master of science thesis - tut · preface i have written this master of science thesis for the...

TAMPERE UNIVERSITY OF TECHNOLOGY

Degree program in Information Technology

A.K.M.NAJMUL ISLAM

CNR ESTIMATION AND INDOOR CHANNEL MODELING OF GPS

SIGNALS

Master of Science Thesis

Examiners: Docent Elena-Simona Lohanand Prof. Markku RenforsExaminers and topic approved inthe council meeting of the Faculty ofComputing and Electrical Engineeringon the 16th Jan, 2008

Abstract

TAMPERE UNIVERSITY OF TECHNOLOGYDegree Program in Information Technology, Department of CommunicationsEngineeringISLAM, A.K.M.NAJMUL: CNR estimation and indoor channel modeling of GPSsignalsMaster of Science Thesis, 68 pages, 3 appendix pagesMarch, 2008Major: Communications EngineeringExaminers: Dr. Elena-Simona Lohan, Prof. Markku RenforsKeywords: Binary Offset Carrier, Binary Phase Shift Keying, Carrier to Noise Ratio,Global Positioning System, Galileo, Pseudolites, Satellites

In recent studies, accurate positioning of terminals has received much attention inwireless communications research. One reason is that of the requirement for emergencycall positioning imposed by the authorities. The positioning algorithms based on theGlobal Positioning System (GPS) have limitations in the indoor environments becausethe signal experiences severe attenuation in such situations.

Estimation of the Carrier to Noise Ratio (CNR) is one of the most important func-tionalities of the Global Navigation Satellite Systems (GNSSs) receivers. However, theconventional GPS receivers are not able to estimate the CNR accurately enough in mod-erate or severe indoor reception. In this thesis, several moment-based CNR estimatorsare derived and the author shows the results for both Binary Offset Carrier (BOC) andBinary Phase Shift Keying (BPSK) modulated signals. BOC modulation is to be used inmodernized GPS signals and for Galileo, the European navigation system, while BPSKis currently employed by basic GPS signals. The results of different estimators are com-pared in order to find the most robust estimator.

On the other hand, the indoor propagation characteristics of the GPS signals are re-quired to be well understood in order to derive good navigation algorithms suitable forindoor environments. In this thesis, the indoor propagation channel using pseudolites andsatellites are also analyzed, based on the measurement data collected in different scenar-ios.

i

Preface

I have written this Master of Science thesis for the Department of Communications Engi-neering, Tampere University of Technology, Finland. I have done the work for this thesisat the Department of Communications Engineering under the projects, Advanced Tech-niques for Personal Navigation (ATENA) and Future GNSS Applications and Techniques(FUGAT) funded by the Finnish Funding Agency for Technology and Innovation (Tekes)and some participating companies. I would like to express my gratitude to my thesis su-pervisors Dr. Elena Simona Lohan and Prof. Markku Renfors for their valuable guidanceand assistance during the thesis work. I would also like to thank Dr. Yuan Yang, DanaiSkournetou, and Hu Xuan for their friendly support during the work. Finally, I expressmy gratitude to my parents for their endless love and inspiration.

This endeavor is dedicated to my wife, Nasreen Azad.

Tampere, Finland.25th March, 2008

A.K.M. Najmul Islam

Insinoorinkatu 60 B 8633720 TAMPEREnajmul.islam(at)tut.fiTel. int. +358 50 934 2886

ii

Contents

Abstract i

Preface ii

List of Abbreviations vi

List of Symbols viii

1 Introduction 11.1 Motivation for the research topic . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Fading channel modeling overview 52.1 Multi-path channel parameters . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Time dispersion parameters . . . . . . . . . . . . . . . . . . . . 52.1.2 Coherence bandwidth . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Doppler shift and Doppler spread . . . . . . . . . . . . . . . . . 72.1.4 Coherence time . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Fading channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Rician fading channel . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Rayleigh fading channel . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Log-normal fading channel . . . . . . . . . . . . . . . . . . . . . 102.2.4 Loo fading channel . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.5 Nakagami fading channel . . . . . . . . . . . . . . . . . . . . . 11

3 Overview of GPS and Galileo systems 133.1 Basic GPS overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

iii

CONTENTS iv

3.2 Modernized GPS system overview . . . . . . . . . . . . . . . . . . . . . 153.3 Galileo system overview . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Measurement campaigns 184.1 Pseudolite based measurement campaign . . . . . . . . . . . . . . . . . . 18

4.1.1 Single pseudolite based measurement . . . . . . . . . . . . . . . 184.1.2 Multiple pseudolite based measurement . . . . . . . . . . . . . . 21

4.2 Satellite based measurement campaign . . . . . . . . . . . . . . . . . . . 24

5 Measurement data analysis 255.1 Acquisition of C/A code . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1.1 Search window . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.1.2 Search strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.1.3 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.2 Drift estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Navigation data bit estimation . . . . . . . . . . . . . . . . . . . . . . . 305.4 Coherent integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6 CNR Estimation 336.1 Signal model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.1.1 Coherent integration outputs . . . . . . . . . . . . . . . . . . . . 336.1.2 Non-coherent integration outputs . . . . . . . . . . . . . . . . . 356.1.3 PDFs and CDFs . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.2 Moment-based CNR estimators . . . . . . . . . . . . . . . . . . . . . . . 376.2.1 First-order moments (1STO) . . . . . . . . . . . . . . . . . . . . 386.2.2 Second-order moments, method 1 (2NDO-M1) . . . . . . . . . . 386.2.3 Second-order moments, method 2 (2NDO-M2) . . . . . . . . . . 396.2.4 Combined second (central) and first (non-central) order moments

(2NDO-1STO-M1) . . . . . . . . . . . . . . . . . . . . . . . . . 396.2.5 Combined second (non-central) and first (central) order moments

(2NDO-1STO-M2) . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.6 Combined fourth and second order moment (4THO-2NDO) . . . 406.2.7 Combined fourth and first order moments (4THO-1STO) . . . . . 41

6.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.3.1 Results for single path channel . . . . . . . . . . . . . . . . . . . 426.3.2 Results for multi-path channel . . . . . . . . . . . . . . . . . . . 446.3.3 Envelope vs. squared envelope as nonlinearity . . . . . . . . . . 46

CONTENTS v

6.4 CNR mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.5 CNR estimators results with measurement data . . . . . . . . . . . . . . 486.6 CNR estimation results for 4THO-1STO using different navigation bit

estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.7 Computational complexity of the estimators . . . . . . . . . . . . . . . . 49

7 Channel models based on measurement data 567.1 Proposed combined fading channel models . . . . . . . . . . . . . . . . 567.2 Fading distribution matching . . . . . . . . . . . . . . . . . . . . . . . . 57

7.2.1 Pseudolite results . . . . . . . . . . . . . . . . . . . . . . . . . . 577.2.2 Satellite results . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7.3 Average path number and time dispersion parameters . . . . . . . . . . . 627.3.1 Pseudolite results . . . . . . . . . . . . . . . . . . . . . . . . . . 627.3.2 Satellite results . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

7.4 Comparison between pseudolites and satellite results . . . . . . . . . . . 66

8 Conclusions and Future Works 678.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

References 69

Appendix A: Phase variation and Delay error estimation 74

List of Abbreviations

ATENA Advanced Techniques for Personal Navigation

AWGN Additive White Gaussian Noise

BOC Binary Offset Carrier

BPSK Binary Phase Shift Keying

C/A Coarse/Acquisition code of GPS

CDF Cumulative Distribution Function

CIR Channel Impulse Response

CNR Carrier-to-Noise Ratio

DS-SS Direct sequence Spread Spectrum

E2-L1-E1 Frequency band centered in 1575.42 MHz

ESA European Space Agency

FFT Fast Fourier Transform

FUGAT Future GNSS Applications and Techniques

GNSS Global Navigation Satellite System

GPS Global Positioning System

I In-Phase

vi

LIST OF ABBREVIATIONS vii

IF Intermediate Frequency

LOS Line of Sight

MBOC Multiplexed Binary Offset Carrier

MSE Mean Square Error

NLOS Non Line of Sight

OS Open Service

PL Pseudolite

PRN Pseudo Random Number

PDF Probability Distribution Function

Q Quadrature

RHCP Right Hand Circular Polarization

RMS Root-Mean-Square

RMSE Root-Mean-Square Error

RF Radio Frequency

SNR Signal-to-Noise Ratio

TUT Tampere University of Technology

List of Symbols

A Envelope of the LOS delay

α Complex channel coefficient

Bw Bandwidth

c Speed of Light

∆ fD Doppler Error

∆τ Delay Error

∆θ Phase difference of two consecutive millisecond outputs

E(·) Statistic average

Eb Signal Power

Eb Signal Power in a correct bin

fc Carrier frequency

fD Maximum Doppler shift

fds Doppler spread

fCombined−M1() Combined distribution method-1



viii

List of Symbols ix

fLogn() Lognormal distribution

fLoo() Loo distribution

fNaka() Nakagami distribution

fRayl() Rayleigh distribution

fRice() Rician distribution

KRice Rician factor

I0 Modified 0th order Bessel function

n Degree of freedom of chi-square distributed variable

m Nakagami factor

µ Mean

Nc Coherent Integration length

Nnc Non-coherent Integration length

N0 Noise Power

N () Normal Distribution

RBOC BOC/BPSK autocorrelation function

σ2 Variance

CorridorSAT Satellite data captured in office corridor

RoomSAT Satellite data captured in office room

List of Symbols x

MultiplePL Data captured with multiple pseudolites

SinglePL Data captured with single pseudolite

θn Phase of nth millisecond output

Tcoh Coherence Time

Tms Integration time in ms

vm Maximum Doppler velocity

vs Doppler velocity of satellite

w Signal level

xQ,o Imaginary part of correlation out-of-peak

xI,o Real part of correlation out-of-peak

xI,p Real part of correlation peak

xQ,p Imaginary part of correlation peak

yI,p Real part of correlation peak after Nc ms

yQ,p Imaginary part of correlation peak after Nc ms

yI,o Real part of correlation out-of-peak after Nc ms

yQ,o Imaginary part of correlation out-of-peak after Nc ms

zo Correlation out-of-peak after Nnc ms

zp Correlation peak after Nnc ms

χ2() Chi-square distribution

Chapter 1

Introduction

This chapter gives an introduction to the thesis, beginning with the motivation to investi-gate the particular research topic. This is followed by a discussion of the research objec-tives and, finally, the thesis outline.

1.1 Motivation for the research topic

The satellite-based navigation was started in the early 1970s. After some small-scalesystem studies, the GPS program was approved in December 1973. Since its launch,GPS has emerged as the most dominant technology for providing precise location andnavigation capability to the end users. But GPS cannot provide adequate accuracy insome environments, such as indoor and densely populated urban areas. As a result, thereis a clear requirement for developing a new navigation system that will overcome thelimitations of the GPS and will be compatible with the GPS. The European navigationsystem, Galileo is planned to meet the overall requirements. Galileo is expected to operateby 2010 [15]. Galileo is an initiative of the European Commission and the EuropeanSpace Agency (ESA). The new satellites are not yet in the orbit but the signal propertiesare already standardized in a first phase so that we can start to analyze the characteristicsof these signals.

Most of the applications of GPS are considered as outdoor applications but nowadays,the indoor personal navigation applications are getting popularity. In such situations, thetypical GPS receivers suffer degraded performance or sometimes even complete failurebecause the signal experiences severe attenuation in the indoor environments. One ofthe most important personal positioning applications is the emergency call positioning inthe cellular network, imposed by the authorities. The accuracy is very critical for suchapplications. Galileo is planned to increase the accuracy level for such applications. Still

1

Introduction 2

the characteristics of the indoor propagation need to be well understood to be able todevelop the solution for the indoor positioning problem.

In the outdoors, there are combinations of Line-Of-Sight (LOS) and Non Line-Of-Sight (NLOS) signals available, whereas in the indoors there is NLOS propagation only.Most of the time, there is no LOS signals available in the indoors due to the variousobstructions. For the purpose of deriving indoor navigation algorithms, the satellite-to-indoor propagation and its fading statistics have great importance. There are severalstudies that attempted to develop channel models for GPS-indoor channel. In [35] theauthors used a strong reference outdoor signal to augment indoor processing capabilitiesand conduct coherent integrations of up to 160 ms. The existence of deep fades and theirimpact on indoor signals were observed. In [48] the author analyzed high bandwidthraw GPS data with high sensitivity techniques to characterize fading and the multi-pathindoor characteristics. In [27], the authors showed that the GPS-indoor channel fadingamplitudes of the first arriving peak matches well with the Nakagami-m fading model.In [26, 28], satellite-to-indoor propagation channel characteristics have been analyzed. Itwas shown that that the indoor signal is expected to be very weak and embedded in noise.Thus, long coherent and non-coherent integrations are required.

Pseudolites (PLs), placed on earth surface, especially indoors, are a relatively newtechnology with great potential for a wide range of positioning and navigation applica-tions. They can be used either as augmentation of space-based positioning systems or asindependent systems for indoor positioning and capable of showing better performance[36, 47]. That is why, the PL-to-indoor propagation and its fading statistics have alsogreat importance.

The receivers should have the capability to estimate the Carrier to Noise Ratio (CNR)as accurately as possible. In the indoors the signal power remains very low, which affectsthe delay estimation accuracy, and, thus, the position accuracy. As a result, the conven-tional GPS receivers are not able to estimate the CNR accurately for the location servicesin moderate indoor reception. Although the topic of CNR estimation in the GPS receiversis addressed in the literature [22, 33, 38], not much of the published analysis is basedon the correlation of the incoming signal. Also few moment-based CNR estimators arefound in literature, but these estimators have not been developed based on the correlationfunction of the BPSK/BOC modulated signals [40]. Furthermore, the author is not awareof extensive comparisons between different CNR estimation methods.

Introduction 3

1.2 Objective of the thesis

As a part of the Advanced Techniques for Personal Navigation (ATENA) and FutureGNSS Applications and Techniques (FUGAT) projects, the objective of this thesis hasbeen to analyze the different measurement data captured from different satellites andpseudolites in different indoor scenarios. The purpose has been to estimate the CNRaccurately and derive a suitable channel model. The ATENA and FUGAT projects areresearch projects carried out at Tampere University of Technology (TUT) in cooperationwith some industrial partners during the years 2005-2008. The overall objectives of theATENA and FUGAT projects are very wide scale and thus this thesis only covers a verysmall part of that.

