an architecture similar to the TV Band detector is proposed and displayed in Figure

9.4. Here the feature detectors are designed exclusively for the detection of WLAN signals

while the adaptive-threshold energy detector is used to detect the remaining signals.

Figure 9.4: ISM Band Hybrid detector flowgraph.

73

The 2.4 GHz ISM Band can be divided into three main sub-bands with 25 MHz of bandwidth

each. One of these sub-bands is represented in Figure 9.5. The WLAN signal occupies 20 MHz if

OFDM modulated and 22 MHz if DSSS modulated. Since DSSS signals can’t be detected by CP-

based methods, the alternative cyclostationary detector (ACD), described in Chapter 3, was

chosen to replace them. For OFDM detection, although, the CP-based GLRT method is simpler

and has better performance, the ACD is already incorporated in the device for the detection of

the 802.11b signal, so both options are satisfactory. The AED algorithm was chosen for

detecting the remaining signals because it’s simpler and its performance doesn’t vary as much

as the FCME with the sparsity of the received signal.

Figure 9.5: Bluetooth, Zigbee and WLAN channels in one of the three 25 MHz wide ISM sub-bands.

The ACD detector detects the DSSS WLAN signal cyclic frequencies at different lag

parameters in order to be able to detect different types of spreading codes. At P = 0, the cyclic

frequency with the greatest amplitude matches with the chip rate of the WLAN/DSSS standard,

that is, 11 MHz. Thus, a sampling rate of at least 22 MS/s is needed at the input of this

detector to be able to detect this peak.

The CP-based GLRT method must operate with a sampling rate equal to the bandwidth of

the OFDM signal. Taking this factor into consideration, a 4/5 decimation block was placed at its

input. A fractional decimation of 4/5 is accomplished using an interpolator with an

interpolation factor of 4 followed by a decimator of factor 5. In order not to increase the

sampling rate to 100 MS/s in the interpolator-decimator connection, which would drastically

increase the power consumption, a special architecture for this fractional decimator is

suggested in Figure 9.6. The FIR filter has a polyphasic structure composed by N taps where N

is a multiple of 4 and has a cutoff frequency equal to 10 MHz. To avoid the synchronization

step with the received OFDM signal, the altered GLRT method was used which is not only

based on the real part of the R[n].

The AED algorithm uncoherent nature makes it capable of operating at any sampling rate.

Restrictions are, however, imposed by the hardware components. The architecture of the AED

shown in Figure 9.4 was especially designed for the case where operating at 25 MS/s

represents a challenge for the available hardware components. The frequency shift and

decimator divides the 25 MHz ISM sub-band into 5 different 5 MHz bands that are, then,

74

processed sequentially by the AED. The disadvantage implied in this sampling rate reduction is

the increase of the required detection time by a factor of 5.

Figure 9.6: Fractional 4/5 decimator structure with FIR filter of N taps where N=4k, k=1,2,…

75

Chapter 10 Conclusions

In this dissertation, a theoretical and experimental analysis of some of the state-of-the-art

spectrum sensing algorithms was made. There was a special concern in testing these detectors

for signals with features similar to those from modern wireless communication technologies

such as Zigbee and WiFi.

Two versions of the CP-based Sliding Window detector were implemented and tested in

GNU Radio. Both have shown great theoretical and empirical performance results; however,

they have also shown a considerable sensitivity to noise uncertainty. Furthermore, they are

only able to detect OFDM modulated signals.

The time-domain Cyclostationary Detector is more complex than the CP-SW, however, it

can be used for different types of signals and belongs to the CFAR category, i.e., it doesn’t

require any a priori knowledge of the noise power to meet the required probability of false

alarm. It also doesn’t show any sensitivity to frequency offset. In this dissertation, an

alternative CD implementation was proposed that increases the flexibility and performance

and reduces the complexity of the traditional CD by switching the FFT block for IIR filters that

compute the DFT for a limited number of cyclic frequencies using the Goertzel Algorithm.

