Master of Science Thesis

Transcription

1 TAMPERE UNIVERSITY OF TECHNOLOGY Department of Information Technology Institute of Communications Engineering Danai Skournetou DELAY ESTIMATORS FOR TRACKING LOW CNR GNSS SIGNALS Master of Science Thesis Examiners: Dr. Elena-Simona Lohan and Prof. Markku Renfors Examiner and topic approved in the Information Technology Department Council meeting on the 20th of August 2007

2 Abstract TAMPERE UNIVERSITY OF TECHNOLOGY Master s Degree Program in Information Technology Danai Skournetou : DELAY ESTIMATORS FOR TRACKING LOW CNR GNSS SIGNALS Master of Science Thesis, 95 pages, 5 Appendix pages October 2007 Major: Digital transmission Examiners: Dr. Elena Simona Lohan and Prof. Markku Renfors Keywords: GNSS, Galileo, code tracking, CNR estimation, multipath The emergence of new Global Navigation Satellite System (GNSS) applications and the continuous demand for Quality of Service set stricter requirements on the accuracy of positioning. Moreover, high accuracies are nowadays required in critical environments for GNSS, such as densely urban areas and indoor areas, where we have to cope with the unwanted effects of multipath propagation and low Carrier to Noise Ratios (CNRs). Code tracking is one of the main functions of a GNSS receiver and its task is to give an accurate estimate of the code delay, which is further used to calculate the pseudorange and consequently the position solution. Therefore, designing accurate code delay estimators is a timely topic. This thesis deals with the challenging problem of code delay estimation in multipath and low CNR environments. The research methodology consists of two parts, the method development and the method evaluation. The development part follows the conceptual analytical approach and it is based on the Divide and Conquer method. The evaluation part is based on computer simulations. This thesis has two main contributions. First, it proposes a novel CNR identifier, that distinguishes between indoor and outdoor environment. The results suggest that the use of the proposed CNR estimator can lead to a successful distinction between indoor and outdoor environment for 95% of the cases, while retaining the success rate above 67% even in the worst case scenario. Second, a novel method for code delay estimation in multipath and low CNR environment, called, is proposed. It is shown that is very robust at low CNRs in terms of Mean Time To Lose Lock for both static and fading multipath channel profiles and for both Galileo and GPS signal types. Moreover, performs very well in terms of Root Mean Square Error when static channel is considered, while its performance deteriorates at higher CNRs in the case of fading channel. i

3 Preface This Master of Science Thesis has been written for the Department of Information Technology at the Tampere University of Technology, Tampere, Finland. This work was carried out in the projects Advanced Techniques for Personal Navigation (ATENA) and Future GNSS Applications and Techniques (FUGAT), both funded by the Finnish Funding Agency for Technology and Innovation (Tekes). I would like to express my gratitude to my supervisor Prof. Markku Renfors for trusting in me, for offering me a research position in the Institute of Communication Engineering, for supporting me during my studies and for his very useful comments on the thesis. I deeply thank my supervisor Dr. Elena Simona Lohan for being for me a role model in research, for encouraging me, for being available whenever I needed, for giving me research freedom and for the very good student-supervisor relationship. I am also very grateful to Tarja Erälaukko, Ulla Siltaloppi and Elina Orava for being always smiling, sweet and helpful. I would like to express my appreciation to lecturer Jukka Koskinen for teaching me a lot on Master thesis writing and project management. I am thankful to my project colleagues Hu Xuan and Nazmul Islam for offering me their help whenever I needed and for sharing their opinions with me. Moreover, I would like to say to my work colleagues, Toni Levanen, Tero Isotalo and Yaning Zou, that they have supported me with their friendship and that they are one of the reasons I like so much my work environment. I am thankful to all of my friends in Greece, that they did not let the distance to fade our friendship and they have been always standing by me. Especially, I thank Petros for being a very good friend and for making Finland look more like home. Many thanks to my parents Giorgos and Vasiliki, my sister Juli and my aunts Despoina and Gianna for believing in me, supporting me and being happy for me. At the end, I want to deeply thank my loved, Artem, for helping me, supporting me, advising me, believing in me, taking care of me and truly loving me. ii

4 Contents List of Abbreviations List of Symbols v viii 1 Introduction 1 2 Background Satellite-Based Positioning Navstar Global Positioning System Galileo Galileo Services Galileo Signals Binary Offset Carrier Modulation Galileo/GPS Key Differences Code Synchronization in GNSS Signal Acquisition Search methods Detection Signal Tracking Code Tracking Carrier Tracking Research Methodology 25 5 Novel Contributions CNR Estimation Level Crossing Rate Concept LCR-Based CNR Identifier Multipath/Noise Mitigation Code Delay Estimation iii

5 CONTENTS iv 5.4 Procedure Simulation Results and Performance Analysis CNR Estimation Code Delay Estimation Simulation Parameters and Performance Criteria Results for SinBOC(1,1)-modulated signals Results for BPSK-modulated signals Conclusions and Future Work 69 Appendix A: Improved, and 71 References 76

6 List of Abbreviations Acf Averaged Correlation Function ACF AutoCorrelation Function AWGN Additive White Gaussian Noise AltBOC Alternative Binary Offset Carrier AME Absolute Mean Error BOC Binary Offset Carrier BPSK Binary Phase Shift Keying C/A Coarse/Acquisition CDBOC Complex Double Binary Offset Carrier CDMA Code Division Multiple Access CNR Carrier-to-Noise-Ratio CosBOC Cosine Binary Offset Carrier CRC Cyclic Redundancy Check CS Commercial Service DaC Divide and Conquer Differential Order 2 Discontinuity Tracker DLL Delay Locked Loop DoD Department of Defense DP Discontinuity Point DS Direct Sequence DS-CDMA Direct Sequence-Code Division Multiple Access DSP Digital Signal Processing DSSS Direct Sequence Spread Spectrum E Early Early Late Slope EML Early Minus Late EU European Union ESA European Space Agency FEC Forward Error Correction v