1.3 Thesis contributions

The novel contributions of the thesis are given below:

• A study on different navigation data bit estimation methods for GPS signals.

• Derivation of three moment-based CNR estimators based on the correlation of theincoming signal. A comparison of these estimators has been performed includingfour other estimators derived in similar way. A procedure has also been proposedfor choosing the required noise samples for estimating the CNR accurately.

• Combined fading channel models have been proposed for matching with the mea-surement data.

1.4 Thesis outline

This thesis consists eight chapters. The structure of the thesis is given below.Chapter 1 has introduced the motivation, related previous studies and the overall

objective of the research.Chapter 2 discusses the currently available fading channel modeling techniques which

are used in the communication systems.Chapter 3 introduces the GPS and Galileo systems to the readers from the point of

view of signal characteristics.Chapter 4 discusses the measurement setups for the different indoor measurement

campaigns for GPS based pseudolites and satellites.

Introduction 4

Chapter 5 is dedicated to the measurement data analysis. In the navigation dataestimation part of the thesis, different methods are studied.

Chapter 6 describes a signal model and the derived moment-based CNR estimatorsbased on the correlation of the incoming signal. The performance of each estimator istested for simulation based BOC modulated signal and measurement based BPSK mod-ulated signal. The results for different estimators are compared in order to find the mostrobust estimator. A comparative analysis of the navigation data estimation methods de-scribed in Chapter 5 is presented in this chapter too.

Chapter 7 presents proposed theoretical fading channel models along with the chan-nel model based on the raw data to the readers.

Chapter 8 finally presents the conclusions of the overall research.

Chapter 2

Fading channel modeling overview

Fading is the term used to describe the fluctuations in the envelope of a transmitted radiosignal. Fading is a common phenomenon in wireless communication channels causedby the superposition of two or more versions of the transmitted signals which arrive atthe receiver at slightly different times. The resultant received signal can vary widelyin amplitude and phase, depending on various factors such as the relative propagationtime of the waves and bandwidth of the transmitted signal [3, 16]. This chapter startsby discussing the multi-path channel parameters. Then it discusses the currently avail-able fading channel modeling techniques commonly used in the communication sys-tems. The most commonly known statistical representations of fading are: Rayleigh [48],Rice [24, 48], Nakagami-m [27, 49], Log Normal [48], and Loo [31] distributions. Fi-nally, it presents the combined fading channel models by combining two or more models.

2.1 Multi-path channel parameters

2.1.1 Time dispersion parameters

In order to compare different multi-path channels, time dispersion parameters such as theMean excess delay, τ and Root Mean Square (RMS) delay spread, στ are used. Themean excess delay is the first moment of the power delay profile and it can be given by[39]:

τ =∑k

P(τk)τk

∑k

P(τk)(2.1)

where P(τk) is the relative amplitude of the multi-path component at kth delay (τ).

5

Fading channel modeling overview 6

The RMS delay spread is the square root of the second central moment of the powerdelay profile and is given by [39]:

στ =√

τ2− (τ)2 (2.2)

where

τ2 =∑k

P(τk)τ2k

∑k

P(τk)(2.3)

2.1.2 Coherence bandwidth

Coherence bandwidth, Bcoh is the maximum transmission bandwidth over which thechannel can be assumed to be approximately constant in frequency. That is, a signalhaving frequencies within a bandwidth Bcoh will be affected approximately similarly bythe channel. The RMS delay spread and coherence bandwidth are inversely proportionalto each other. If the coherence bandwidth is defined as the bandwidth over which thefrequency correlation function is above 0.9, then the coherence bandwidth is given by[29]:

Bcoh ≈1

50στ(2.4)

If the frequency correlation function is above 0.5, then the coherence bandwidth isgiven by [39]:

Bcoh ≈1

5στ(2.5)


2.1.3 Doppler shift and Doppler spread

The movement of the satellites introduces frequency shifts on the carrier and the code ofthe received signal. This phenomenon is known as the Doppler effect. The maximumDoppler shift, fD can be given by [45]:

fD =vs fc

c(2.6)

where vs is the speed of the satellite, fc is the carrier frequency and c is the speed oflight.

The Doppler spread, fds is defined as the range of frequencies over which the re-ceived Doppler spectrum is essentially non-zero. An example Doppler spectrum is givenin Figure 2.1 based on Jake’s model. The maximum Doppler shift used in this figure is 10Hz.

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency shift from the carrier [Hz]

Nor

mal

ized

Dop

pler

pow

er s

pect

ral d

ensi

ty

Doppler power spectrum

Figure 2.1: Example of Doppler spectrum

2.1.4 Coherence time

Coherence time, Tcoh is the maximum difference in time such that two states of the chan-nel, measured less than Tcoh seconds apart, are still correlated at some extent. The Dopplerspread and coherence time are inversely proportional to each other. A popular rule ofthumb for digital communications is to define the coherence time by [39]:

Tcoh =0.423

fD(2.7)

where fD is the maximum Doppler shift.


2.2 Fading channel models

The general term, fading is used to describe the fluctuations in the envelope of a receivedradio signal. However, when speaking of such fluctuations, it is of interest to considerwhether the observation has been made over short distances or long distances. For awireless channel, the former case will show rapid fluctuations in the signal’s envelope,while the latter will give a more slowly varying, averaged view. For this reason, the firstscenario is formally called small-scale or multipath fading, while the second scenariois referred to as large-scale fading [5]. Small-scale fading is explained by the fact thatthe instantaneous received signal strength is a sum of many contributions coming fromdifferent directions due to many reflections of the transmitted signal reaching the receiver[3]. Large-scale fading is due to shadowing. Rayleigh and Rician models are the commonsmall-scale fading models. The Nakagami distribution also falls in this class. Log-normalcan be used for large-scale fading. Loo model combines both small-scale fading andlarge-scale fading. A brief overview of the fading channel models is presented in thefollowing sub-sections.

2.2.1 Rician fading channel

The Rician distribution models the channel in the situation when there is strong LOSsignal with the presence of some weaker, randomly-distributed multipath components.The envelope of a signal undergoing Rician fading can be expressed by [24, 37]:

fRice(w) =w

σ2Rice

exp(− (w2 +µ2

Rice)2σ2

Rice

)I0

(wµRice

σ2Rice

)(2.8)

where fRice(w) is the probability of the signal amplitude level w, σ2Rice is the variance (can

be given by σ2Rice = (var(I)+ var(Q))/2, where I and Q are the in-phase and quadrature

components of LOS coefficient), µRice =√

mean(I)2 +mean(Q)2, and I0(x) is the modi-fied 0th order Bessel function and can be given by [9]:

I0(x) =∞

∑m=0

(−1)m

m!(m+1)

(ix2

)2m

(2.9)

where i is the imaginary unit.The Rician factor KRice (i.e., the ratio of LOS to multi-path power) is given by KRice =

µ2Rice

2σ2Rice

[37]. Example of Rician distributions is given in Figure 2.2.


0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Rician PDF with σRice

= 1

µRice

=0

µRice

=1

µRice

=2

µRice

=4

Figure 2.2: Example of Rician distributions for different µRice

2.2.2 Rayleigh fading channel

Rayleigh represents the worst case fading case and it can be considered as special caseof Rician distribution when no LOS component is present. The envelope of a signalundergoing Rayleigh fading can be expressed by [37, 48]:

fRayl(w) =w

σ2Rayl

exp(− w2

2σ2Rayl

)(2.10)

where σ2Rayl is given by σ2

Rayl =√

2πmean(

√I2 +Q2) [37]. An example of Rayleigh

distributions is given in Figure 2.3.

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

1.2

1.4Rayleigh PDF

σRayl

=0.5

σRayl

=1.0

σRayl

=1.5

σRayl

=2.0

Figure 2.3: Example of Rayleigh distributions for different σRayl


2.2.3 Log-normal fading channel

Signals that propagate through some attenuating medium have a log-normal power distri-bution [13]. If z is the signal amplitude, the lognormal distribution can be expressed by[48]:

fLogn(w) =1

w√

2πσLognexp

(− (log10 (w)−µLogn)2

2σ2Logn

)(2.11)

where σLogn represents the standard deviation of log10(A) and µLogn represents the meanof log10(A), where A =

√I2 +Q2 is the envelope corresponding to LOS delay. The pa-

rameters σLogn and µLogn depend on the medium of propagation and possibly on the mo-tion of transmitter and receiver. An example of Log-normal distributions with variousσlogn is given in Figure 2.4.

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Log−normal PDF with µlogn

= 1

σlogn

=0.5

σlogn

=1

σlogn

=1.5

σlogn

=2.0

Figure 2.4: Example of Log-normal distributions for different σlogn

2.2.4 Loo fading channel

Loo [31] has developed a statistical distribution assuming that the fading of the shadowedLOS signal is log-normally distributed and the multi-path signals’ fading is Rayleighdistributed. Loo’s distribution model can be expressed by [24, 48]:

fLoo(w) =

(∫ ∞

0

1x

exp(− (log10 (x)−µLogn)2

2σ2Logn

− (x2+w2)2σ2

Loo

)I0

(xz

σ2Loo

)dx

)(w

σ2Loo

√2πσLogn

)(2.12)


where σLogn = std(log10(A)) and µLogn = mean(log10(A)) represent the standard devi-ation and mean of the logarithm of the measured envelope A, respectively, and σLoo =std(A), µLoo = mean(A) are the standard deviation and mean of the measured envelope,respectively. An example of Loo distributions with various σLoo is given in Figure 2.5.

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2

0.25Loo PDF

σLoo

=0.5

σLoo

=1

σLoo

=1.5

σLoo

=2.0

Figure 2.5: Example of Loo distributions for different σLoo

2.2.5 Nakagami fading channel

Three types of Nakagami distributions are found in the literature namely Nakagami-q,Nakagami-n and Nakagami-m distributions. The Nakagami-q distribution is also knownas Hoyt distribution. It can span from one-sided Gaussian fading (q=0) to Rayleigh fading(q=1). The Nakagami-n distribution is also known as the Rician distribution. The Ricianfactor of the Rician distribution and the parameter, n of the Nakagami-n distribution arerelated by KRice = n2. The Nakagami-n distribution spans the range from Rayleigh fading(n = 0) to no fading (n = ∞) [42]. Nakagami-m distribution is a generic model of fadestatistics that is used in the study of mobile radio communications [7, 32]. A wide classof fading channel conditions can be modeled with Nakagami-m distribution [32]. Thisfading distribution has gained a lot of attention lately, since the Nakagami-m distributionoften gives the best fit to land-mobile [2, 41, 43] and indoor mobile multi-path propagationas well as scintillating ionospheric radio links [42].

The PDF of a Nakagami-m fading amplitude can be expressed by [25, 49]:

fNaka(w) =2

Γ(w)

(m

µNaka

)m

w2m−1 exp(− mw2

µNaka

), (2.13)


where µNaka = mean(|α|2) = mean(A2) is the mean of the envelope power (α is the com-plex channel coefficient), m is the Nakagami-m factor and Γ(.) is the Gamma function.The following estimate of m factor can be used (i.e., m is equal to the inverse of thenormalized variance of the squared envelope) [25, 37]:

m =µ2

Nakamean(A2−mean(A2))2 (2.14)

For m = 1, Nakagami-m is equivalent to Rayleigh distribution [32]. Nakagami-m dis-tribution can closely approximate the Nakagami-q distribution by a one-to-one mappingbetween m parameter and the q parameter. The mapping is given by [42]:

m =(1+q2)2

2(1+2q4)2 (2.15)

Another one-to-one mapping can be found between the m parameter and the n pa-rameter allowing the Nakagami-m distribution to closely approximate the Nakagami-ndistribution. The mapping is given by [42]:

m =(1+n2)2

1+2n2 (2.16)

An example of Nakagami-m distribution with various m and µNaka values is given inFigure 2.6.

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

1.2

1.4Nakagami PDF

m=1,µNaka

=1

m=1.0,µNaka

=2

m=2,µNaka

=3

m=3,µNaka

=1

Figure 2.6: Example Nakagami distribution for different m and µNaka values

Chapter 3

Overview of GPS and Galileo systems

This chapter presents the concepts of GPS and Galileo systems. It first starts with thebasic position measurement concepts that have been used in the GPS. Then, it describesthe modernized GPS system, and finally, the new European navigation system, Galileothat is planned to be launched within few years.

3.1 Basic GPS overview

The GPS system is based on the time-of-arrival measurements. The distance between asatellite and a receiver is calculated from the knowledge of how much time it takes forthe signal from the satellite to get to the receiver [8]. The signal from the satellite tothe receiver travels at the speed of light. If we know the travel time of the signal fromthe satellite to the receiver, we can easily calculate the distance. Figure 3.1 demonstratesthe distance based positioning in two-dimensional case. In order to determine the receiverposition, three distances from three satellites are required. Two satellites give two possiblesolutions because two circles intersect at two points. Hence, a third satellite is needed todetermine the receiver position uniquely. For similar reason, to calculate the position inthe three-dimensional plane, four satellites and four distances are required.

In the above discussion, it is assumed that the distance measured from the satellite tothe receiver is very accurate and does not contain any bias error. But actually the measureddistance has an unknown bias error because the receiver clock and the GPS clock are notfully synchronized. In order to resolve this bias error, one more satellite is required andthus in order to find the accurate position five satellites are needed [45]. However, thegeneral statement is that four satellites can be used to find the receiver position, eventhough the measured distance has a bias error [45].

Although, it is enough to know four distances in the process of getting an accurate

13

Overview of GPS and Galileo systems 14

Receiver

Satellite 1 Satellite 2

Satellite 3

Figure 3.1: Two-dimensional user position.

positioning result, it is not enough to have four random satellites flying in the sky. Thesatellites must also know their positions. A global network of ground stations is neededto give the position data to the satellites. In general, the GPS system can be considered ascomprising three segments: the space segment, the control segment and the user segment.The space segment contains all the satellites. The basic GPS system has a total of 24satellites divided into six orbits. Each orbit has four satellites and has an inclination angleof 55-degree. The orbits are separated by 60 degrees and each orbit has a radius of 26,560km. The control segment consists of five control stations. The purpose of this segment isto monitor the performance of the GPS satellites, generate and upload the navigation datato the satellites. The user segment consists of the GPS receivers and the user community.