The fixed and the adaptive threshold energy detectors were tested for a WiFi-like and a

Zigbee-like signal. The theoretical models and limits, in particular the CDFs and the SNR Wall,

were proved by the experimental results for the fixed threshold ED. In the case of the

proposed adaptive threshold ED, the empirical results were also in accord with the theoretical

analysis and the simulations made in Matlab. It was shown that the AED sensitivity to noise

uncertainty is almost inexistent and that it has equal performance to other more complex

adaptive threshold algorithms such as the FCME. In addition to this, when there is no sparsity

in the received signal, the AED can still work properly, however, with a performance lower

than the TED.

Finally, a hybrid detector design composed by the different sensing schemes analyzed

throughout this thesis was proposed. The wideband signals such as DVB-T in the TV band and

WiFi in the ISM band are detected and identified by a CP-based or the ACD algorithm.

Narrowband signals, on the other hand, are detected by the adaptive threshold AED which can

estimate their bandwidth and center frequency and shows great performance when the

received signal is sparse in the frequency domain.

As future work, the impact of fading on these detectors’ performance could be more

extensively analyzed. Another suggestion would be to test other CP-based algorithms such as

the GLRT 2nd which, according to the literature, has better performance than the

cyclostationary detector and is also a CFAR detector. It would also be interesting to design an

OFDMA system in GNU Radio which would define the subcarriers available for allocation based

on spectrum sensing.

76

1

Appendix A ED number of samples required for

detection

For a large number of samples N, according to the central limit theorem,TWGH can be

approximated by a Gaussian distribution with average σ!" and P+σ!" and variance "úû)x and

"<;~úûÁ>x under H and H� respectively, i.e.,

TWGH|1~' \σ!" , 2σ!�' ] (A.1)

TWGH|1�~' \* + σ!" , 2$* + σ!"%"' ] (A.2)

and the *2 and *+, can be expressed as

*2 = *$TGH > γ|1�% = ^<=γ − $P + σ!"%

�2' $P + σ!"%>? (A.3)

*+, = *$TGH > γ|1% = ^<=γ − σ!"

�2'σ!">? (A.4)

Where Q(.) is the standard Gaussian complementary CDF. For the desired *2 and *+,, from

equations (A.2) and (A.3), the number of required samples can be taken using the equation

' = 2c^K�<*+,> − ^K�$*H%$1 + e'f%g"e'fK" (A.5)

In the case of existence of uncertainty of x dB, the estimated noise power varies between

σ!" ∈ Ýσ�" øÞ , øσ�"ß where ø = 10ê �⁄ > 1 and σ�" the center of the variation interval. In the

worst case, the *H and *+, will be:

*H = minúûÁ∈µúüÁ ýÞ ,ýúüÁ·^<=γ − $P + σ!"%

�2' $P + σ!"%>? = ^

<@@@=γ − þP + σ�" øÞ �

�2'_P + σ�" øÞ b>AAA?

(A.6)

*+, = maxúûÁ∈µúüÁ ýÞ ,ýúüÁ·^<=γ − σ!"

�2'σ!">? = ^

<=γ − øσ�"

�2' øσ!">? (A.7)

2

In the cases of low SNR, e'f + 1 ≈ 1 and the number of required samples to meet the *+,

and *2 requirements is

' = 2 µø^K�<*+,> − ^K�$*H% Y1ø + e'f[·" þe'f − Yø − 1ø[�K"

(A.8)

3

Appendix B AED threshold parameter deduction

� CDF deduction

Without loss of generality, considering a clean set Θ formed by ^ out of 'Êô channel

powers eW and considering that the remaining channels have an infinitely large SNR, the

probability of false alarm is,

*+, = * ¡eW > )�� SËWL BeW ≥ SËWL D ¸ ∈ Θ¢ (B.1)

Since SËWL < )�� SËWL for any threshold greater than one, the last equation becomes,

*+, = * ¡eW > )�� SËWL BeW ≥ SËWL D ¸ ∈ ΘWE=¢ ^ − 1^ (B.2)

where j is the channel position of SËWL and ΘWE= is the clean set without SËWL. The last

equation can be rewritten in the form,

*+, ^^ − 1 = *<eW > )�� SËWL ⋂ ¸ ∈ ΘWE=>*<eW ≥ SËWL ⋂ ¸ ∈ ΘWE=> (B.3)