7 LIST OF ABBREVIATIONS vi FLL GLONASS GNSS GPS GPST GST I I&D L LCR LOS MBOC MEO MGD MTLL NCO n-dp NLOS OS P PAC p-dp PDP PLL PPS PRN PRS PSD PT PTF Q QoS RMSE Frequency Locked Loop GLobal Orbiting NAvigation Satellite System Global Navigation Satellite System Global Positioning System Global Positioning System Time Galileo System Time High Resolution Correlator In-phase Integrate and Dump Late Level Crossing Rate Line-Of-Sight Multiplexed Binary Offset Carrier Medium Earth Orbit Matched Filter Multiple Gate Delay Mean Time To Lose Lock Numerically Controlled Oscillator negative-discontinuity Point Narrow Early Minus Late Non-Line-Of-Sight Open Service Precision Pulse Aperture Correlator positive-discontinuity Point Power Delay Profile Phase Locked Loop Precise Positioning Service Pseudo-Random Noise Precise Regulated Service Power Spectral Density Peak Tracking Precise Time Facility Quadrature-phase Quality of Service Root Mean Square Error

8 LIST OF ABBREVIATIONS vii RNSS SAR SinBOC SoL SPS STD TAI ToA US USNO UTC WCDMA Radio Navigation Satellite Service Search And Rescue service Sine Binary Offset Carrier Safety of Life Standard Positioning Service STandard Deviation International Atomic Time Time-of-Arrival Teager Kaiser United States United Sates Naval Observatory Coordinated Universal Time Wideband Code Division Multiple Access

9 List of Symbols α Fading amplitude α Position of the maximum LCR in the Ac f Level α l α 1 α sim γ δ(t) f D η ξ PDP Π( ) τ τ τ l EML m ρ Complex channel coefficient of the l-th path Average amplitude of the l-th path Averaged Acf Level of max LCR based on the simulations-based LCR Decision threshold Dirac pulse Double Delta correlator Residual Doppler error AWGN noise Power decaying profile coefficient Rectangular pulse of unit amplitude and unit support Delay error Estimated delay Channel delay introduced by the l-th path Early-late chip spacing Early-late chip spacing for EML Code epoch index Pseudorange Ac f Level Vector of Acf levels (equal to [0.01 : 0.01 : 1]) Ac f thresh Threshold chosen for Acf n-th complex data symbol b n bn Estimated n-th complex data symbol B W c k,n CandDiscont CurExcArea Di f f 2 thresh thresh E( ) Code epoch bandwidth k-th chip corresponding to the n-th symbol Candidate p-dps Current excluded area Threshold chosen for Threshold chosen for Expectation operation viii

10 LIST OF SYMBOLS ix E b ExcPerc f c f d f d f s J k Level thresh L p aths m thresh N B N c N interp N nc N s PartArea(i) P TB (t) r(t) r i r u R R ( ) R R BOC R pulse s BOC (t) S(ε) S F t d Data bit energy Area exclusion percentage Spreading code rate Doppler shift Estimated Doppler frequency Subcarrier frequency Cost function Boltzmann constant (k = Joule/Kelvin) Matrix with the level thresholds for each (N c,n nc ) pair Number of paths Nakagami-m fading factor Threshold chosen for Modulation order Coherent integration time Interpolation number Non-coherent integration time Oversampling factor Area enclosed by the Acf and the level i from Ac f Level Pulse shaping filter Received signal Vector position of satellite i Vector position of user u Averaged correlation function Code epoch-by-epoch correlation Averaged non-coherent correlation function Auto-correlation of BOC modulation Pulse shaping autocorrelation function BOC modulating waveform Error signal Spreading factor Time bin T 0 Room temperature (T 300K) T B T c T K thresh Pulse duration Chip period Threshold chosen for

11 LIST OF SYMBOLS x TotArea T sym x re f ( ) Total are enclosed by Acf Symbol period Reference modulated PRN code

12 Chapter 1 Introduction Satellite-based navigation is a leading-edge technology that has reached everyday use with a continuously growing market. The concept of autonomous geo-spatial positioning with global coverage was created in mid-1970s and led the United States (U.S.) Department of Defense (DoD) to begin pursuing the idea of developing a Global Navigation Satellite System (GNSS). The efforts of U.S. government resulted to the creation of Global Positioning System (GPS), the first of its kind, which was originally meant only for military use. By the time that GPS became fully operational, the advantages of such a system had become prominent and this gave the initiative for other countries to involve with GNSS development. GPS together with Global Orbiting Navigation Satellite System (GLONASS) are currently the only operational systems. In addition, the development of a new civil-controlled GNSS, Galileo, was initiated by the collaborative efforts between the European Union (EU) and the European Space Agency (ESA). The emergence of new GNSS applications and the continuous demand for Quality of Service (QoS) set stricter requirements on the accuracy of positioning. Moreover, high accuracies are nowadays required in critical environments for GNSS, such as densely urban areas and indoor areas, where we have to cope with low Carrier to Noise Ratios (CNRs). The accuracy depends greatly on the Digital Signal Processing (DSP) part of the GNSS receiver. Code acquisition and tracking are two of the main DSP functions of a GNSS receiver that play crucial role in the accuracy of the position solution. In acquisition, a search process takes place in order to find the visible satellites, producing coarse estimates of the code delay, τ, and the Doppler shifts f d. After the signal is acquired, the tracking module performs code, phase and Doppler shift tracking for (selected) visible satellite signals in order to obtain accurate estimates of the parameters. The estimate of the Line-Of-Sight (LOS) code delay is used to calculate the pseudorange and consequently the positioning solution. The accuracy of the final value of the code phase is 1