There are two main signals: the coarse/acquisition (C/A) and the precision (P) codes.The P code is modified by Y code, which is refereed as P(Y) code. P(Y) is used formilitary purpose and it is not available for civilian users. The basic GPS signal containstwo carrier frequencies: L1 and L2. The center frequency of L1 is at 1575.42 MHz and L2is at 1227.6 MHz. L1 frequency contains C/A and P(Y) signals and L2 frequency containsonly the P(Y) signal. This thesis focuses mostly on the civilian C/A signal. The C/A codeis BPSK modulated with a chip rate of 1.023 MHz while the chip rate of P(Y) signalis 10.23 MHz. The navigation message, which contains information about the satellites,


GPS time, clock behavior and system status is modulated on both the L1 and L2 carriersat a chip rate of 50 bits per second (bps) with a bit duration of 20 ms.

3.2 Modernized GPS system overview

The only navigation system that can be used worldwide is the GPS system. GPS is mil-itary operated, but it is used for many commercial and civilian services nowadays. Itshows very poor performance for the indoor location based services too. As a result GPSdoes not offer enough accuracy or warranty of service and it cannot be used in many vitalpositioning applications. The GPS system has been upgraded to meet the requirements,but still its functionality cannot be trusted in many scenarios. The modernized GPS fre-quency plan is shown in Figure 3.2. The modernized GPS includes a new frequency bandL5 (1176.45 MHz) that provides a wide-band signal. In addition, the new L2C signalwill provide the civilian community a more robust signal that is capable of improvingresistance to interference and allowing longer integration times to the receivers. A newmilitary M-code will also be added to L1 and L2 bands, but will be spectrally separatedfrom the civil codes. It has been decided that the new modulation type for the new Msignal will be Binary Offset Carrier (BOC) modulation.

Figure 3.2: The modernized GPS frequency plan [14].


3.3 Galileo system overview

The European navigation system, Galileo is planned to achieve European sovereignty andservice guarantees through dedicated system under civil control [15]. The overall Galileosystem consists of 30 satellites (27 operational+3 active spares), positioned in three cir-cular Medium Earth Orbit (MEO) planes at 23,222 km altitude above the Earth, and at aninclination angle of the orbital planes of 56 degrees [5]. The services that will be providedby the Galileo are: Open Service (OS), Safety of Life Service (SoL), Commercial Ser-vice (CS), Public Regulated Service (PRS) and Search and Rescue Service (SAR). Thereliability of the Galileo services is higher than that of the GPS [44]. Galileo is meant toprovide better navigation accuracy due to its signal properties. The BOC modulation isplanned to be used in the Galileo signals [5].

The frequency plan for the Galileo system is shown in the Figure 3.3 which consists offour frequency bands: E5a, E5b, E6 and E2-L1-E1. The E2-L1-E1 band with the centerfrequency 1575.42 MHz is the most interesting band as the current GPS signal (C/A) isin it. This thesis mostly focuses on this frequency band. The readers who are interestedin other frequency bands are referred to [17]. Both the GPS C/A code and Galileo OSsignals are transmitted in the same frequency band. But still the signals do not interferesignificantly with each other since different modulation is used. The most important char-acteristics of the Galileo signals, in comparison with the GPS signals, are the differentmodulation types and code lengths. SinBOC(1,1) (briefly denoted as SinBOC) has beenthe candidate modulation type for the Galileo OS signal in the E2-L1-E1 band for manyyears. The code length for the OS signal is 4092 chips, which is four times higher thanthe GPS C/A code length. Recently the GPS-Galileo working group on interpretabil-ity and compatibility has recommended an optimized Multiplexed Binary Offset Carrier(MBOC) spreading modulation that would be used by Galileo for its OS service and alsoby GPS for its L1C signal [18]. However, this thesis presents the simulation results forthe SinBOC(1,1) only. For the technical details of the BOC modulation, the readers arereferred to [18],[4] and [5].


Figure 3.3: Galileo frequency plan [46].

The use of GPS and Galileo at the same time is very interesting. The accuracy canbe increased a lot by using the two systems together. The indoor reception might beimproved in this way to provide the location based services to the users.

Chapter 4

Measurement campaigns

This chapter presents the measurement campaign descriptions to the readers. It first startswith the pseudolite (PL) based measurement campaign where single PL-based and mul-tiple PL-based measurement campaign descriptions are discussed. Then it discusses thesatellite-based measurement campaign. These measurements were captured with the helpof Space Systems Finland (SSF) and u-Nav Microelectronics.

4.1 Pseudolite based measurement campaign

Using PLs, two types of measurement campaigns were undertaken: single PL-based andmultiple PL-based. These measurement setup descriptions are given in the followingsubsections. In these measurements, PRN indexes higher or equal to 32 were used, whichare mostly reserved for non-satellite use. The sampling frequency of the GPS receiver was16.36 MHz. The L1 carrier in the data was down-converted to an intermediate frequency(IF) of 41552 Hz.

4.1.1 Single pseudolite based measurement

The measurements were first carried out in the Tamppi arena building, then in the Festiabuilding of TUT, Finland during June, 2005. Two synchronized GPS receivers were used.One receiver was used as reference receiver and was connected to the PL via cable. Theother receiver was connected to an indoor antenna measuring the signal coming from theair. The transmit antenna was placed in a fixed position at the first floor, with an elevationof around 7 meters with respect to the receiver. The radiation patterns of the helix an-tenna (transmit antenna) used in the measurements was Right Hand Circular Polarization(RHCP), where the main beam was within ±30/35 from the antenna pointing direction.

18

Measurement campaigns 19

Attenuation in PL software was 20 dB.The measurement process was carried out in 5 sets:

• SET −1: It was captured in the Tamppi arena sports hall. The receiver was movedfrom inside the main beam to the outside. The photo of the environment is shownin Figure 4.1 and the schematic representation of the measurement set is shown inFigure 4.2.

Figure 4.1: Photo taken in the Tamppi arena sports Hall from the transmitter position.

• SET − 2: It was also captured in the Tamppi Arena sports hall. But this time thereceiver was moved inside the main beam only. The schematic representation of themeasurement set is shown in Figure 4.2.

• SET − 3: It was the last set that was captured in the Tamppi Arena sports hall.The receiver was moved outside of the main beam. The antenna pointing directionwas parallel to the direction of the movement. The schematic representation of themeasurement set is shown in Figure 4.3.

• SET − 4: It was captured in the Festia main hall. The receiver movement waswithin the main beam with few times out of LOS.


Antenna Pointing Direction

6 m 9m

7 m

Receiver

35


6 m 9m

7 m

Receiver

35

Receiver

Figure 4.2: Transmitter and receiver positions for the PL-based indoor propagation mea-surement in the Tamppi Arena. Left: during SET-1, SinglePL. Right: during SET-2,SinglePL.


Receiver

Sports Hall

Figure 4.3: Transmitter and receiver positions for the PL-based indoor propagation mea-surement in the Tamppi Arena during SET-3, SinglePL.


Figure 4.4: Transmitter and receivers position for the PL-based indoor propagation mea-surement in the Fiesta building during SET-4, SinglePL and SET-5, SinglePL.

• SET − 5. This set was also captured in Festia main hall. The receiver movementwas within NLOS condition (almost always behind obstructions).

In Figure 4.4, two pictures of the environment taken both from the transmitter an-tenna position and receiver antenna position are shown for SET-4, SinglePL andSET-5, SinglePL. The schematic representation of these measurement sets is shownin Figure 4.5.

4.1.2 Multiple pseudolite based measurement

Multiple PLs based measurements were also carried out in TUT during November, 2005.The measurements were first carried out in Tietotalo main corridor, and then in the Insti-tute of Communications Engineering (ICE) offices in 5 sets:

• SET −1: It was captured in Tietotalo main corridor with 2 active PLs: PL1 (PRN33, used as reference) and PL3 (PRN 34) were placed according to Figure 4.6. ThePLs were placed in the second floor at a height of 5 meters, and the receivers werein the ground level. The receiver movement was started from 10.5 m away fromPL1, first towards PL3, then towards PL1, and so on. The attenuation in PL1 andPL3 were about 55- 60 dB.


Receiver

Antenna Pointing Direc tion

Festia Main Hall 1st

Level

Ground Level

Obstructions Obstructions

Figure 4.5: Transmitter and receivers position for the PL-based indoor propagation mea-surement in the Fiesta Main Hall during SET-4, SinglePL and SET-5, SinglePL.

• SET − 2: This set was captured in the same environment setup as SETmultiple− 1.But one more active PL was used: PL2 (PRN 32, attenuation 50 dB). The receiverwas first moved towards PL1, then towards PL3 and at last below the bridge wherePL2 was placed.

• SET − 3: This set was also captured with three active PLs (PL1: PRN 33, attenu-ation 55 dB; PL2: PRN 32, attenuation 40 dB, PL3: PRN 34, attenuation 55 dB).PL1 and PL3 were placed at the same location as before, but PL2 was placed onelevel up, at the third floor, above the window ceiling of Tietotalo.

• SET −4: It was captured in the office corridor of ICE with three active PLs. Theywere placed in a triangle. PL1 also used as reference (PRN 33, attenuation 60 dB).PL2 and PL3 attenuation was 60 dB and 55 dB respectively. The receiver movementwas along the corridor.

• SET −5: It was captured with the same configuration as for SET −4, MultiplePL(same attenuation and same PRNs), but PL2 was used as reference.

Figure 4.7 shows a schematic representation of the measurement setup for SET −4,MultiplePL and SET −5, MultiplePL.


15.8 m

Receiver

PL1

H=5 m

4 m 15.8 m

PL2

H= 5 m

PL3

H=5 m

Figure 4.6: Schematic representation of measurement SET − 1, SET − 2 and SET − 3,MultiplePL (the PLs are shown in red and the receiver in black).

PL 1

H=1.45 m

PL 3

H=1.4 m

15.4 m

Offices

Offices

Offices

PL 2

H= 0 . 97 m

6.1 m

Receiver

Figure 4.7: Schematic representation of measurement SET−4, MultiplePL and SET−5,MultiplePL.


4.2 Satellite based measurement campaign

Two satellite based measurement campaigns were undertaken by TUT and u-Nav micro-electronics, Finland during March, 2004. In both campaigns, the transmitters were thedifferent GPS satellites available in view during the measurement date and the receiverswere the integrated GPS receivers with sampling rate of 16.36 MHz. Two GPS receiverssynchronized to a common clock, operating in parallel were used. The first one wasused to acquire the signal from an outdoor antenna placed on the roof of the building.This signal was quite strong, and it was used as the reference signal for code-phase andDoppler frequency acquisition, as well as for frequency drift estimation and correction.The second receiver was moved in the indoor environment to capture the indoor signal.The down-converted intermediate frequency (IF) was same as the PLs.

Among the two measurements, one was carried out in typical office-room scenario andthe other was carried out in typical office-corridor scenario. The first scenario, denoted byRoomSAT , shown in Figure 4.8 (left), corresponds to a small room without any window(about 5m2), where in the front there was small corridor with large windows. Here theLOS signal is more likely to be absent. The second scenario, denoted by CorridorSAT ,shown in Figure 4.8 (right), corresponds to a long corridor with open windows and doors.The receiver movement inside the environments was random and it was at the walkingspeed. All the measurements were taken for a duration of 1-2 mins for reliable statistics.

Figure 4.8: Photo of RoomSAT (left) and CorridorSAT (right) scenario.

Chapter 5

Measurement data analysis

This chapter discusses the data analysis steps that are followed to compute the ChannelImpulse Response (CIR) estimates. The setup block diagram is detailed in Figure 5.1. Aninitial Doppler drift estimate (incorporating the drift due to low IF sampling) and an initialdelay estimate are obtained based on the reference signal by scanning the whole delay-Doppler space. Also, the code drift, frequency drift and navigation data are estimatedbased on this reference signal and then removed from the wireless signal. Then, the wire-less signal is correlated with the replica code, by taking into account the delay-Dopplerestimates and their drifts. In the indoor environment the coherent integration must belonger than 20 ms in order to compensate for the increase in the noise level. For thisreason, the removal of the navigation data must be done before the coherent integration,similar with [26], [27] and [28]. The most important parts of Figure 5.1 are discussed inthe following sections.

bankCorrelators Correlation

on 1 msDoppler, delay

estimatesand drift

Navigationdata estimates

Ref

signal

Dataremoval

Integrationon Nc ms CIR estimates

replica GPS codeIndoorsignal

Figure 5.1: Block diagram of the measurement data processing.

25

Measurement data analysis 26

5.1 Acquisition of C/A code

For any DS-SS (Direct sequence Spread Spectrum) system, it is necessary to estimatethe timing and the frequency shift of the received signal in order to be able to de-spreadthe received signal and to obtain the original data. For that, it is required to define theposition where there is an alignment between the received signal and the spreading code[23]. This is done to estimate the Doppler shift and initial delay. The process is doneusing cross-correlation, which measures the similarity of the code and the delayed replicaof the same code. The search process is usually two-dimensional by which both the timeshift (i.e., delay) and Doppler shift can be determined [22]. The value of the Doppler shiftchanges over time according to the place and speed of the satellite. It is naturally muchmore easier to look for the correct frequency, if the probable Doppler shift is known inadvance. According to [45] the maximum Doppler velocity, vs of the satellite is 929 m/s.The Doppler frequency caused by the land vehicle is often very small. For a stationaryobserver the maximum Doppler shift on the carrier is

fD =vs fc

c

=929×1575.42×106

3×108∼= 5kHz

where c is the speed of light and fc is the L1 carrier frequency. In the measurementcampaigns, the receiver was moved in a low speed which was around 1−2 km/hr. So themaximum Doppler shift was around ±5 kHz. However, if a receiver is moved by usinga high speed aircraft, it is reasonable to assume the maximum Doppler shift is ±10 kHz[45].

On the other hand the Doppler shift on the C/A code is quite small because of thelow frequency of the C/A code. The C/A code has a frequency of 1.023 MHz which is1,540 (1575.42/1.023) times lower than the carrier frequency. For a stationary observerthe maximum Doppler shift on the C/A code is

fD =vs fc

c

=929×1.023×106

3×108∼= 3.2Hz

where fc is the C/A code frequency. If the receiver is moved at high speed, the Dopplershift can be assumed as ±6.4 Hz.