For the sake of simplicity, two approximations will be made. 'Êô usually has a relatively

high value so eW distribution for ¸ ∈ ΘWE= isn’t considerably affected by the removal of SËWL

from the set ΘWE=. In addition to this, for high enough number of spectral averagesÉ3, both eW and SËWL, according to the central limit theorem, can be approximated by the normal

distributions:

eW~'\hL", hL�É3] , ¸ ∈ ΘWE= (B.4)

SËWL~'<aËWL� , G�kËWL� > (B.5)

where aËWLH and G�kËWLH

are the puSËWLw and ��kueËWLw for a number Q of unoccupied

channels, respectively. The numerator and denominator of the right side of equation (B.3)

have the following solutions,

* ¡eW > )�� SËWL D ¸ ∈ ΘWE=¢ = ��ó$�%$0% (B.6)

* ¡eW > SËWL D ¸ ∈ ΘWE=¢ = �Ió$�%$0% (B.7)

where �J$. % is the CDF function for the Gaussian random variable X, KW<^> = )�� SËWL − eW and LW<^> = SËWL − eW, with ¸ ∈ ΘWE=. Taking into account that KW<^> and LW<^> are linear

combinations of asymptotically normal distributions, their distributions can be approximated

by,

4

KW$^%~'\)�� aËWLH − hL", )�� "G�kËWL� + hL�É3] (B.8)

LW$^%~'\aËWL� − hL", G�kËWL� + hL�É3] (B.9)

Meeting the desired probability of false alarm *+,234, corresponds to using a )�� obtained

from the following equation:

: = ��ó$�%$0% = *+,234 ^^ − 1�Ió$�%$0% (B.10)

For ^ over 10, : can be approximated by:

: = *+,234 ^^ − 1�Ió$�%$0% ≈ *+,234 (B.11)

However, during the testing, this approximation will not be considered since it decreases

the probability of false alarm when the signal is less sparse (^ < 10).

� Smin mean and variance expressions

SËWL expected value and variance can be expressed through the following equations,

aËWL� = puSËWLw = ? …? minuSWw~�K� ì ��ó$eW%

�WM� Ae�…Ae�~�

K� (B.12)

G�kËWL� = ��kueËWLw = pu$SËWL − aËWL$^%%"w (B.13)

where ��E…�M<e�, … , e�> = ∏ ��ó$eW)�WM� is the joint PDF of the variables eW which are

considered independent. The CDF and PDF of SËWL, taking into account that SW mean value and

noise variance is the same for different channels, can be obtained from

��OóP$�) = 1 −ì*$eW > �%�WM� = 1 − $1 − ��$�%%� (B.14)

��OóP$�% = Q��OóP$l%Ql RêM, = ^��$�%$1 − ��$�%%�K� (B.15)

The expected value and variance then becomes,

puSËWLw = ? S^$1 − ��$S%%�K��$S%~� AS = pu^$1 − ��$e%%�K�ew (B.16)

��kueËWLw = pu^$1 − ��$e%%�K�$e" − puSËWLw"%w (B.17)

Using integration by parts,

5

aËWLH = puSËWLw = ? $1 − ��$S%%�~� AS (B.18)

G�kËWL� = ��kueËWLw = ? 2S$1 − ��$S%%�~� AS − puSËWLw" (B.19)

However, the last two equations don’t give any hint about the relation between aËWLH and G�kËWL�

with the noise power hL". For the AED to be insensitive to the noise level, it has still to

be proven that )�� is completely independent from hL".

� Proportionality of Smin to noise power

• TUVWXW = YZ[W\:

� With Chi-squared distributions:

aËWLH = puSËWLw = ? þ1 − �]Á�Á \2É3hL" S]��~� AS (B.20)

Changing the variable S for l = 2m^PÁ S,

aËWLH = puSËWLw = ? \1 − �]Á�Á $l%]� hL"2É3~� Al = ï�hL" (B.21)

where

ï�$^, É3% = 12É3? \1 − �]Á�Á $l%]�~� Al (B.22)

� With Normal distributions:

aËWLH = puSËWLw = ? þ1 − �� \S RhL", hL�É3]��~� AS (B.23)