13 Introduction 2 strictly connected to the accuracy of the pseudorange measurement later on. In addition, if the tracking module fails to follow the code phase changes that occur over time, the signal needs to be acquired again and such re-acquisition process is considered to be quite time-consuming. Thus, the stage of code tracking is very critical when the GNSS receiver design is considered. Several code tracking algorithms (or code delay estimators) have been proposed in the literature both for GPS and Galileo signals. Given a certain sufficiently small Doppler shift, these algorithms are based on what is typically called a feedback delay estimator and they are implemented based on a feedback loop. The most known feedback delay estimators are the Delay Lock Loops (DLLs) [4, 11, 17, 25, 26, 54]. However, the classical DLLs fail to deal with the multipath propagation [79]. Therefore, researchers had to invent more sophisticated algorithms that would be multipath resistant, especially when the paths are closely spaced to each other. One class of these enhanced DLL techniques is based on the idea of narrowing the spacing between early and late correlators (i.e., narrow correlator class) [21, 41, 62]. Another class of enhanced DLL structures uses a modified reference waveform for the correlation at the receiver, that narrows the main lobe of the cross-correlation function, at the expense of a deterioration of signal power. Examples belonging to this class are the gated correlator [62], the strobe correlators [29, 41], the pulse aperture correlator [24], and the modified correlator reference waveform [41, 88]. Another category of improved DLL techniques uses some form of multipath interference cancellation, by estimating not only the delay of the LOS path, but also the delays, phases, and amplitudes of the Non-LOS (NLOS) paths [26, 54, 77]. Besides the multipath propagation, low CNR environments (e.g. urban areas, indoors) contribute also to the performance deterioration of the various delay estimators. This implies that CNR-adaptive signal processing methods can be of great potential in the GNSS context. Moreover, the emerging need for indoor positioning requires smart identifiers of the environment for successful distinction between indoor and outdoor. Typical CNR estimators for GNSS signals are based on the first and higher-order moments of the complex envelope of the received signal (e.g., second-order and fourth-order moments) [70, 76, 85] and they require rather heavy computations at the receiver. However, there are not so many CNR estimators for GNSS signals in the literature and the existing ones either fail to deal with low CNR conditions or they are too complex. To summarize the above discussion, CNR estimators for GNSS signals are still rather scarce, and multipathresistant delay estimators which are capable to cope with the various CNR levels are still to be found.

14 Introduction 3 The research problem this thesis is dealing with is the complex problem of code delay estimation in multipath and low CNR environments. The objective is to design a method capable of coping with the above-mentioned problems. The research methodology of this thesis consists of two parts, the method development and the method evaluation. The development part follows the conceptual analytical approach and it is based on the Divide and Conquer method (DaC). The evaluation part is based on computer simulations. In particular, we chose Monte Carlo type of simulation in order to represent in the most realistic way the effects due to the random nature of the transmission channel. The contributions of this thesis are multiple. First, we suggest an on/off type of CNR estimator, that distinguishes between indoor and outdoor environments. Second, we propose a method for code delay estimation in multipath and low CNR environment, called. Additional contributions of this thesis include the enhancement of an existing code delay estimator (namely Early Late Slope) and a wide overview of the various aspects of satellite navigation where the focus is on the field of code delay estimation in connection with the problems of multipath mitigation and CNR estimation. The remainder of this thesis is structured in the following manner: Chapter 2 presents the basic principles of satellite-based positioning and gives a brief history of Global Navigation Satellite Systems (GNSSs), focusing on the two main GNSSs, the American Navstar GPS and the European Galileo. Chapter 3 provides the basic principles of code synchronization in GNSS systems, focusing on the code tracking stage. Chapter 4 describes the research methodology, which was adopted in this thesis in order to deal with the research problem. Chapter 5 includes the main contributions of this thesis. Chapter 6 presents the simulations results together with the performance analysis. Chapter 7 provides the conclusions based on the findings as well as a discussion about the future work.

15 Chapter 2 Background This chapter presents the basic principles of satellite-based positioning and includes an overview of the history of Global Navigation Satellite Systems (GNSSs). The focus is put on the two main GNSSs, the Navstar Global Positioning System (GPS) and the European Galileo, as well as on their key differences in the signal processing level. We remark that more focus is on Galileo because it is a newer system and many of its challenges have not been fully addressed yet. 2.1 Satellite-Based Positioning Location-aware services have received increased attention during the last decade. It is not only the maturity of the market that contributed to the acceptance of such services, but also the remarkable progress that has been achieved in mobile positioning technologies. Several positioning techniques can be found in the literature which share common targets for increased accuracy and availability. These techniques can be divided into three major groups: handset-based, network-based and hybrid techniques. A detailed description of the various positioning methods can be found in [90]. The most important positioning techniques include the employment of satellite signals. These techniques belong to the handset-based group where the mobile device uses the signals transmitted by satellites in order to calculate its own position. In particular, the position determination using a GNSS is based on measuring the distances between the mobile device (GNSS receiver) and several satellites at known locations. The measured distance is defined as the pseudorange, ρ, the name of which implies that it is an estimate ( pseudo ) of the distance. If we denote the position of each satellite, i, with the vector r i = [x i y i z i ] T, and the position of the unknown mobile user with the vector r u = [x u y u z u ] T, then the pseudorange ρ is defined as: 4

16 Background 5 ρ i = r i r u = (x i x u ) 2 + (y i y u ) 2 + (z i z u ) 2 (2.1) In order to calculate the pseudorange, we measure the Time-Of-Arrival (TOA) of the transmitted satellite signal, which in combination with the known (but biased) transmission time gives the propagation time. When this propagation time is multiplied with the signal speed (speed of light), the result is the distance between the satellite and the receiver. From mathematical point of view, four satellites is the minimum required number for position determination, however, the higher the number of satellites is, the higher accuracy we can achieve. The above mentioned method is commonly known as triangulation or trilateration. The accuracy of the positioning method is hindered by the measurement errors which appear either in the form of noise or bias. Examples of such errors include satellite clock and ephemeris errors, or errors caused by atmospheric changes (in ionosphere and troposphere), multipath and receiver noise. In this thesis, we focus on the errors caused by multipath effects and noisy environments. However, the interested reader may refer to [63] for an excellent description of the various error sources in pseudorange measurements. The first country that took full advantage of the benefits of satellite positioning was United States. In 1973, Navy and Air Force programs, directed by U.S. government, were combined to form the Navigation Technology Program. This program later on evolved into the Navstar Global Positioning System, more commonly known as GPS. Originally, GPS was meant for military use only, however, the U.S. Department of Defense (DoD) soon realized the large benefits arising from the civilian use and GPS was defined to be free for the public. In 1976, the former Soviet Union began the development of its own GNSS, called GLObal NAvigation Satellite System (GLONASS). By 1995, GLONASS was fully operational till the time that Soviet Union collapsed when it fell into disrepair. It is estimated that GLONASS will become fully operational again, with the help of India, by China is also in process of expanding their regional navigation satellite system, called Beidou, into global. Galileo will be the Europe s own GNSS and, in contrast with GPS, it will be under civilian control. Galileo is the outcome of the European Satellite Navigation Program which is a joint initiative of the European Commission and the European Space Agency. Galileo will offer positioning and timing services worldwide. In the following sections we provide detailed information about GPS and Galileo systems.