In the search process, all possible code delays and frequencies are searched throughwith some predefined search steps. The search space is typically equal to the lengthof the spreading code in the code-delay domain. In the Doppler frequency domain, thesearch interval can be several kHz or even tens of kHz [11]. If some a priori information(i.e., assistance data) about the Doppler frequency is available, the frequency intervalmay be just few tens of Hz [11]. In order to accomplish the search in a short time, thebandwidth of the searching program cannot be very narrow. Using a narrow bandwidthfor searching means taking many steps to cover the desired frequency range and it is timeconsuming. On the other hand, searching with wide bandwidth provides low sensitivity.So the bandwidth should be selected properly. For measurement data, 1023∗16 samplesare searched in the initial stage with a frequency step of 400 Hz. In the next stage awindow of 200 correlators is used with smaller frequency step of 20 Hz to get betterphase estimate and check the correctness of the frequency estimated from the previousstage. The correct delay of the C/A code for SET-1, SinglePL is shown as an example inFigure 5.2 after the initial stage.

−600 −400 −200 0 200 400 6000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Delay [chips]

Nor

mal

ized

cor

rela

tion

pow

er

Figure 5.2: The correct delay of C/A code of SET-1, SinglePL.

5.1.1 Search window

Each tentative code-phase is called a code bin (or a time bin) and each tentative frequencyshift is denoted as a Doppler bin (or a frequency bin). One code bin together with oneDoppler bin compose a search bin (or a test cell). The whole code-frequency uncertaintyregion can be divided into several search windows and each window can be divided intoseveral time-frequency bins. The time-frequency search window defines the decision re-


gion [22].

5.1.2 Search strategy

In the search stage, the search windows are examined to see whether the time-frequencyestimate is correct or not. The search process is started from one search window, with acertain tentative Doppler frequency and a certain tentative delay. All delays and frequen-cies, which correspond to the size of the search window at issue, are searched throughwith the predefined search steps. If the window is decided to be dismissed, the searchprocess moves on to the next search window, and the same procedure is continued, untilthe correct window and the correct delay-frequency combination is found [22, 23]. Ahybrid search is used in this thesis.

5.1.3 Correlation

The tentative time-frequency bins are tested and possible signals are detected via cross-correlation. This means that the received signal is correlated with the reference code withdifferent tentative delays and frequencies, and the resulting values are then combined toachieve a two-dimensional correlation output for the whole search window. From thecorrelation output, it can be further determined whether the search window is corrector not via a correlation peak which appears for correct delay-frequency combination.The correlation process is described in detail in [22, 34]. The correlation properties ofthe spreading codes are very important. If the auto and cross-correlation properties areperfect, the correlation function would appear as a pure impulse at the correct delay andwill have zero values elsewhere. But actually there is always some interference and noisepresent, which affects the correlation output of the received signal and reference code. Anexample correlation function is shown in Figure 5.3 for SET-1, SinglePL data.

The initially estimated carrier and delay for each set of PL signals are shown in Table5.1. Also the carrier and delay for each set of satellite signal for different PRNs are shownin Table 5.2.

5.2 Drift estimation

As discussed in the previous section, the satellite orbital motion can cause a Doppler shiftup to 5 kHz for stationary receiver. In addition, satellite clock drift affects the actualfrequency emitted from the GPS satellites, causing a further Doppler effect. The carrierphase estimation is highly affected by the frequency and phase drifts. According to [48],


−8 −6 −4 −2 0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Delay [chips]

Nor

mal

ized

cor

rela

tion

pow

er

Figure 5.3: One dimensional (left) and two dimensional (right) correlation of C/A codefor SET-1, SinglePL after 1ms integration.

Table 5.1: Delay and Carrier for different sets of PL signal.SinglePL MultiplePL

Set Delay (ms) Carrier (Hz) Delay (ms) Carrier (Hz)1 263.95 39200 689.62 392102 560.07 39190 611.07 389903 604.22 39290 645.33 394404 242.33 39270 621.70 394205 311.99 39300 646.72 39400

Table 5.2: Delay and Carrier for satellite data.CorridorSAT RoomSAT

PRN Delay (ms) Carrier (Hz) Delay (ms) Carrier (Hz)3 980.58 42620 511.38 43200

15 911.63 42800 620.21 4002016 752.64 38600 711.11 3980018 197.76 36400 211.56 3820021 621.39 39400 525.24 3942026 311.39 42420 325.33 42100


a 2nd order polynomial fitting model can be used to estimate the drifts. In the drift estima-tion of the measurement data, 2nd order polynomial fitting model is used. The estimatedphase and the effects of multi-paths on phase estimation for a few data sets are discussedin Appendix A.

5.3 Navigation data bit estimation

The C/A code is a bi-phased code signal which changes the carrier phase between 0 to πat a rate of 1.023 MHz. The navigation data bit is also bi-phased code but its rate is 50Hz. Each data bit is 20 ms long. Since C/A code is 1 ms, there are 20 C/A code symbolsin one data bit. Thus, in one data bit all 20 C/A codes have the same phase. It is necessaryto find the phase transitions to estimate the navigation bits. For this purpose the followingtwo methods are compared:

• Threshold approach

• Signum (sgn) function approach

The phase difference between the adjacent millisecond outputs can be represented by:

∆θ = θn+1−θn (5.1)

In the threshold approach three thresholds (π/2,π,2π/3) are studied. The idea is thatif the absolute phase difference between adjacent millisecond outputs is beyond a certainthreshold, there is a data transition. These points are the navigation data points. Afterfinding the navigation points, the navigation data are estimated and designated as +1 and-1. The sign of first navigation bit is arbitrarily chosen. The sub-sequent bits are chosenbased on the thresholds. For example, if abs(∆θ)≤ π/2, the current navigation bit has thesame sign as the previous bit, otherwise the current bit has different sign. In the signumfunction approach, the sign of the phase difference is directly mapped to the navigationdata bits (i.e., +1 and -1).

For each method, the CIR envelope is computed and CNR is estimated in order to findthe most accurate method based on the estimated CNR variance in the overall data. Theresults are discussed in Section 6.6 of Chapter 6. The following steps are used to convertthe phase transition to navigation data:

1. Find all the navigation data transitions. The beginning of the first navigation datashould be within the first 20 ms of output data because the navigation data are 20 ms


long. The first phase transition is used to find the beginning of the first navigation data.The first phase transition detected in the output data is the beginning of the navigationdata. If the first phase transition is within the first 20 ms of data, this point is also thebeginning of the first navigation data. If the first phase transition occurs at a later time,a multiple number of 20 ms is subtracted from it. The remainder is the beginning of thefirst navigation data. For simplicity let us just call it the first navigation data point insteadof the beginning of the first navigation data. The first navigation data point can be paddedwith data points of the same sign to make the first navigation data point always occurat 21 ms. This approach creates one navigation data point at the beginning of the datafrom partially obtained information. For example, if the first phase transition occurs at97 ms, by subtracting 80 ms from this value, the first navigation data point occurs at 17ms. These 17 ms of data are padded with 4 ms of data of the same sign to make thefirst navigation data 20 ms long. This process makes the first navigation data point at 21ms. This operation also changes the rest of the beginnings of the navigation data by 4ms. Thus, the navigation data points occur at 21, 41, 61, and so on. Figure 5.4 illustratesthe above example. The adjusted first navigation data point at 21 ms is stored. If the firstphase transition occurs at 40 ms, by subtracting 40, the adjusted first navigation data pointoccurs at 0 ms. Twenty-one ms of data with either + or - can be added in front of the firstnavigation data point to make it occur at 21 ms.

21 41 61 81 101

37 57 77

Adjusted 1 st

navigation data

at 21 ms

1 st phase

shift occurs at

97 ms

1 st navigation

data point at 17

ms

Padded with 4

ms of data

Figure 5.4: Adjustment of the first navigation data point.

2. Once the navigation data points are determined, the validity of these transitionsmust be checked. These navigation data points are separated by multiples of 20 ms. If


these navigation data points do not occur at a multiple of 20 ms, the data contain errorsand should be discarded.

3. After the navigation data points pass the validity check, these outputs are convertedinto navigation data. Every 20 outputs (or 20 ms) convert into one navigation data bit. Thesign of the first navigation data is arbitrarily chosen. The navigation data are designatedas +1 and −1.

5.4 Coherent integration

The GPS signals are expected to be rather weak. The common approach to find a weaksignal is to increase the acquisition data length. The advantage of this approach is theimprovement in signal-to-noise ratio. One simple explanation is that an FFT with 2 ms ofdata produces a frequency resolution of 500 Hz in comparison with 1 kHz resolution of 1ms of data. Since the signal is narrow band after the spectrum is de-spreaded, the signalstrength does not reduce by the narrower frequency resolution. Reducing the resolutionbandwidth reduces the noise to half; therefore, the signal-to-noise ratio improves by 3 dB.For the measurement based data, high coherent integration lengths (50, 200) are used. Anexample of CIR snapshots is given in Figure for PRN 3, RoomSAT . The left plot of thisfigure shows the CIRs without applying coherent integration and the right plot shows theCIRs after applying the coherent integration of 200 ms.

−8 −6 −4 −2 0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Snapshot of CIR envelope, Nc=1ms

Delay error [chips]

CIR

en

ve

lop

e

ReferenceIndoor

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1


Delay error [chips]

CIR

en

velo

pe

ReferenceIndoor

Figure 5.5: Example snapshot of correlation based CIR envelope, PRN 3, RoomSAT .

Chapter 6

CNR Estimation

This chapter starts by describing a signal model for BOC/BPSK modulated signals, thenit describes the derivation of the moment based CNR estimators based on the correlationof the incoming signal. Finally, the performance of each estimator for simulation basedBOC modulated signal and measurement based BPSK modulated signal are presented tothe readers. An initial analysis of such moment based CNR estimators assuming a signalmodel is presented in [21]. More detailed analysis including a procedure of choosingappropriate number of noise samples are presented in this thesis.

6.1 Signal model

As described in the starting part of this chapter, the signal model used here has beenpresented in [21]. All the CNR estimators are derived based on this signal model. So, thesignal model has been discussed here again for better understanding.

6.1.1 Coherent integration outputs

Suppose xI and xQ denote the real and imaginary parts of the correlation function after1 ms integration computed between the incoming BOC/BPSK-modulated signal and thereference BOC/BPSK-modulated codes. If it is assumed that the channel is AdditiveWhite Gaussian Noise (AWGN) with double sided power-spectral density N0/2, then theI and Q components of the noise are Gaussian distributed with 0 mean and variance N0/2.The complex noise variance is N0/2+N0/2 = N0. It is also assumed that the signal poweris Eb, that is the Signal to Noise Ratio (SNR) is Eb/N0 and the Carrier to Noise ratio in 1

33

CNR Estimation 34

kHz bandwidth is [6]:

CNR[dBHz] = 10log10Eb

N0+10log10(Bw)

= 10log10Eb

N0+30 (6.1)

where Bw = 1 kHz bandwidth. The statistics of the correlation function after 1 ms in-tegration obey a normal (Gaussian) distribution N (mean,variance): In the correct bins(peaks) [30]:

xI,p ∼ N(

F (∆τ,∆ fD)√

Eb,N02

)

xQ,p ∼ N(

0, N02

) (6.2)

In the incorrect bins (out-of-peaks) [21]:

xI,o ∼ N(

0, N02

)

xQ,o ∼ N(

0, N02

) (6.3)

Above, F (∆τ,∆ fD) can be given by [21]:

F (∆τ,∆ fD) = RBOC/BPSK(∆τ)sinc(π∆ fDTms), (6.4)

where sinc(x) = sin(x)/x, ∆τ is the delay error, ∆ fD is residual Doppler error comingfrom acquisition stage, RBOC/BPSK(∆τ) is the BOC/BPSK autocorrelation function andTms is the 1-ms integration time. For simplicity reason, it is assumed from now on that theresidual Doppler error is 0 and the bit energy (or signal power per bit) in a correct bin isdenoted by:

Eb = R 2BOC/BPSK(∆τ)Eb. (6.5)

There might be several correct bins, according to the steps of scanning the time axis. Themaximum peak corresponds to 0 delay error (RBOC/BPSK(∆τ) = 1 and Eb = Eb). Thestatistics after 1 ms integration can be written as [21]:

xI,p ∼ N(√

Eb,N02

)

xQ,p,xI,o,xQ,o ∼ N(

0, N02

) (6.6)

where the subscript p stands for a peak value and the subscript o stands for an out-of-peak value.

CNR Estimation 35

If yI and yQ are denoted as the real and imaginary parts of the correlation functionafter coherent integration on Nc ms, yI and yQ can be represented [21]:

yI,k = 1Nc

Nc

∑i=1

xI,i+kNS

yQ,k = 1Nc

Nc

∑i=1

xQ,i+kNS

(6.7)

where NS is the oversampling factor. yI,Q are still Gaussian distributed, of variance1

N2cNc

N02 = N0

2Nc, and mean 0 (for yQ,p,yI,o, and yQ,o) or 1

NcNc

√Eb = Eb (for yI,p). Thus, the

statistics after coherent integration can be written as [21]:

yI,p ∼ N(√

Eb,N02Nc

)

yQ,p,yI,o,yQ,o ∼ N(

0, N02Nc

) (6.8)

6.1.2 Non-coherent integration outputs

If the output after non-coherent integration on Nnc blocks is denoted by z, it can be repre-sented by [21]:

z =1

Nnc

( Nnc

∑k=1

y2I,k +

Nnc

∑k=1

y2Q,k

)=

Nnc

∑k=1

(yk√Nnc

)2

(6.9)

where yk is the complex modulus (magnitude) of yI,k + yQ,k. In Equation (6.9), thereis a sum of squares of Gaussians of equal variance σ2 = 1

Nncvar(y) = N0

2NcNnc. Thus z is

a chi-square distributed variable [37], either central or non-central according to the binplacement (peak zp or out-of-peak zo):

zp ∼ χ2nc

(Eb,

N02NcNnc

,2Nnc

)

zo ∼ χ2c

(N0

2NcNnc,2Nnc

) (6.10)

where χ2nc(s

2,σ2,n) is a non-central chi-square distribution with n = 2Nnc degrees of free-dom, underlying variance σ2 = N0

2NcNncand non-centrality parameter s2 = Nnc

EbNnc

+0 = Eb.And χ2

c(σ2,n) above is a central chi-square distribution with n = 2Nnc degrees of freedomand underlying variance σ2 = N0

2NcNnc. According to [37], the mean, second-order moment

and variance can be derived as follows:

CNR Estimation 36

Central distributions:

E(zo) = nσ2 = N0Nc

E(z2o) = 2nσ4 +n2σ4 = N2

0N2

c( 1

Nnc+1)

var(z2o) = 2nσ4 = N2

0NncN2

c

(6.11)

Non-central distributions:

E(zp) = nσ2 + s2 = N0Nc

+ Eb

E(z2p) = 2nσ4 +4σ2s2 +(nσ2 + s2)2

= N0Nc

(1

Nnc+1

)(2Eb + 1

Nc

)+ E2

b

var(z2p) = 2nσ4 +4σ2s2 = N2

0NncN2

c+ 2N0Eb

NcNnc

(6.12)

Above, E(·) is the expectation operation. For ergodic processes, the statistic average isequal to the time average. However, for one observation of the correlation function (seean example in Figure 6.1), typically there is one (or very few) ’peak’ values, and severalout-of-peak values. Thus, the statistical average can be assumed by:

E(zp) ≈ zp

E(zo) ≈ 1N

N

∑k=1

zo,k(6.13)

where N ≥ 1 is the number of out-of-peak values used to estimate the mean. An exampleof peak and out-of-peak values based on the non-coherently averaged correlation functionis given in Figure 6.1 with an oversampling factor, NS equals to 4 (for SinBOC(1,1)) or16 (for BPSK) and modulation order, NB equals to 2 (for SinBOC(1,1)) or 1 (for BPSK).The modulation order, NB for BOC(n,m) can be given by NB = 2n/m.