Changing the variable t for x = _MÅ ÆKúûÁúûÁ ,

aËWLH = puSËWLw = ? <1 − ��$l|0, 1%>�~�K_m

hL"_É3 Al = ï�hL" (B.24)

where

ï�$^, É3% = 1_É3? <1 − ��$l|0, 1%>�~�K_m Al (B.25)

6

• àbUVWXW = Y\[Wc:

� With Chi-squared distributions:

��ËWLH = ��kueËWLw = ? 2Sþ1 − �]Á�Á \2É3hL" S]��~� AS − puSËWLw" (B.26)

Changing the variable S for l = 2m^PÁ S,

p±SËWL"² = ? hL"É3 l \1 − �]Á�Á $l%]� hL"2É3~� Al (B.27)

G�kËWLH = þ 12É3"? l \1 − �]Á�Á $l%]�~� Al − ï�"�hL� = ï"hL� (B.28)

where

ï"$^, É3) = 12É3"? l \1 − �]Á�Á $l%]�~� Al − ï�" (B.29)

� With Normal distributions:

G�kËWLH = ��kueËWLw = ? 2S þ1 − �� \S RhL", hL�É3 ]��~�

AS − puSËWLw" (B.30)

Changing the variable S for l = _É3 TK^PÁ^PÁ ,

p±SËWL"² = ? 2\ hL"_É3 l + hL"] <1 − ��$l | 0, 1%>�~�K_m

hL"_É3 Al

= d 2<l +_É3><1 − ��$l | 0, 1%>� ^P)m Al~�K_m

(B.31)

G�kËWLH = \ 1É3? 2<l +_É3><1 − ��$l | 0, 1%>�~�K_m Al − ï�"]hL�

= ï"hL� (B.32)

where

ï" = 2 1É3? l<1 − ��$l | 0, 1%>�~�K_m Al + 2ï� − ï�" (B.33)

� )�� expression

The �Ió$�%$0% only depends on ^ and É3 and can be solved as follows,

7

�Ió$�%$0|a, h"% = 12<@=1 + erf

<=− ï� − 1

�2¡ï" + 1É3¢>?

>A? (B.34)

where a = aËWL − hL" and h" = G�kËWLH + ^P)m. The ��ó$�% can then be rewritten as,

��ó$�%$0|a, h"% = *+,234 ^^ − 1�Ió$�%$0% = : (B.35)

where a = )�� aËWL − hL" and h" = )��"G�kËWLH + ^P)m. Solving it for )�� :

0 = ��$�%K� $:|a, h"% = a + h√2. erfK�$2: − 1% ⇔

⇔ )��" ¡<aËWLH >" − �"G�kËWLH ¢ − 2)�� aËWLH hL" + hL� \1 − �"É3] = 0

(B.36)

where � = √2. erfK�$2: − 1%. Since aËWLH = ï�hL" and G�kËWLH = ï"hL�, dividing the last

equation by hL�, it becomes

)��"$ï�" − �"ï"% − 2)�� ï� + \1 − �"É3] = 0 ⇔

⇔ )�� = ï� − �� 1É3 $ï�" − �"ï"% + ï"ï�" − �"ï"

(B.37)

8

9

Appendix C AED and TED performance for a

WLAN/OFDM modulated PU signal

Figure C.1: Empirical variation of the probability of detection with SNR for the traditional and proposed energy

detectors using fg = ZhZi as the number of spectral averages and jk\ = jl\

Figure C.2: Empirical variation of the probability of detection with SNR for the traditional and proposed energy

detectors using mn = ZhZi as the number of spectral averages and jk\ = Zo jl\

10

Figure C.3: Variation of the probability of detection for each output bin with the SNR of the 10th bin for the

proposed energy detector using fg = ZhZi as the number of spectral averages and jk\ = jl\.

11

Appendix D Additional CP-SW empirical and

simulated results

Figure D.1: CDF of the probability of detection of the CP- SW(abs) detector.

Figure D.2: CP-SW(real) sensitivity to a noise uncertainty of 1 dB.

12

13

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Spectrum Sensing Algorithms for Cognitive Radio Networks · Spectrum Sensing Algorithms for Cognitive Radio Networks Francisco de Castro Paisana Nº 63097 Dissertation Submitted for