17 Background Navstar Global Positioning System From architectural point of view, GPS consists of three components. First component is the space segment which includes a constellation of 24 satellites distributed in six orbital planes. Second GPS component is the control segment which consists of the master control station, monitor stations, and ground antenna upload stations. Each station has several GPS receivers that continuously track the visible GPS satellites. The master control station operates remotely the other stations and processes the received measurements to estimate the navigation data parameters, such as satellite orbits and clock errors. The third component comprises the user segment, which defines the GPS receiver equipment [93]. The position determination in GPS is done based on the method of triangulation, as it was discussed in section 2.1. The GPS signals are transmitted on two radio frequencies in the L-band, referred to as Link 1 (L1) and Link 2 (L2). The center frequencies of L1 and L2 correspond to the values of MHz and MHz respectively. GPS signals use a Direct Sequence Spread Spectrum (DSSS) technique, and they are based on Code Division Multiple Access (CDMA) principles [67, 82], needed for sufficient distinction among satellites. There are currently two types of signals transmitted by GPS satellites. The first type, known as Coarse/Acquisition (C/A) code, is transmitted on L1 and it is freely available for public use. The second type is an encrypted precision code (P(Y)), transmitted on both L1 and L2 carrier frequencies and it is meant only for military purposes. Each signal consists of three components: an RF carrier frequency, a PseudoRandom Noise (PRN) code that serves as a ranging code, and a navigation message that contains the ephemeris and the almanac data needed for the calculation of the position solution. The ranging code is combined with the navigation data and then this composite signal is modulated onto the carrier wave using the Binary Phase Shift Keying (BPSK) scheme. Each satellite transmits a unique PRN code with each signal type and it is used in order for the receiver to be able to identify each satellite and consequently to calculate the time of arrival of the signal. The PRN codes used in GPS are Gold codes and they are chosen in such a way that good cross-correlation properties are achieved. The C/A code has the length of 1023 chips and transmission rate of Mchips/sec. The length of P(Y) code is much longer than C/A ( chips) and its transmission rate is ten times higher than that of the C/A code [93]. GPS currently offers two types of services: a Standard Positioning Service (SPS) for public use and a encoded Precise Positioning Service (PPS), primarily intended for use by the DoD. The limitations of the current GPS civil signal and the new wide range of GNSS

18 Background 7 applications were two main reasons for the design of new GPS signals with enhanced capabilities. The new signals will offer new modulations, new signal structures, longer codes, dataless codes, faster transmission rates, new data encoding, a new navigation message format, etc [93]. This process represents the efforts that have been put for the modernization of GPS. 2.3 Galileo Galileo is Europe s initiative for a state-of-the-art global navigation satellite system, providing a highly accurate, guaranteed global positioning service under civilian control. Galileo is designed to be interoperable with the U.S GPS and the Russian GLONASS and it is expected to be fully operational in [28]. Galileo will consist of a constellation of 30 satellites in Medium Earth Orbit (MEO) which will be equally distributed in 3 orbital planes inclined at 54 and at an altitude of around km. This is the simplest system to launch, operate and maintain and one that provides the greatest reliability for an operational service. The proposed architecture for the Galileo ground system includes three components: a Navigation System Control Center, a network of stations monitoring Galileo satellite orbits and synchronization and several tracking, telemetry and command ground stations. Generally, a lot of sophisticated technology will go into it, such as highly advanced atomic clocks for greater accuracy and stability. This advanced technology will offer to Galileo several advantages as compared to GPS [27]: Galileo has been designed and developed as a non-military application, while nonetheless incorporating all the necessary protective security features. It therefore provides, for some of the services offered, a very high level of continuity required by modern business, in particular with regard to contractual responsibility. It is based on the same technology as GPS and provides a similar - possibly higher - degree of precision, thanks to the structure of the constellation of satellites and the ground-based control and management systems planned. Galileo is more reliable as it includes a signal integrity message informing the user immediately of any errors. In addition, it will be possible to receive Galileo signals in towns and in regions located in extreme latitudes. It represents a real public service and, as such, guarantees continuity of service provision for specific applications.

19 Background 8 In addition, Galileo and GPS will be complementary to each other as [27]: Using both infrastructures in a coordinated manner, offers real advantages in terms of precision and in terms of security, should one of the two systems become unavailable. The existence of two independent systems is of benefit to all users since they will be able to use the same receiver to receive both GPS and Galileo signals Galileo Services Galileo will provide worldwide and independently from other systems the following services [2]: The Open Service (OS) which will be free of user charge. The Safety of Life Service (SoL) which improves the open service performance through the provision of timely warnings to the user when it fails to meet certain margins of accuracy (integrity). The Commercial Service (CS) which provides access to two additional signals (encrypted), and thus it allows for a higher data throughput rate and improved accuracy. The Public Regulated Service (PRS) which provides position and timing to specific users requiring a high continuity of service, with controlled access. The Search And Rescue Service (SAR) for humanitarian search and rescue activities Galileo Signals Galileo will provide 10 navigation signals in Right Hand Circular Polarization (RHCP) in the frequency ranges MHz (E5a and E5b), MHz (E6) and MHz (E2-L1-E1), which are part of the Radio Navigation Satellite Service (RNSS) allocation. The frequency bands used in Galileo are depicted in Fig For a specific service and frequency, all Galileo satellites will share the same nominal frequency, making use of Code Division Multiple Access compatible with the GPS approach. Six signals, including three data-less channels, so-called pilot tones (ranging codes not modulated by data), are accessible to all Galileo users on the E5a, E5b and L1 carrier frequencies for Open Services and Safety-of-life Services. Two signals on E6 with encrypted ranging codes, including one data-less channel, are accessible only to some