6.1.3 PDFs and CDFs

The Probability Distribution Functions (PDFs) of the output of non-coherent integrationin the correct zp and incorrect zo bin hypotheses are given by the non-central and centralχ2 PDFs, respectively [37]:

fncentr(zp) = NcNncN0

(zp

Eb

)Nnc−12

exp(− (Eb+zp)NcNnc

N0

)INnc−1

(2NcNnc

√zpEb

N0

)(6.14)

with Iα(x) being an α-order modified Bessel function of first kind, and

fcentr(zo) = 1(N0

2NcNnc

)Nnc

2Nnc Γ(Nnc)

zNnc−1o exp

(− zoNcNnc

N0

)(6.15)

CNR Estimation 37

−4 −3 −2 −1 0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Delay[chips]

No

rma

lize

d n

on

−co

he

ren

t co

rre

latio

n

Single path static channel

Peak valuesOut−of−peak values

−4 −3 −2 −1 0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Nor

mal

ized

non

−coh

eren

t cor

rela

tion

Delay[chips]

Single path static channel

Peak valuesOut−of−peak values

Figure 6.1: Example of peak and out-of-peak values for a non-coherently averaged corre-lation function in single path static channel. A ’peak’ means a correct bin. SinBOC(1,1)signal (left) with Nc = 200, Nnc = 1, Ns = 4 and BPSK signal (right) with Nc = 200,Nnc = 1, Ns = 16, .

with Γ(Nnc) = (Nnc−1)! being Gamma (Euler) function.The Cumulative Distribution Functions (CDFs) for peak and out-of-peak non-coherent

correlation values are [37]:

Fncentr(zp) = 1−QNnc

(√2NcNncEb

No,

√2NcNnczp

No

)(6.16)

Fcentr(zo) = 1− exp(− zoNcNnc

N0

)Nnc−1

∑k=0

1k!

(zoNcNnc

N0

)k

(6.17)

where Qm(a,b) is the generalized Marcum Q function.

6.2 Moment-based CNR estimators

The moment-based CNR estimators are not new in literature. But there has been nocomparison between these moment-based estimators, specially for the GPS/Galileo signalaccording to the author’s knowledge. In this thesis, the estimators are derived basedon the autocorrelation function of the incoming signal which is not done before. Someestimators, namely 1STO, 2NDO-M1, 2NDO-M2, and 4THO-1STO have been the resultof previous, co-authored work in the laboratory [21]. The other estimators are derivedby the author in the similar way and a detailed analysis of all the estimators has been

CNR Estimation 38

performed. An algorithm for choosing the appropriate out-of-peak points is also proposedin this thesis. The main advantage of the proposed algorithm is that we are able to estimatethe CNR accurately while using lower number of out-of-peak points.

6.2.1 First-order moments (1STO)

From the means given in Equations (6.11) and (6.12), the following two means can befound:

E(zp) =N0

Nc+ Eb

E(zo) =N0

Nc

From the second equation, we have, N0 = E(zo)Nc and replacing the value of N0 in thefirst equation, we get Eb = E(zp)−E(zo). Thus, using the values of N0 and Eb in Equation(6.1), the following estimate of CNR can be obtained:

CNR = 10log10E(zp)−E(zo)

E(zo)Nc+30. (6.18)

The mean values, E(zp), and E(zo) can be computed by using Equation (6.13).

6.2.2 Second-order moments, method 1 (2NDO-M1)

From the second-order moments given in Equations (6.11) and (6.12), the following twoequations can be found:

E(z2p) =

N0

Nc

(1

Nnc+1

)(2Eb +

1Nc

)+ E2

b (6.19)

E(z2o) =

N20

N2c

(1

Nnc+1

)(6.20)

Thus, N20 =

E(z2p)N2

c

1+ 1Nc

. By replacing this value in Equation (6.19) above, and using the

notation x = EbN0

, the second-order equation can be written as:

E(z2o)N

2c Nnc

1+Nncx2 +2xNcE(z2

o)+E(z2

o)(N2nc +1)

Nnc(1+Nnc)−E(z2

p) = 0. (6.21)

CNR Estimation 39

Equation (6.21) has one negative and one positive root. However, SNR should have apositive value, therefore the positive root is the correct one. Thus, the positive solution ofEquation (6.21) gives the CNR estimate:

CNR = 10log10

(− 1+Nnc

NcNnc+ 1

Nc

√(1+ 1

Nnc

)(E(z2

p)E(z2

o)+ 1

Nnc

))+30. (6.22)

Above, the estimates of the mean squared peak and out-of-peak values can be obtained

via: E(z2p)≈ z2

p and E(z2o)≈ 1

N

N

∑k=1

z2o,k.

6.2.3 Second-order moments, method 2 (2NDO-M2)

Another possibility to estimate CNR is by making the following observation, again basedon Equations (6.11) and (6.12):

E(zp)−E(zo)std(z2

o)=

N0Nc

+ Eb− N0Nc√

N20

NncN2c

=EbNc

√Nnc

N0(6.23)

where std(z2o) =

√var(z2

o) is the standard deviation. Thus, the CNR estimate can beobtained via:

CNR = 10log10E(zp)−E(zo)Nc√

Nncstd(zo)+30. (6.24)

Here, at least two out-of-peak values are needed in order to compute the standard devia-tion std(z2

o).

6.2.4 Combined second (central) and first (non-central) order mo-ments (2NDO-1STO-M1)

From the second (central) order moments given in Equation (6.11), the following equationcan be found:

E(z2o) =

N20

N2c

(1

Nnc+1

)(6.25)

Using Equation (6.25) and the value of E(zp) from Equation (6.12), it is straightfor-ward to show that an estimate of CNR can be obtained in the form:

CNR = 10log10

(E(zp)−(

E(z2o)(

1+ 1Nnc

)) 1

2

Nc

(E(z2

o)(1+ 1

Nnc

)) 1

2

)+30. (6.26)

CNR Estimation 40

Again, the approximations, E(zp)≈ zp and E(z2o)≈ 1

N

N

∑k=1

z2o,k can be used.

6.2.5 Combined second (non-central) and first (central) order mo-ments (2NDO-1STO-M2)

From the second (non-central) order moments given in Equation (6.12), the followingequation is taken:

E(z2p) =

N0

Nc

(1

Nnc+1

)(2Eb +

1Nc

)+ E2

b

(6.27)

Equation (6.27) has one negative and one positive root. However, SNR should have apositive value, therefore the positive root is the correct one. Thus, the positive solution ofEquation (6.27) gives the Eb estimate:

Eb = −(

1+ 1Nnc

)N0Nc

+

√(1+ 1

Nnc

)2N2

0N2

c−

(1+ 1

Nnc

)N0N2

c+E(z2

p). (6.28)

Again, from the means given in Equation (6.11), the following equation is found:

E(zo) =N0

Nc

Therefore, N0 = E(zo)Nc.The estimated CNR can be obtained in the form:

CNR = 10log10Eb

NcE(zo)+30. (6.29)

where Eb is given according to the Equation (6.28).

6.2.6 Combined fourth and second order moment (4THO-2NDO)

The fourth order moment of a central ξ2 distribution of variance σ2 and n degrees offreedom is [1]:

E(z4o) = nσ8n(n+2)(n+4)(n+6)

=N4

0N4

c

(1+

1Nnc

)(1+

2Nnc

)(1+

3Nnc

)(6.30)

CNR Estimation 41

N0 can be written in the following form:

N0 = Nc

(E(z4

o)(1+ 1

Nnc

)(1+ 2

Nnc

)(1+ 3

Nnc

)) 1

4

. (6.31)

By using Equation 6.31, the estimated CNR can be obtained in the form:

CNR = 10log10Eb

Nc

(E(z4

o)(1+ 1

Nnc

)(1+ 2

Nnc

)(1+ 3

Nnc

)) 1

4+30. (6.32)

where Eb is again given according to the Equation 6.28.

6.2.7 Combined fourth and first order moments (4THO-1STO)

Using Equation (6.31) and the value of E(zp) from Equation (6.12), it is straightforwardto show that an estimate of CNR can be obtained in the form:

CNR = 10log10

(E(zp)−(

E(z4o)(

1+ 1Nnc

)(1+ 2

Nnc

)(1+ 3

Nnc

)) 1

4

Nc

(E(z4o)(

1+ 1Nnc

)(1+ 2

Nnc

)(1+ 3

Nnc

)) 1

4

)

+30. (6.33)

Again, the approximations, E(zp)≈ zp and E(z4o)≈ 1

N

N

∑k=1

z4o,k can be used.

6.3 Simulation results

The common parameters used in the simulation are given in Table 6.1.

Table 6.1: Common parameters for the simulation.Parameter Symbol Value Unit

Over-sampling rate Ns 4 -Modulation order NB 2 -Spreading factor SF 21 Chips

Correlation window - 7 Chips

CNR Estimation 42

6.3.1 Results for single path channel

The results regarding the average errors between the estimated CNR and the true CNRare shown in Figure 6.2 for single-path static channel, when squared envelope is used asnon-linearity. Small spreading factor (SF = 21) is used in the simulations for the purposeof increasing the simulation speed. Small differences is expected, if the spreading factoris increased (e.g., to 1023 chips, as used in GPS/Galileo). In Figure 6.2, the continuous

15 20 25 30 35 40 45 500

1

2

3

4

5

6

7

8

9

10Absolute Mean Error

Ab

solu

te M

ea

n E

rro

r [d

B]

CNR [dBHz]

2NDO−M2, N=422NDO−M1, N=421STO, N=422NDO−1STO−M2, N=422NDO−1STO−M1, N=424THO−2NDO, N=424THO−1STO, N=422NDO−M2, N=12NDO−M1, N=11STO, N=12NDO−1STO−M2, N=12NDO−1STO−M1, N=14THO−2NDO, N=14THO−1STO, N=1

15 20 25 30 35 40 45 500

2

4

6

8

10

12RMSE

RM

SE

[d

B]

CNR [dBHz]

2NDO−M2, N=422NDO−M1, N=421STO, N=422NDO−1STO−M2, N=422NDO−1STO−M1, N=424THO−2NDO, N=424THO−1STO, N=422NDO−M2, N=12NDO−M1, N=11STO, N=12NDO−1STO−M2, N=12NDO−1STO−M1, N=14THO−2NDO, N=14THO−1STO, N=1

Figure 6.2: Examples of CNR estimates for single-path static channel (Absolute MeanError and RMSE), Nc = 20 and Nnc = 2.

lines are used to indicate that the CNR computation takes more than one out-of-peakvalues (N > 1) in order to estimate E(zo). All methods use only one value (the globalpeak value) to estimate E(zp). The dashed lines use only 1 out-of-peak value (with theexception of the method 2NDO-M2 which uses N = 2 out-of-peak samples for estimatingthe standard deviation but only 1 point to estimate the statistical averages). Based onFigure 6.2, all the proposed estimators seem to have similar performance if enough out-of-peak values are employed in computing the statistical averages. The performance of allthe methods deteriorates when N decreases, especially at low CNRs (when CNR is highenough, the number of samples N used in the estimation is not important any more). Thepoorer CNR estimates at lower CNR (compared with mid CNRs) can be explained by thefact that, the lower the CNR is, the less accurate the above formulas are according to [21].The poorer CNR estimates at high CNR (compared with mid CNRs) can be explainedby some calculus approximations errors that occur in Matlab when input CNR is above acertain threshold. This can be partly overcome by increasing the number of random pointsused in the statistics. In the CNR range of 20 till 45 dB, an RMSE in CNR estimation

CNR Estimation 43

around 2 dB is obtained with all the 7 methods (if N = 42 samples). However with N = 42samples, the complexity is much higher in comparison with N = 1. So the target is to uselower number of out-of-peak points and still get low RMSE. From Figure 6.3, it is foundthat N ≥ 20 is good to use to get low RMSE.

0 5 10 15 20 25 30 35 40 451

2

3

4

5

6

7CNR=25

RM

SE

[d

B]

N

2NDO−M22NDO−M11STO4THO−1STO2NDO−1STO−M14THO−2NDO2NDO−1ST−M2

0 5 10 15 20 25 30 35 40 451

2

3

4

5

6

7CNR=40

RM

SE

[d

B]

N

2NDO−M22NDO−M11STO4THO−1STO2NDO−1STO−M14THO−2NDO2NDO−1ST−M2

Figure 6.3: RMSE vs. N plots for different CNRs for single-path static channel, Nc = 20and Nnc = 2.

Choosing the appropriate number of out-of-peak points is an important task as de-scribed in the previous paragraph. The following procedure can be used to choose theappropriate number of out-of-peak points.

• Find the global peak point.

• Find the other peak points which are within NS ∗NB samples from the main peak ineither direction.

• Mark all other points as out-of-peak points. Suppose NTotal is the total number ofout-of-peak points.

• Compute the mean, MEANPeaks of all the peak points including the global peak.

• Set a threshold, T HRESHOLD = 2.5∗MEANPeaks and compute the number of truepeaks by comparing the the points above the T HRESHOLD. Suppose NPeaks is thetotal number of true peaks.