20 Background 9 Figure 2.1: Galileo signal in space [34]. dedicated users that gain access through a given Commercial Service provider. Finally, two signals (one in E6 band and one in E2-L1-E1 band) with encrypted ranging codes and data, are accessible to authorized users of the Public Regulated Service [34] Binary Offset Carrier Modulation BOC modulation was first introduced by Betz as a strong candidate for GPS modernization [8]. Such type of modulation allows for placing the signal energy away from the band center, thus avoiding overlapping with C/A and P(Y) code signals. Several variants of BOC modulation have also been considered, including SinBOC (Sine BOC) [8], Cos- BOC (Cosine BOC) [8], Alternate BOC (AltBOC) [35], Complex Double BOC (CDBOC) [60] and the currently selected, for modulating OS signals at L1 frequency, Multiplexed BOC (MBOC) [3, 33]. The choice of SinBOC(1,1) modulation for L1 OS signals under the terms of the 2004 US/EC agreement, instead of the traditional BPSK-modulation used in GPS C/A signals, is considered to be a primary reason for the improvement of tracking accuracy and multipath mitigation. A BOC modulated signal is usually noted as BOC( f s, f c ), where f s is the subcarrier frequency and f c is the spreading code rate. Very often someone can see the notation BOC(n,m), where n = f s f re f [MHz] and m = f c f re f [MHz], and f re f is equal to 1.023[MHz]. It can be shown that the normalized Power Spectral Density (PSD) of baseband SinBOC-

21 Background 10 modulated signal, when 2 f s f c is even, is given by [8]: ( ( sin π f ) ( 2 f G s ( f ) = G SinBOC( fs, f c )( f ) = f s sin π f c π f cos ( π f ) 2 f s f c ) ) 2 (2.2) In Fig. 2.2 we show the power spectral densities for SinBOC(1,1) (in blue color) and BPSK signals (in red color). From the figure we see that at the points where the lobes for BPSK are at maximum level, the BOC lobes are zero, thus allowing for efficient spectral separation. Figure 2.2: PSD for SinBOC(1,1) and BPSK signals The transmitted signal x(t) can be written as the convolution between the modulating waveform s BOC (t), the pseudorandom (PRN) CDMA code, including data modulation, and the pulse shaping filter p TB (t) [57]: x(t) = E b s BOC (t) + S F n= k=1 b n c k,n δ(t nt sym kt c ) (2.3) where E b is the data bit energy, is the convolution operator, b n is the n-th complex data symbol (in case of a pilot channel, it is equal to 1), T sym is the symbol period, c k,n is the k th chip corresponding to the n th symbol, T c = 1/ f c is the chip period, S F is the spreading factor (S F = T sym /T c ), δ(t) is the Dirac pulse, and p TB (t) is the pulse shaping filter applied to pulses of duration T B = T c /N B. Here, N B is a modulation-related parameter, also named as BOC-modulation order (this was detailed in [57]). For example, for the most encountered GNSS modulations, namely BPSK and sine-boc(1,1) modulations, we have: N B = 1 and N B = 2, respectively. For example, if infinite bandwidth is assumed, p TB (t) will be a rectangular pulse of unit amplitude for 0 t T B and 0 otherwise. Above, s BOC (t) stands for both BPSK and sine BOC-modulated signals, and it can be expressed

22 Background 11 as in eq. (2.4) [57] (for cosine-boc modulation, the detailed expression of s BOC (t) is given in [57]): ( s BOC (t) = sign sin ( NB πt T c N B 1 = p TB (t) i=0 )), 0 t T c ( 1) i δ(t it B ) (2.4) The signal x(t) is typically transmitted over a multipath static or fading channel, where all interference sources (except the multipath) are lumped into a single additive Gaussian noise term η(t): r(t) = L l=1 α l x(t τ l )e j2π f Dt + η(t), (2.5) where r(t) is the received signal, L is the number of channel paths, α l is the complex coefficient of the l-th path, τ l is the channel delay introduced by the l-th path, f D is the Doppler shift introduced by the channel, and η(t) is the additive Gaussian noise of zero mean and double-sided power spectral density N 0. Typically, the signal-to-noise ratios for GNSS signals are expressed with respect to the code epoch bandwidth B W, namely B W = 1 khz [49, 86], under the name of Carrier-to-Noise Ratio (CNR). The relationship between CNR and bit-energy-to-noise ratio is as follows: CNR[dB/Hz] = E b N log 10 (B W ). (2.6) Sometimes, CNR is expressed in dbm, and the relationship with bit-energy-to-noise ratio becomes: CNR[dBm] = E b N log 10 (B W ) + 10log 10 (kt 0 ). (2.7) where, k is Boltzmann constant (k = Joule/Kelvin) and T 0 is the room temperature in Kelvin (T 300 K). That is, CNR[dBm] CNR[dB/Hz] 174 dbm/hz. (2.8) Both acquisition and delay tracking stages (i.e., code synchronization) are usually based on the code epoch-by-code epoch correlation R ( ) between the incoming signal and the reference x re f ( ) modulated PRN code, with a certain candidate Doppler frequency f D and delay τ: ( 1 mtsymb ) R ( τ, f D,m) = E r(t)x re f ( τ, f D )dt, (2.9) T symb (m 1)T symb