• Compute the appropriate number of out-of-peak points, NAppropriate = NTotal/NPeaks.

CNR Estimation 44

The simulation results using the above procedure for choosing the appropriate out-of-peak points are shown in Figure 6.7. In this simulation, 20 out-of-peak points are usedon the average. From the results, it is found that 4THO-1STO gives the lowest absolutemean error and RMSE. Here, Nc = 200 and Nnc = 1 are used, similar to what is used forprocessing the measurement data. A plot showing how many out-of-peak points are usedfor computing the different CNR levels is given in Figure 6.5. From this figure, it can bestated that lower number of out-of-peak points are necessary for high CNR estimation incomparison to the low CNRs.

20 22 24 26 28 30 32 34 36 38 400

0.2

0.4

0.6

0.8

1

1.2

1.4Absolute Mean Error

Abs

olut

e M

ean

Err

or [d

B]

CNR [dBHz]

2NDO−M22NDO−1STO−M11STO2NDO−1STO−M22NDO−M14THO−2NDO4THO−1STO

20 22 24 26 28 30 32 34 36 38 401.4

1.6

1.8

2

2.2

2.4

2.6

2.8RMSE

RM

SE

[dB

]

CNR [dBHz]


Figure 6.4: Examples of CNR estimates for single-path static channel (Absolute MeanError and RMSE), Nc = 200 and Nnc = 1.

The estimators were also used to estimate the CNR for single-path fading channel.Figure 6.6 shows the results for such a channel. The CNRs are estimated in the same wayas the single-path static channel in Figure 6.7. The results for the fading channel is quitesimilar with the results for the static channel (i.e., 4THO-1STO shows lowest absolutemean error and RMSE).

6.3.2 Results for multi-path channel

The CNR estimation for multi-path channels are also studied using the moment-basedestimators. The results are given in Figure 6.7. The same procedure, described in theprevious subsection for choosing the out-of-peak points is used. From this figure, we findthat only two estimators namely, 4THO-1STO and 4THO-2NDO give acceptable RMSEvalues around 2.5− 3 dBHz. These two estimators give around 0.5− 1 dBHz worseperformance in terms of RMSE for multi-paths compared to single path.

CNR Estimation 45

20 22 24 26 28 30 32 34 36 38 4016

16.5

17

17.5

18

18.5

19

19.5

20

NAppropriate

vs. CNR

CNR [dBHz]

NA

pp

rop

ria

te

Figure 6.5: NAppropriate vs. CNR for single-path static channel, Nc = 200 and Nnc = 1.

20 22 24 26 28 30 32 34 36 38 400

0.2

0.4

0.6

0.8

1

1.2

1.4Absolute Mean Error

Ab

solu

te M

ea

n E

rro

r [d

B]

CNR [dBHz]


20 22 24 26 28 30 32 34 36 38 401.4

1.6

1.8

2

2.2

2.4

2.6

2.8RMSE

RM

SE

[d

B]

CNR [dBHz]


Figure 6.6: Examples of CNR estimates for single-path fading (Nakagami m=0.8) channel(Absolute Mean Error and RMSE), Nc = 200 and Nnc = 1.

CNR Estimation 46

20 22 24 26 28 30 32 34 36 38 400

1

2

3

4

5

6

7

8Absolute Mean Error

Abs

olut

e M

ean

Err

or [d

B]

CNR [dBHz]

2NDO−M22NDO−M11STO2NDO−1STO−M22NDO−1STO−M14THO−2NDO4THO−1STO

20 22 24 26 28 30 32 34 36 38 402

3

4

5

6

7

8

9

10

11RMSE

RM

SE

[d

B]

CNR [dBHz]

2NDO−M22NDO−M11STO2NDO−1STO−M22NDO−1STO−M14THO−2NDO4THO−1STO

Figure 6.7: Examples of CNR estimates for multi-path (2-4 paths) fading (Nakagamim=0.8) channel (Absolute Mean Error and RMSE), Nc = 200 and Nnc = 1.

The overall performance of all these estimators can be improved if we are able toreduce the effects of multi-paths by incorporating multi-path mitigating algorithms. It isleft as future research topic.

6.3.3 Envelope vs. squared envelope as nonlinearity

The moment-based estimators are derived by assuming the squared envelope of the non-coherent blocks. It is also interesting to examine how the estimators perform if the enve-lope is used instead of the squared envelope as non-linearity. That means the χ2 statisticsare no longer valid. The results are given in Figure 6.8 from where it is easy to find that us-ing of envelope instead of squared envelope gives approximately 5 dB poor performancein all the methods.

6.4 CNR mappings

An important question is to know how to map the CNR obtained via a certain (Nc,Nnc)pair to another CNR value, when the integration times are increased. For example, if fromthe simulations a good tracking result at CNR equal to CNR1 = 30 dBHz with Nc1 = 10ms and Nnc1 = 1 block is achieved, the question is: what kind of integration times (Nc2 ,Nnc2) is needed in order to achieve a similar performance at CNR1 = 20 dBHz.

For this, the following equation can be used according to [21]:

CNR Estimation 47

20 22 24 26 28 30 32 34 36 38 401

2

3

4

5

6

7

8

92NDO−M2

CNR [dBHz]

RM

SE

[dB

]

Squared EnvelopeEnvelope

20 22 24 26 28 30 32 34 36 38 401

2

3

4

5

6

72NDO−M1

CNR [dBHz]

RM

SE

[dB

]


20 22 24 26 28 30 32 34 36 38 401

1.5

2

2.5

3

3.5

4

4.5

5

5.5

61STO

CNR [dBHz]

RM

SE

[dB

]


20 22 24 26 28 30 32 34 36 38 401

1.5

2

2.5

3

3.5

4

4.5

5

5.54THO−1STO

CNR [dBHz]

RM

SE

[dB

]


20 22 24 26 28 30 32 34 36 38 401

2

3

4

5

6

74THO−2NDO

CNR [dBHz]

RM

SE

[dB

]


20 22 24 26 28 30 32 34 36 38 401

1.5

2

2.5

3

3.5

4

4.5

5

5.5

62NDO−1STO−M1

CNR [dBHz]

RM

SE

[dB

]


20 22 24 26 28 30 32 34 36 38 401

2

3

4

5

6

72NDO−1STO−M2

CNR [dBHz]

RM

SE

[dB

]


Figure 6.8: Examples of CNR estimates for the Envelope Vs. the Squared envelope forsingle path fading channel, Nc = 20 and Nnc = 2.

CNR Estimation 48

CNR2[dBHz] = CNR1[dBHz]−10log10(Nc1

√Nnc1)+10log10(Nc2

√Nnc2) (6.34)

For example, if a certain performance at CNR1 = 30 dBHz is achieved with Nc1 = 20ms and Nnc1 = 1 block, then, in order to achieve the same performance at CNR1 = 10dBHz, it is needed, for example: Nc2 = 100 ms and Nnc2 = 1 block, or Nc2 = 10 ms andNnc2 = 100 blocks, or Nc2 = 5 ms and Nnc2 = 400 blocks, or Nc2 = 4 ms and Nnc2 = 625blocks. Based on this mapping the authors in [21] have stated that the target should be toachieve reasonable performance for CNRs as low as 24 dBHz.

As far as the border between indoor/outdoor environments is concerned, there areseveral authors in the scientific community who discussed it. Particularly, in [10] theauthors considered this border to be about −155 dBm, or approximately equal to 18−19dBHz. In [12] the indoor environment is characterized by CNR values less than 25 dBHz,while in [19] it is stated that the indoor acquisition requires successful signal detection attypically 20 dBHz CNR level.

6.5 CNR estimators results with measurement data

The moment based CNR estimators of Section 6.2 are used to estimate the CNR for thePL based data as well as for Satellite based data from the normalized CIR amplitudescomputed over Nc = 200. The used PRNs for the satellite data are 3,15,16,18,21 and26. One snapshot of normalized CIR envelope was given in Figure 5.5 of Chapter 5.A window of 200 correlators (i.e., about ±6.25 chips around the global peak) was used(we recall that the oversampling factor was 16.367/1.023 ≈ 16 samples per chip). Theout-of-peak points are the points those were 16 samples outside the main peak in bothdirections. A total of 168 out-of-peak points are detected. The same procedure, describedin subsection 6.3.1 for choosing appropriate out-of-peak points is used while estimatingthe CNR for measurement data. For the measurement data, 80 out-of-peak points areused on the average. The CNR estimation standard deviation (std) results are given in theTable 6.2 (for PLs) and Table 6.3 (for satellites). From the results it is easy to find thatthe 4THO-1STO estimator gives the lowest std most of the times. The PL results alsoshow high CNR std and low mean CNR in MultiplePL in comparison with SinglePL dueto more interference in MultiplePL data as three PLs were used. The results of satellitedata show similar results (i.e. high CNR std in RoomSAT compared to CorridorSAT )due to less probability of having LOS path in RoomSAT than CorridorSAT . However,comparing with satellite and PL results, it is possible to find that the PL reference signal

CNR Estimation 49

remains almost constant (i.e., small std) in comparison with the satellite data over thecaptured time as expected. This is due to the fact that the reference receiver was connectedto a PL directly via cable.

6.6 CNR estimation results for 4THO-1STO using differ-ent navigation bit estimators

As discussed in the previous section, the 4THO-1STO is the best estimator among themoment based estimators. Here the different navigation bit estimators of Section 5.3 aretested in the context of CNR estimation while using the 4THO-1STO method.The naviga-tion bit estimators include different phase thresholds and the signum function approach,as discussed in Section 5.3. The target is to select the best method based on the lowestCNR std. From Table 6.4 (for PLs) and Table 6.5 (for satellites), it is easy to find that π isthe best threshold for navigation data bit estimation. So, from the overall results, it can bestated that 4TH-1STO estimator using π as the threshold to estimate the navigation bitsis the best way to estimate the CNR. The mean CNR using 4THO-1STO estimator foreach data set is given in Table 6.6 (for PLs) and Table 6.7 (for satellites). Here, it shouldbe mentioned that the estimated CNR varies at most 3 dBHz depending on the differentestimators. The fades in the tables are the differences between the reference signal andthe indoor signal. From the tables, it is found that for PLs the reference signal can havea mean CNR value approximately equal to 40− 50 dBHz while indoor signal can havea mean CNR value of 30− 40 dBHz. The mean fades in the PLs can be approximatelyequal to 5− 15 dBHz. For satellites, the reference signal’s mean CNR values of 38-42dBHz are observed while the indoor signal can have a mean CNR value of 19-23 dBHz.The mean fades in the satellite data can be 18−20 dBHz. Estimated CNRs and fades fora few data sets are shown in Figure 6.9.

6.7 Computational complexity of the estimators

The computational complexity of these estimators have been reduced by using appropriateout-of-peak points. But still these estimators are complex enough from the computationpoint of view. Especially, the estimators with higher order moments (e.g., 4THO-1STOand 4THO-2NDO) require many exponential operations. The estimator, 4THO-2NDOshows almost similar results like 4THO-1STO in terms of RMSE for multi-path channelsin the simulation and for measurement based data. The estimators namely, 2NDO-M1,

CNR Estimation 50

Table 6.2: CNR standard deviation [dBHz] for different estimators for PL data, Nc = 200.SinglePL MultiplePL

SET Estimator std (Reference, Indoor) std (Reference, Indoor)1 1STO 2.59,3.28 2.80,3.18

2NDO-M1 1.20,1.73 1.26,1.752NDO-M2 0.92,1.58 1.24,1.73

2NDO-1STO-M1 1.15,1.73 1.26,1.752NDO-1ST-M2 2.65,3.28 2.84,3.18

4THO-1STO 0.40,1.16 0.58,1.484THO-2NDO 0.42,1.17 0.59,1.49

2 1STO 2.23,3.93 2.23,4.262NDO-M1 0.67,3.05 0.88,3.502NDO-M2 0.66,3.02 0.85,3.59

2NDO-1STO-M1 0.67,3.04 0.89,3.172NDO-1STO-M2 2.23,3.94 1.79,4.27

4THO-1STO 0.26,2.86 0.37,3.184THO-2NDO 0.26,2.87 0.20,3.18

3 1STO 1.11,3.93 1.92,4.262NDO-M1 0.44,3.48 0.79,3.832NDO-M2 0.42,3.42 0.79,3.76

2NDO-1STO-M1 0.44,3.47 0.80,3.822NDO-1STO-M2 1.12,3.94 1.92,4.34

4THO-1STO 0.22,3.43 0.36,3.544THO-2NDO 0.22,3.44 0.36,3.55

4 1STO 1.09,4.25 3.70,3.622NDO-M1 0.66,4.09 1.53,1.822NDO-M2 0.60,3.94 1.50,1.77

2NDO-1STO-M1 4.08,6.66 1.53,1.822NDO-1STO-M2 1.09,4.30 3.70,3.61

4THO-1STO 0.41,3.84 0.69,1.364THO-2NDO 0.42,3.85 0.69,1.36

5 1STO 0.08,2.05 3.48,3.572NDO-M1 0.61,1.50 1.52,1.972NDO-M2 0.57,1.35 1.53,1.77

2NDO-1STO-M1 0.62,1.44 1.63,1.872NDO-1STO-M2 0.81,2.11 3.48,3.51

4THO-1STO 0.46,1.28 0.75,1.284THO-2NDO 0.47,1.33 0.76,1.30

CNR Estimation 51

Table 6.3: CNR standard deviation [dBHz] for different estimators for satellite data, Nc =200.