23 Background 12 where m is the code epoch index and E( ) is the expectation operation, with respect to the PRN code, and x re f ( τ, f D ) = ( s BOC (t) + n= S F k=1 bn c k,n δ(t ) nt sym kt c ) p TB (t) e + j2π f D t, (2.10) where b n are the estimated data bits. For Galileo signals, a separate pilot channel with known data bits is transmitted, thus the data bits are known at the receiver [86]. In order to reduce the noise level, both coherent and non-coherent integration are typically used. The averaged non-coherent correlation function R ( τ, f D ) can be written as: R ( τ, f D ) = 1 1 N nc N nc N c N c m=1 R ( τ, f D,m) 2 (2.11) where N c is the coherent integration time (expressed in code epochs or ms for GPS/Galileo signals) and N nc is the non-coherent integration time, expressed in blocks of length N c ms. If we assume that pilot channels are available or, equivalently, that data bits are perfectly estimated ( b n = b n ), that the random processes (i.e., noise, PRN codes, etc) are ergodic, and that the PRN codes have ideal correlations (i.e., E(c k,n c m,p ) = 1 if m = k and n = p, and E(c k,n c m,p ) = 0 if m k or n p), by replacing eqs. (2.3), (2.4), (2.5), (2.9), and (2.10) into eq. (2.11), we get, after several manipulations, that: L 2 R ( τ, f D ) = E b l R BOC ( τ τ l )sinc(π f D N c T symb ) + η(τ) l=1α 2, (2.12) where R BOC ( ) is the auto-correlation of the BOC/BPSK modulation, including pulse shaping [57]): R BOC (τ) = N B 1 i=0 N B 1 i 1 =0 ( 1) i+i 1 R pulse (τ it B + i 1 T B ), (2.13) R pulse (τ) = p TB (τ) p TB (τ) is the pulse shaping autocorrelation function (e.g., for rectangular pulses, R pulse,tb (τ) is a triangle of unit amplitude and support [ T B,T B ]), f D = f D f D is the residual Doppler error, and η(τ) is the filtered (coloured) noise of power spectral density N 0 Π( f N c 2B W ), with Π( ) is the rectangular pulse of unit amplitude and unit support. Above, sinc(x) = sin(x)/x. Examples of the averaged correlation function of eq. (2.12), for BPSK and sine-boc(1,1) modulation, one and two in-phase path channels, no noise, zero residual Doppler error and unit bit energy are shown in Fig. 2.3.

24 Background BPSK sine BOC(1,1) BPSK sine BOC(1,1) Averaged correlation Averaged correlation Delay error [chips] Delay error [chips] Figure 2.3: Examples of averaged correlation function with pulse shaping for BPSK and sine-boc(1,1) modulation. Left plot: single-path. Right plot: two in-phase static paths, spaced at 0.3 chip distance; second path is 1 db lower than the first. 2.4 Galileo/GPS Key Differences Now, it is interesting to know the key differences between Galileo L1 OS signals and GPS C/A signals. Below we see a list with some of the major differences as they are mentioned in [12]: Signal types: GPS has one public and one encrypted type of signals, while Galileo will have three types (See Sections 2.2 and 2.3.1). Spreading codes: GPS uses a spreading code of 1023 chips, whereas Galileo will use code lengths of 96 chips. The chipping rates are the same for both GPS and Galileo, but all Galileo codes on L1 are combined with a subcarrier signal (BOC signals). In addition, the transmitted GPS L1 signals are bandwidth limited to MHz, whereas the corresponding Galileo signals are limited to four times bigger bandwidth than of GPS signals. Data structure: Galileo system will use a superframe, frame, subframe construction similar to GPS. It is expected that the construction of the data part in Galileo will be different from the GPS messages. Synchronization word (preamble): GPS is using an 8-bit pattern while Galileo is likely to use a 10-bit pattern. Channel coding: In addition to the Cyclic Redundancy Check (CRC) for error detection, Galileo will use Forward Error Correction (FEC) to detect and correct data corruption. This will facilitate correction of a much larger amount of corruption compared to GPS where only one bit per subframe can be corrected.

25 Background 14 Modulation: Galileo uses BOC(1,1) modulation, whereas GPS uses BPSK. Time reference: Galileo will use a reference time called Galileo system Time (GST), whereas GPS uses GPS time (GPST). GST will be steered to International Atomic Time (TAI) at the Galileo Precise Time Facility (PTF), while GPST is steered to a real-time representation of Coordinated Universal Time (UTC) by the U.S. Naval Observatory (USNO). Satellite constellation: The number of satellites, their orbit altitude and their orbital period as well as the constellation type, are all different for GPS and Galileo.

26 Chapter 3 Code Synchronization in GNSS This chapter provides the necessary information for understanding the principles of code synchronization in GNSS systems. In order to determine the difference between the signal transmission time from the satellite and the signal reception time, a GNSS receiver synchronizes a locally-generated PRN code (reference code) with the PRN code in the received signal. This synchronization process is a two-stage process and includes the stages of signal acquisition and signal tracking. In Fig. 3.1 we see a simplified block diagram for a GNSS receiver, where the synchronization functions are surrounded by red-dashed line. Here, we describe each of the synchronization modules, but our main research focus will be on the code tracking module. Figure 3.1: Block diagram of a GNSS receiver 15

27 Code Synchronization in GNSS Signal Acquisition The purpose of acquisition is to identify all the satellites visible to a user. As soon as a satellite is found, the acquisition stage produces coarse estimates for the frequency ( f d ) and the code phase ( τ d ) of the transmitted signal. The frequency band to be searched is defined as +/- maximum Doppler shift from the carrier frequency ( f c ), where the Doppler shift is caused by the relative speed between the satellite and the receiver. Because the acquisition process can be very slow, it is not possible to search for the whole frequency band or all the possible code phases, therefore, we divide the searching space into frequency bins and time bins, respectively. The combination of one code bin and one frequency bin forms a cell. Then, the problem is to find the cell which is most likely to contain the unknown pair of parameters ( τ d, f d ) and it has been depicted in Fig Figure 3.2: Code acquisition problem When there is no a-priory information, the acquisition is referred to as cold start, and it is the most time-consuming of the cases (in contrast to warm start, where almanac information is used from previous estimation). The main operations of code acquisition include a plan of actions to achieve the acquisition state and a function to identify the presence or not of alignment. The former is known as the search strategy while the latter corresponds to the receiver detector structure [50]. The target of acquisition is to minimize the mean acquisition time which depends on both acquisition operations (search and detection) Search methods There are several search methods for code acquisition and they can be divided into three classes: serial, parallel and combination of serial and parallel (or hybrid) acquisition meth-