CorridorSAT RoomSATPRN Estimator std (Reference, Indoor) std (Reference, Indoor)

3 1STO 1.92,3.56 1.81,2.942NDO-M1 1.55,3.66 1.79,2.852NDO-M2 1.41,3.54 1.43,2.82

2NDO-1STO-M1 1.54,3.55 1.72,2.832NDO-1ST-M2 1.92,3.65 1.94,2.98

4THO-1STO 1.10,3.54 1.14,2.634THO-2NDO 1.11,3.49 1.19,2.65

15 1STO 1.64,2.58 2.03,3.022NDO-M1 176,2.68 2.19,3.042NDO-M2 1.55,2.68 2.19,2.99

2NDO-1STO-M1 1.58,2.67 2.15,3.012NDO-1STO-M2 1.72,2.59 2.03,3.03

4THO-1STO 1.83,2.30 1.99,2.474THO-2NDO 1.88,2.35 2.02,2.55

16 1STO 1.95,2.29 1.94,2.372NDO-M1 1.62,2.26 1.66,2.252NDO-M2 1.54,2.15 1.60,2.21

2NDO-1STO-M1 1.61,2.18 1.66,2.222NDO-1STO-M2 1.96,2.36 1.92,2.42

4THO-1STO 1.29,2.15 1.31,2.194THO-2NDO 1.30,2.25 1.35,2.26

18 1STO 2.64,1.51 1.65,1.862NDO-M1 1.66,1.85 1.71,1.852NDO-M2 1.50,1.65 1.66,1.72

2NDO-1STO-M1 1.59,1.85 1.72,1.922NDO-1STO-M2 1.59,2.64 1.72,2.48

4THO-1STO 0.96,0.97 1.08,1.284THO-2NDO 0.98,1.02 1.12,1.22

21 1STO 1.46,2.09 1.66,3.112NDO-M1 1.22,2.14 1.32,3.152NDO-M2 1.16,2.02 1.17,3.03

2NDO-1STO-M1 1.22,2.04 1.41,3.162NDO-1STO-M2 1.46,2.18 1.46,3.21

4THO-1STO 0.86,1.98 0.82,2.944THO-2NDO 0.86,2.06 0.87,2.95

26 1STO 1.00,1.73 1.73,1.862NDO-M1 1.07,1.42 1.63,1.772NDO-M2 0.93,1.28 1.33,1.99

2ND-1STO-M1 1.00,1.41 1.73,1.742NDO-1STO-M2 1.17,1.74 1.72,1.72

4THO-1STO 0.78,1.09 1.37,1.654THO-2NDO 0.83,1.09 1.40,1.70

CNR Estimation 52

Table 6.4: 4THO-1STO, CNR standard deviation [dBHz] for PL data, Nc = 200.SinglePL MultiplePL

SET Method Used thresh. std (Reference, Indoor) std (Reference, Indoor)1 Threshold π/2 0.97,1.17 0.82,1.63

π 0.40,1.16 0.58,1.482π/3 0.63,1.20 0.99,1.60

Signum 0.73,1.41 1.14,1.90

2 Threshold π/2 0.45,3.15 0.79,3.36π 0.26,2.86 0.37,3.18

2π/3 0.97,3.00 0.87,3.26Signum 1.35,3.52 0.98,4.02

3 Threshold π/2 0.48,3.48 0.50,3.60π 0.22,3.43 0.36,3.54

2π/3 0.81,3.49 0.97,3.63Signum 1.21,3.56 1.30,3.62

4 Threshold π/2 0.81,4.01 0.82,1.63π 0.41,3.84 0.69,1.36

2π/3 0.89,4.00 0.99,1.60Signum 0.99,4.25 1.17,1.90

5 Threshold π/2 0.81,1.76 1.05,1.63π 0.46,1.28 0.75,1.28

2π/3 0.99,1.73 0.97,1.46Signum 1.41,2.01 1.17,1.77

CNR Estimation 53

Table 6.5: 4THO-1STO, CNR standard deviation [dBHz] for satellite data, Nc = 200.CorridorSAT RoomSAT

PRN Method Used thresh. std (Reference, Indoor) std (Reference, Indoor)3 Threshold π/2 1.22,3.62 1.92,2.94

π 1.10,3.54 1.14,2.632π/3 1.16,3.59 1.41,2.93

Signum 1.42,3.76 1.54,3.55

15 Threshold π/2 2.04,2.66 2.18,2.67π 1.83,2.30 1.99,2.47

2π/3 2.05,2.70 2.22,2.86Signum 2.26,3.17 2.40,3.19

16 Threshold π/2 1.47,2.26 1.47,2.27π 1.29,2.15 1.31,2.19

2π/3 1.48,2.27 1.41,2.44Signum 1.97,2.53 1.56,2.62

18 Threshold π/2 1.13,1.14 1.40,1.48π 0.96,0.97 1.08,1.28

2π/3 1.07,1.43 1.41,1.94Signum 1.37,1.74 1.78,2.00

21 Threshold π/2 1.12,2.07 0.94,3.18π 0.86,1.98 0.82,2.94

2π/3 0.94,2.16 0.99,3.09Signum 1.66,2.40 1.54,3.55

26 Threshold π/2 1.09,1.29 1.45,1.73π 0.78,1.09 1.37,1.64

2π/3 1.00,1.20 1.41,1.78Signum 1.63,1.75 1.54,2.33

Table 6.6: 4THO-1STO, mean CNR [dBHz] for PL data, Nc = 200.SinglePL MultiplePL

SET Reference Indoor Fade Reference Indoor Fade1 46.32 41.66 4.66 43.59 31.35 12.242 47.99 41.05 6.94 46.00 34.21 11.793 45.57 39.20 6.37 45.96 34.19 11.774 49.76 40.29 11.47 44.34 30.72 13.625 49.12 40.52 10.60 42.34 31.22 11.12

CNR Estimation 54

Table 6.7: 4THO-1STO, mean CNR [dBHz] for satellite data, Nc = 200.CorridorSAT RoomSAT

PRN Reference Indoor Fade Reference Indoor Fade3 41.68 22.96 18.20 39.94 20.57 19.3715 39.40 20.50 18.90 40.29 19.62 20.6721 42.31 23.10 19.21 40.46 20.76 19.7018 38.94 20.18 18.76 40.15 19.45 20.7021 39.85 21.74 18.11 39.88 19.15 20.7326 42.04 23.71 18.33 39.80 21.16 18.64

0 20 40 60 80 100 1200

5

10

15

20

25

30

35

40

45

50

Time (sec)

CN

R e

stim

ates

(dB−

Hz)

SET−2, SinglePL,Mean CNR (Ref, Indoor) =[47.9875 41.0507] dB

RefIndoorFades

0 20 40 60 80 1005

10

15

20

25

30

35

40

45

50

Time (sec)

CN

R e

stim

ates

(dB−

Hz)

SET−2, MultiplePL,Mean CNR (Ref, Indoor) =[46.0074 34.2083] dB

RefIndoorFades

0 10 20 30 40 50 6010

15

20

25

30

35

40

45

Time (sec)

CN

R e

stim

ates

(dB−

Hz)

PRN 15, CorridorSAT,Mean CNR (Ref, Indoor) =[39.3967 20.5097] dB

RefIndoorFades

0 10 20 30 40 50 605

10

15

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25

30

35

40

45

50

Time (sec)

CN

R e

stim

ates

(dB−

Hz)

PRN 15, RoomSAT, Mean CNR (Ref, Indoor) =[40.2955 19.6254] dB

RefIndoorFades

Figure 6.9: Examples of CNR estimates and the fades for PLs (upper) and satellite (lower)data, Nc = 200 ms.

CNR Estimation 55

2NDO-1STO-M1 and 2NDO-1STO-M2 have lower computational complexity comparedto the estimators using higher order moments. The simulation shows that 2NDO-1STO-M1 gives the best results among these three estimators. From the measurement baseddata same conclusion has been obtained. The most computational efficient estimators are1STO and 2NDO-M2. But these estimators are not best in terms of RMSE. However, forsingle-path case, 1STO shows quite acceptable results in terms of RMSE. If RMSE (forsimulation), std (for measurement data) and computational complexity are considered,then 2NDO-1STO-M1 will be the best estimator. However, in this thesis, the author haschosen the best estimator in terms of RMSE (for simulation) and std(for measurementdata).

Chapter 7

Channel models based on measurementdata

This chapter discusses channel modeling based on the measurement data obtained in themeasurement campaigns described in Chapter 4. The fading distribution of the indoorsignal is compared with the Rayleigh [48], Rice [24, 48], Nakagami-m [27, 49], LogNormal [48], and Loo [31] discussed in Chapter 2 and combined distributions discussedin the first section of this chapter. This chapter first presents the proposed fading channelmodel. Then, it discusses the results of fading distribution matching. Following that, itdiscusses the number of paths and time dispersion parameters of the indoor signals. Thistype of results were previously presented in [20] and [26] for a total of 4 sets of PL dataand 2 sets of satellite data, respectively. More detailed analysis has been performed byusing more PL data as well as satellite data in this thesis.

7.1 Proposed combined fading channel models

According to [20], no fading distribution matches fully with the PL data. So it is interest-ing to check the combined distributions also for better match. The following models aredeveloped consisting of weighted distribution of Nakagami, Log-normal, Rayleigh andLoo distributions.

fCombined−M1(w) = C fNaka(w)+D fLogn(w)+E fRayl(w)fCombined−M2(w) = E fNaka(w)+D fLogn(w)+C fRayl(w)fCombined−M3(w) =

√(D2−E2) fLoo(w)+

√(C2 +D2) fLogn(w)

(7.1)

where C, D and E are the weighting factors representing the probability of having

56

Channel models based on measurement data 57

single path, 2-3 paths and more than 3 paths, respectively, and fRayl, fLogn, fNaka, fLoo

are the Rayleigh, Log-normal, Nakagami-m and Loo PDFs, respectively. The weightingfactors are estimated from the measurement data by computing the true channel peaks ofCIR amplitudes. All the peaks above a threshold of 2.5 ∗mean(CIR) are considered asthe true channel peaks. Example Plots of combined distributions are shown in Figure 7.1.

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7Combined PDF

Combined−M1Combined−M2Combined−M3

Figure 7.1: Different combined distributions

7.2 Fading distribution matching

7.2.1 Pseudolite results

The best fit with theoretical distributions (of the instantaneous and averaged amplitudedistributions) is searched by minimizing the Mean Square Error (MSE) between mea-surement data CDF and theoretical distribution CDF. The probability that the envelope ofthe received signal does not exceed a specified value, W is given by corresponding CDFand can be defined in terms of PDF in the following way [39]:

F(W ) =∫ W

0f (w)dw (7.2)

The CDF is computed for each theoretical distribution as well as for the measurementdata distribution. The best theoretical distribution is then chosen based the minimumMSE between the theoretical CDF and the measurement data CDF. The LOS delay iscomputed in two ways: either as the delay corresponding to the peak of the referencesignal τLOS,re f (using the fact that the two receivers are synchronized), or as the delay of


the global peak in the wireless signal τpeak,air. According to the minimization criterion,the results are shown in Table 7.1 and Table 7.2 for different PL data. The notations, M1,M2 and M3 represent the three combined PDFs discussed in the previous section. Thetables show both best amplitude distribution fits at τLOS,re f and τpeak,air. A p sign is addedin the tables to present best amplitude distribution at τpeak,air. For example, (Rayl, M1p)means that Rayleigh is the best fit at τLOS,re f and M1 is the best fit at τpeak,air. The firstrow of these tables shows the best fit for instantaneous amplitude distribution (Nc = 1),and the last two rows show the best fit for averaged amplitude distribution, for Nc = 50and Nc = 200 ms coherent integration.

Table 7.1: Best amplitude distribution fit at τLOS,re f and τpeak,air, SinglePLNc SET 1 SET 2 SET 3 SET 4 SET 51 ms Rayl, Raylp Rayl, Ricep M1, M1p M1, M1p M1, M1p

50 ms M1, M1p M1, M1p M1, M1p M1, M1p M1, M1p


Table 7.2: Best amplitude distribution fit at τLOS,re f and τpeak,air, MultiplePLNc SET 1 SET 2 SET 3 SET 4 SET 51 ms Rayl, Lognp Rayl, M2p Rayl, Ricep M2, Lognp M2, Raylp


200 ms M2, M2p M2, M2p M2, M2p M2, M2p Logn, M2p

It is observed that for SinglePL, the best distribution for the instantaneous ampli-tudes is surely Combined-M1 distribution with a few exceptions. For averaged amplitudes(Nc = 50 and Nc = 200) of SinglePL, still Combined-M1 is the best fit. For MultiplePL,Combined-M2 distribution is the best match with some exceptions. The MSE betweentheoretical and measured distributions are shown for SET-1, SinglePL in Table 7.3 andTable 7.4 for the distribution matching at τLOS,re f and at τpeak,air, respectively. The corre-sponding few PDF matching plots are shown in Figure 7.2. The upper and lower plots arefor the distribution matching at τLOS,re f and τpeak,air respectively.

7.2.2 Satellite results

The best fit with theoretical distributions (of the instantaneous and averaged amplitudedistributions) of the satellite data for PRN 3, 15, 16, 18, 21 and 26 are searched in similar


Table 7.3: MSE between the theoretical and measured distributions at τLOS,re f , SET-1,SinglePL

Nc Rayl Rician Naka-m Loo Logn M1 M2 M31 ms 0.0056 0.0060 0.0107 0.0057 0.0347 0.0089 0.0062 0.034050 ms 0.0316 0.0354 0.0099 0.0354 0.0346 0.0075 0.0271 0.0341200 ms 0.0328 0.0390 0.0142 0.0390 0.0258 0.0120 0.0275 0.0254

Table 7.4: MSE between the theoretical and measured distributions at τpeak,air, SET-1,SinglePL

Nc Rayl Rician Naka-m Loo Logn M1 M2 M31 ms 0.0101 0.0077 0.0145 0.0080 0.0248 0.0130 0.0087 0.024550 ms 0.0305 0.0344 0.0108 0.0343 0.0299 0.0083 0.0265 0.0295200 ms 0.0322 0.0381 0.0159 0.0381 0.0217 0.0133 0.0277 0.0213

0 0.5 1 1.5 2 2.5

x 104

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F

Amplitude distribution, indoor channel, Nc=1 ms

RayleighRice.Nakagami−m.LooLog−normalCombined−M1Combined−M2Combined−M3Measurements

0 0.5 1 1.5 2 2.5

x 104

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Amplitude CDF, indoor channel, Nc=1 ms


0 0.5 1 1.5 2 2.5 3

x 104

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CD

F



Figure 7.2: PDF and CDF matching based on wireless signal instantaneous amplitude atτLOS,re f (upper) and τpeak,air (lower), SET-1, SinglePL, Nc = 1 ms.


way as for PLs and the results are shown in Tables 7.5 and 7.6. The same type of tablerepresentations are used as for PLs (i.e., the meaning of p is same as for PLs).