28 Code Synchronization in GNSS 17 ods [49]. Serial acquisition is the most commonly used in CDMA systems but also the most time consuming. The search is done sequentially through all the possible values of frequency and time bins. Various methods for serial acquisition of CDMA signals can be found in [13, 36, 38, 46, 64, 66, 68, 69, 75, 84]. Serial acquisition methods specifically designed for BOC modulated signals have also been proposed in [61], while in [56] we can find acquisition methods that employ Filter-Bank-Based approaches. In Fig. 3.3, we see the block diagram of the most commonly used acquisition method. We see that the concept is based on multiplication of locally generated PRN codes and carrier signals, which produces the in-phase (I) and quadrature (Q) signals. Then the I and Q signals are integrated (coherently) and finally squared and added. Afterwards, noncoherent integration over N nc blocks is taking place and the output is compared with a predefined threshold (γ). If the threshold is exceeded, the cell will be chosen and the corresponding code phase and Doppler shift values are used as the initial values in tracking. Ideally, the signal power is placed in the I part of the signal, as the code is modulated only onto that. However, due to the phase uncertainty of the signal at the receiver side, both I and Q parts need to be investigated in order to increase the possibility of detecting the signal [12]. Figure 3.3: Serial search acquisition For strong signals, a coherent integration period of 1ms (i.e. for C/A code) might be sufficient, but for weak signals, the correlation period must be extended to improve the CNR at the correlator output [20]. More precisely, when conducting coherent integration, signal power increases by N c, while the noise power increases by N c, thus a gain of Nc is achieved. Moreover, coherent integration allows for a narrow pre-detection signal bandwidth, which enhances the acquisition of weak signals in the presence of strong in-band interference [91]. However, coherent acquisition requires a more extensive frequency search, which may not be desirable for fast signal acquisition. In addition, coherent acquisition is limited by the oscillator stability, the residual Doppler drifts and the presence of navigation data. Therefore, additional non-coherent integration is used by

29 Code Synchronization in GNSS 18 squaring the signal. The advantage of non-coherently integrating the signal is that it requires neither knowledge of carrier phase nor precise carrier frequency, both of which are not available before the signal has been acquired [49]. However, with this approach the noise is also squared, resulting in what is known as squaring loss. In the case of parallel acquisition, the number of code phase and carrier frequency combinations to be searched are lower than in serial method and this is done by parallelizing one of the two (or both) search dimensions. Typically, Fourier transform is used in order to detect the carrier in a single step. Examples of parallel acquisition techniques can be found in [16, 22, 72, 73, 83]. In Fig. 3.4, we see the block diagram for parallel acquisition, when the frequency dimension is parallelized.the output of the mixer is a continuous wave signal which is translated to frequency domain via Fourier transformation. Figure 3.4: Acquisition with parallel search in frequency dimension. In terms of performance, parallel acquisition offers shorter acquisition times at the expense of complexity, when compared to simple serial-search methods. The increased complexity is because of the use of Fourier transform and the efficiency depends on the speed of the used Fourier algorithm. Hybrid serial-parallel approaches have been proposed as an alternative attractive solution for the trade-off between acquisition speed and implementation complexity [6, 48, 74, 92] Detection The detection stage of the signal is a statistical process because in each cell, the correlation result contains the noise together with the signal or only the noise. Each of these two cases has its own probability density function [49]. In particular, the statistic is commonly based on the comparison of signal energy against a selected threshold (γ). If the signal energy in a time bin (t d ) is greater than the predefined threshold, then t d is considered as a correct cell, else as wrong. Finding a suitable value for γ is known as threshold setting problem.

30 Code Synchronization in GNSS 19 The presence of noise may cause two types of errors in the acquisition stage: false alarm and miss. A false alarm occurs when the decision statistic exceeds the threshold for an incorrect bin, while miss occurs when the decision statistic falls below the threshold for a correct bin. A false alarm will cause an incorrect bin value to be sent to the tracking loop, and the receiver will not be able to lock on the signal. Following on, the acquisition process will be activated again, thus requiring more time. The time needed to evaluate a single assumed time (or frequency) bin is called dwell time and proper choice of its value together with proper choice of the decision threshold are needed to minimize the acquisition time. Typically, in order to acquire attenuated signals, a longer dwell time is required [49]. 3.2 Signal Tracking In order to be able to demodulate the signal, we need to have perfectly aligned code and carrier replicas. These replicas can be tracked using two tracking loops: code and carrier. The tracking stage is initiated only after the initial acquisition has taken place, where coarse code and frequency estimates have been produced Code Tracking The general idea of code tracking is to generate a local signal (reference code) and then to measure the code phase error between the local and the received signal, with the target of keeping this error at the minimum level. One choice for the tracking structure loop, widely used both for GPS and Galileo signals, is called Delay Locked Loop (DLL), several applications of which can be found in [4, 11, 17, 25, 26, 54]. The block diagram of a non-coherent Early-Minus-Late correlator (EML) is depicted in Fig We see that the input signal r(t) is split and is the input to the early (E) and the late (L) correlators. In both the early and late correlation channels, the output of the correlator is coherently integrated over N c microseconds and then squared. The code detector error signal S(ε) is the difference between the early and late correlation channel outputs and it is driven to zero by the DLL in normal tracking operation [1]. The resulting combination of early-late correlators is commonly known as discriminator function. The performance of the DLL is best illustrated by the so called S-curve, which represents the expected value of the error signal as a function of the reference parameter error (i.e., the code phase error) [79]. An example is given in Fig. 3.6 for the case of EML correlator where the delay error is equal to zero (indicated by the central zero crossing of the S-curve).