Table 7.5: Best amplitude distribution fit at τLOS,re f and τpeak,air, CorridorSATNc PRN 3 PRN 15 PRN 16 PRN 18 PRN 21 PRN 261 ms M2, M2p M2, M3p Rayl, M3p M2, M3p M2, M3p M2, M3p

50 ms M1, Lognp M2, M3p M3, M3p M2, M3p M2, M3p M2, M3p

200 ms M3, Lognp M2, M3p M3, M3p M2, M3p Rayl, M3p M2, Nakap

Table 7.6: Best amplitude distribution fit at τLOS,re f and τpeak,air, RoomSATNc PRN 3 PRN 15 PRN 16 PRN 18 PRN 21 PRN 261 ms M2, M3p M2, M3p M2, M3p M2, M3p M2, M3p M2, M3p

50 ms M3, M3p M3, M3p M3, M3p M3, M3p M3, M3p M3, M3p

200 ms M3, M3p Naka, M3p M3, M3p M1, M3p M1, M3p M3, M3p

For the CorridorSAT , the best distribution fit corresponding to τLOS,re f is Combined-M2 distribution and the best distribution fit corresponding to τpeak,air is Combined-M3distribution. For RoomSAT , it is seen that the best fading distribution is Combined-M3for both τLOS,re f and τpeak,air. An example of PDF matching with theoretical distributionis shown in Figure 7.3 for PRN 21, CorridorSAT . The upper and lower plots are for thedistribution matching at τLOS,re f and τpeak,air, respectively.

The combined distributions do not seem good enough for satellites, in the sense thatthey depend on the environment. That is why, the ’next best fit’, meaning the best match-ing among all the other distributions, except the combined ones are presented in Table7.7 and Table 7.8 for CorridorSAT and RoomSAT , respectively. From these tables, it isseen that no distribution matches perfectly with the measured distribution. So, it can bestated that combined distributions offer some degree of good match, but no distributionfits perfectly with the satellite data.

Table 7.7: The ’next best fit’ amplitude distribution fit at τLOS,re f and τpeak,air,CorridorSAT

Nc PRN 3 PRN 15 PRN 16 PRN 18 PRN 21 PRN 261 ms Rayl, Lognp Rayl, Lognp Rayl, Raylp Rayl, Lognp Rayl, Lognp Rayl, Nakap

50 ms Logn, Lognp Rayl, Lognp Logn, Lognp Rayl, Lognp Rayl, Lognp Rayl, Nakap

200 ms Logn, Lognp Naka, Nakap Logn, Lognp Naka, Nakap Rayl, Lognp Naka, Nakap


0 500 1000 1500 20000

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0 500 1000 1500 20000

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Figure 7.3: PDF and CDF matching based on wireless signal instantaneous amplitude atτLOS,re f (upper) and τpeak,air (lower), PRN 21, CorridorSAT , Nc = 1 ms.

Table 7.8: The ’next best fit’ amplitude distribution fit at τLOS,re f and τpeak,air, RoomSATNc PRN 3 PRN 15 PRN 16 PRN 18 PRN 21 PRN 261 ms Rayl, Lognp Rayl, Lognp Rayl, Raylp Rayl, Lognp Rayl, Lognp Rayl, Nakap

50 ms Logn, Lognp Rayl, Lognp Logn, Lognp Rayl, Lognp Rayl, Lognp Rayl, Nakap

200 ms Logn, Lognp Naka, Lognp Logn, Lognp Naka, Lognp Naka, Lognp Naka, Nakap


7.3 Average path number and time dispersion parame-ters

The number of paths is searched from the indoor CIR estimates over 200 ms. The localpeaks of CIR amplitudes are detected and all the local peaks higher than a certain thresh-old are considered as true channel peaks. The chosen threshold is 2.5∗mean(CIR). Thescaling factor in the threshold is chosen according to the trial and error basis with thetarget of estimating correct number of paths in the indoors. Also, in order to comparedifferent multi-path channels, time dispersion parameters such as the mean excess delayand RMS delay spread discussed in Chapter 2 are computed for each set of measurementdata.

7.3.1 Pseudolite results

For the PLs, one example CIR snapshot with the specified threshold is shown in Figure7.4. The number of peaks is computed from this type of CIRs and its mean, maximum andstandard deviation are shown in Table 7.9. The table shows that there can be 1-2 pathsfor PL signals. The MultiplePL contains more paths than SinglePL due to the use ofmultiple PLs. It is observed from CNR estimation results of Chapter 6 that MultiplePLsignal is noisier than SinglePL and can be verified by checking higher mean, standarddeviation and maximum values of the paths from the table. It is also observed from thesimulation results that in the PL data, only one path is detected most of the times witha few exceptions of detecting two or more paths. The average, maximum, and standarddeviation of the successive path spacing, when more than 1 path is present, are given inTable 7.10. Clearly, if more that 1 path is present, the successive paths are spaced at veryshort distance from the first one. Also, the RMS delay spread and the mean excess delayare given in Table 7.11. Here, it is needed to mention that one chip delay means 977.5 nsand corresponds to 293.25 m error distance. RMS delay spreads of few meters are noticedwhich are as expected in such indoor scenarios.

7.3.2 Satellite results

For the satellites, one example CIR snapshot with the specified threshold is shown inFigure 7.5. The number of peaks is computed from this type of CIRs and its mean,maximum and standard deviation are shown in Table 7.12. The table shows that therecan be 1-2 paths for satellite signals also. However, the RoomSAT contains more pathsthan CorridorSAT due to more multi-paths in rooms. It is also observed from the results


−8 −6 −4 −2 0 2 4 6 80

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CIR

env

elop

e

RefIndoorthreshold

−8 −6 −4 −2 0 2 4 6 80

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CIR

env

elop

e

RefIndoorthreshold

Figure 7.4: Example snapshots of CIR envelope and threshold, SET-5, SinglePL.

Table 7.9: Estimated number of channel paths (indoor channel) for PLSinglePL MultiplePL

SET mean std max mean std max1 1.17 0.43 5 1.16 0.40 42 1.14 0.41 4 1.12 0.60 63 1.07 0.43 6 1.18 0.68 54 1.04 0.19 2 1.20 0.56 55 1.07 0.29 3 1.18 0.62 4

Table 7.10: Successive path spacing (indoor channel) for PL in [chips].SinglePL MultiplePL

SET mean std max mean std max1 0.10 0.30 1.43 0.03 0.14 1.372 0.12 0.36 1.16 0.07 0.08 1.313 0.03 0.19 1.19 0.04 0.10 1.854 0.03 0.17 1.38 0.06 0.15 1.915 0.05 0.22 1.37 0.07 0.21 1.75


Table 7.11: Average RMS delay spread and average excess delays for PL.SinglePL MultiplePL

SET RMS [ns] Excess delay [ns] RMS [ns] Excess delay [ns]1 0.65 2.19 14.84 34.012 0.51 2.07 34.30 81.973 15.35 43.98 36.29 92.224 10.33 27.08 20.93 70.125 7.30 20.60 34.22 79.12

of the analysis that the probability of detecting single path in CorridorSAT data set isslightly higher than that of RoomSAT . Sometimes up-to 6 paths are noticed in both of thedata sets. The average, maximum, and standard deviation of the successive path spacing,when more than 1 path is present, are given in Table 7.13. This table shows that the pathsare very closely spaced for both satellite data sets, if more than 1 path is present. Again,RMS delay spread and the mean excess delay are given in Table 7.14. The computedRMS and mean excess delay are much higher than the PL results. However, the valuesare still within one chip and gives few tens of meters of error distance.

−8 −6 −4 −2 0 2 4 6 80

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CIR

env

elop

e

ReferenceReceivedthreshold

−8 −6 −4 −2 0 2 4 6 80

0.5

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Delay error [chips]

CIR

env

elop

e

ReferenceReceivedthreshold

Figure 7.5: Example snapshots of CIR envelope and threshold, PRN 3, CorridorSAT .


Table 7.12: Estimated number of channel paths (indoor channel) for satellitesCorridorSAT RoomSAT

PRN mean std max mean std max3 1.28 0.53 3 1.35 0.64 515 1.22 0.48 4 1.20 0.47 316 1.26 0.58 4 1.34 0.66 518 1.39 0.76 5 1.38 0.79 621 1.19 0.46 3 1.32 0.62 426 1.2 0.5 4 1.31 0.71 5

Table 7.13: Successive path spacing (indoor channel) for satellites in [chips].CorridorSAT RoomSAT

PRN mean std max mean std max3 0.19 0.66 6.43 0.05 0.29 3.81

15 0.24 1.3 7.16 0.20 0.91 6.1216 0.13 0.7 6.19 0.09 0.44 4.9318 0.22 1.13 7.93 0.15 0.70 5.6021 0.17 0.95 9.9 0.19 0.85 6.8126 0.10 0.68 8.5 0.10 0.48 5.91

Table 7.14: Average RMS delay spread and average excess delays for satellites.CorridorSAT RoomSAT

PRN RMS [ns] Excess delay [ns] RMS [ns] Excess delay [ns]3 78.89 189.30 26.24 62.92

15 74.49 239.80 70.16 218.0016 62.68 162.11 40.54 109.9718 88.82 219.00 74.21 172.6021 70.03 167.91 82.64 215.9826 47.39 133.50 77.5 172.22


7.4 Comparison between pseudolites and satellite results

From the results of the PLs and satellites, it was observed in Chapter 6 that the indoorCNR of PLs was higher than that of satellites. In the current chapter, it is also observedthat higher number of paths are available in the satellite signals in comparison to the PLs.However, more closely spaced paths are observed in the PLs. But in both PLs and satellitedata, the path spacing is less than one chip. The RMS delay and mean excess delay forthe satellite data is higher than those of the PLs, as expected. But still these values arewithin one chip.

Chapter 8

Conclusions and Future Works

The conclusions of the work, some discussions, and possible future research topics arepresented in this chapter. Even though it is impossible to make one final conclusion dueto the wide topic area of the thesis, all the main results are presented in this chapter inbrief manner.

8.1 Conclusions

Based on the simulation based BOC modulated signal and measurement based BPSKsignal from the PLs and satellites, an analysis of the CNR estimators has been performedfor the purpose of identifying the most robust CNR estimator. It was noticed that theproposed 4THO-1STO estimation method showed the lowest RMSE to estimate the CNRfor the simulation based SinBOC(1,1) modulated signal. It was also noticed that 4THO-1STO was the most robust in the GPS based PLs and satellites signals.

Based on measurement data of PLs and using the GPS C/A signal, an analysis ofthe indoor fading channel model was also performed for the purpose of deriving a goodchannel model for GPS signals in the typical indoors. It was noticed that the amplitudevariations can be best modeled by the proposed Combined-M1 (combination of Nak-agami, Log-normal and Rayleigh) distribution for single PL measurements. For multiplePLs measurements, the proposed Combined-M2 (combination of Nakagami, Log-normaland Rayleigh with different weighting factors than Combined-M1) was the best fit. It wasalso noticed that typical indoor channels have few paths spaced at short distances (i.e., lessthan 1 chips). The RMS delay spreads were also within one chip, or few hundred meters.For the satellite measurements, combined distributions offer some degree of good match,but no distribution fits perfectly with the satellite data. In the corridors, it was noticed thatthe indoor signal’s amplitude variations corresponding to the peak of the reference signal

67

Conclusions and Future Works 68

can be best modeled by Combined-M2 distribution. However, for the satellite measure-ments in the office rooms, it was noticed that the amplitude variations can be best modeledby Combined-M3 (combination of Loo and Log-normal) distribution.

8.2 Future Works

In this thesis, the focus was on SinBOC(1,1) as the candidate BOC modulation. However,this work can be extended as analyzing the performance of these estimators for otherrepresentative BOC modulation such as CosBOC(15,2.5), CosBOC(10,5) and especiallyMBOC that has been chosen as the modulation technique for the future Galileo OS signalat L1 frequency, and also by GPS for its modernized L1C (i.e., L1 Civil) signal in therecent studies.

The future research also focuses on the update the moment-based estimators by up-dating the assumptions of the statistical averages of the peak and out-of-peak points toachieve better CNR estimates.

Finally, although the CNR estimators are tested for GPS based measurement data, itwould be beneficial to test the estimators in the measured Galileo data and also derivethe channel model for measurement based Galileo signals, provided that Galileo signalsbecome available from the sky.

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Appendix: Phase variation and Delayerror estimation

Phase variation

The estimation of the phase between the I and Q components of the correlator outputis carried out for all the measurement data and few snapshots for few data sets are shownin Figure A.1. The measured phase of the received signal is analyzed over the course ofthe data sets to detect any instances of severe phase change, which may indicate changingmulti-path conditions. The figure shows the phase estimates only for few seconds for bet-ter understanding. Theoretically, the phase shape should remain relatively constant over aperiod multiple of 20 ms in the presence of navigation data. In the absence of navigationdata, the mean of the phase should be around 0. The phase estimates shown in the figureare in the absence of the navigation data. But still, some phase changes are found. Anychange in the shape can be explained by the presence of the multi-path propagation.

The carrier phase measurements are useful for LOS estimation if there is a clear singlepath. But, the multi-paths are mostly available in the indoors and it can be considered asa major source of errors. Several techniques can be found from the literature for dealingwith the problem of carrier phase multi-paths. An well-known technique for mitigatingthe carrier phase multi-paths is the Multi-path Estimating Delay Lock Loop (MEDLL)which detects and removes the multi-paths. But, its implementation is very complex.Another technique is found in the literature based on the electromagnetic modeling thatcan model and remove errors in the carrier phase observation.

74

Appendix A: Phase variation and Delay error estimation 75

0 50 100 150 200−4

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Figure A.1: Phase estimates of the indoor signals for PLs (upper plots) and satellites(lower plots), Nc = 1 ms.

Appendix A: Phase variation Delay error estimation 76

Delay error estimation

The delay of the global peak based on the indoor signal is compared with the delay ofthe global peak from the reference signal, in order to find out more about the LOS errordistribution. The histograms of the peak delay differences are illustrated in Figure A.2.The upper plots of the figure are for PLs while the lower two plots are for satellites. Onlyfour example plots are shown for four data sets. From the PL plots, it is possible to findthat most of the times either there is 0 LOS delay error or very short delay error withinone chip. But for the satellites data, although less than one chip delay error is found mostof the times, still there is some possibility of getting longer delay error. Similar types ofresults were obtained for other PL sets and satellite PRNs.

−4 −3 −2 −1 0 1 2 3 40

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PRN 16, RoomSAT, Histogram of delay error

Delay difference (Indoor peak−Reference peak) [chips]

His

togr

am (%

)

Figure A.2: LOS delay error based on the comparison between reference and air signalsfor PLs (upper plots) and satellites (lower plots), Nc = 200 ms.

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