31 Code Synchronization in GNSS 20 Figure 3.5: EML block diagram Normalized EML S curve, =0.1 chips, SinBOC(1,1) Non coherent EML 0.6 Feedback error [chips] Delay error [chips] Figure 3.6: S-curve for EML

32 Code Synchronization in GNSS 21 Although classical DLLs have been very popular at early times, they fail to deal with the multipath propagation effects [79]. Therefore, researchers had to invent more sophisticated techniques that would be multipath resistant, especially in the case where the paths are closely spaced to each other. One class of these enhanced DLL techniques is based on the idea of narrowing the spacing between early and late correlators. A widely known delay estimator of this class is the Narrow Early Minus Late correlator (), introduced in GPS receivers by NovAtel Inc. [21]. was among the first approaches to mitigate multipath effects by reducing the spacing between the early and the late code to less than 1 chip (see Fig. 3.5). The idea of spacing reduction was based on the assumption that the distortion of the cross-correlation function near its peak due to multipath is less severe than that at regions away from the peak [21]. The discriminator function of is expressed as: D (τ) = E 1 L 1 = R(τ + 2 ) 2 R(τ ) 2 (3.1) 2 where E 1 and L 1 are the early and the late delayed versions of the reference code, respectively, R(τ) is the averaged correlation function between the received signal and the stored replica, and is the early-late chip spacing (see Fig. 3.6). Another popular DLL based technique, namely Double Delta ( ), utilizes two correlation pairs, in difference with which uses one. The name comes from the design of correlator, where the wider pair has twice bigger chip spacing than the narrow pair. Illustration of this concept is given in Fig. 3.7 and the discriminator function is formed as: D = a(e 1 L 1 ) b(e 2 L 2 ) (3.2) where the early and the late delayed versions of the reference code, E i and L i, for 1 = 1,2, are defined as E i = R(τ + i DD 2 ) 2 and L i = R(τ i DD 2 ) 2 for i = 1,2, correspondingly, and DD is the early-late chip spacing. The notations E i,i = 1,2, are used for the early and the late versions of the reference code, where the spacing between the first and the second early-late pair is denoted by DD and 2 DD, respectively, and R(τ) is the ideal autocorrelation function. When a = 1 and b = 2 1, one more popular delay estimator is formed, namely High Resolution Correlator () [62]. Very similar to the discriminator function is the Multiple Gate Delay (MGD) structure, which uses also 2 correlation pairs but different coefficient (a and b) values and some type of normalization [19]. Other variations utilizing the Double Delta correlator concept include the Pulse Aperture Correlator (PAC) [24], and the strobe correlators [29, 41].

33 Code Synchronization in GNSS 22 Figure 3.7: Concept of Double Delta correlator [41] An estimator that employs a modified reference waveform for the correlation at the receiver, that narrows the main lobe of the cross-correlation function, is the modified correlator reference waveform. However, this spacing narrowing results in a deterioration of the signal power [41, 88]. Also, an optimized MGD structure is presented in [81] and which outperforms the and [37, 81]. Other enhanced DLL techniques include some form of multipath interference cancellation, by estimating not only the delay of the LOS path, but also the delays, phases, and amplitudes of the Non-LOS (NLOS) paths [26, 54, 77]. In general, code delay estimators (or code tracking algorithms) can also be categorized into feedback and feedforward estimators [55, 59]. The main characteristic of feedback estimators is that the estimated delay at stage i is fed back so as it can be used to the next estimation stage i + 1. Such function is typically implemented using a feedback loop and examples belonging to this group are,, Double Delta correlator, etc.. Feedforward estimators make use of an open loop structure where the estimation is done in a single step, without any feedback information to be needed [59]. A general classification of open-loop solutions for WCDMA applications can be found in [55, 58]. One of the simplest feedforward delay estimators is the so called correlator or Matched Filter, where the choice of the LOS delay is based on a simple thresholding of the Acf [39, 45, 58]. First, the threshold ( thresh ) is computed based on the sum of second highest peak of the ideal AutoCorrelation Function (ACF) and the estimated noise variance. Second, the LOS delay is estimated as the first local maximum of the Averaged correlation function (Acf) which is higher than thresh. Another feedforward delay estimator is the one which utilizes the non-linear quadratic Teager Kaiser () operator [32]. This operator was first introduced for measuring the real physical energy of a system [47] and it has been also recently used in CDMA applica-

34 Code Synchronization in GNSS 23 tions due to its good performance in multipath environment [30, 31, 32, 55]. The concept of -based estimator is similar to the one of estimator, with the only difference that the functions of threshold computation and delay estimation take place on the Acf after operator has been applied [32]. One more interesting feedforward estimator is the one that is based on the 2nd-order differential () operator. Here, it is assumed that the amplitude of the LOS signal is always higher than the amplitude of the multipath, although this is not always the case in real life scenarios (e.g. if the direct path is attenuated the multipath signal can be stronger) [5]. The concept is similar to the -based estimator, and the only difference lies in that the threshold computation and delay estimation functions are applied on the 2nd order differentiated Acf [10]. Another algorithm belonging to the class of feedforward estimators, is the so called Early Late Slope () and it is based on the slope difference of the correlator output between the received and locally generated reference signals [18, 42]. The main advantage of feedforward estimators is that they are less affected by the initial error coming from acquisition stage. This is because, unlike feedback estimators, they do not depend on previous estimates, thus they prevent erroneous feedback. However, feedforward estimators require more correlators, compared to feedback estimators that are characterized by lower implementation complexity. One way to improve the performance of delay estimation methods is to combine the basic function of feedforward and feedback estimators. An example where this idea has been realized, is the Peak Tracking estimator [9]. It employs a combination of feedback/feedforward techniques, and also utilizes the concept of (PT()). The estimated delay is a function of multiple weights which are assigned to a set of candidate peaks. Our group has also modified some of the existing feedforward estimators, particularly, and, such that the benefits of feedback techniques are incorporated. In the case of, the estimated code delay is a function of the previous estimated delay. In addition, the method of threshold computation has been modified (this modification belongs to the author s contibutions) and such modifications resulted in improved performance at lower CNRs. For the cases of and, when the estimation is done with low CNR, the LOS delay corresponds to the candidate peak which is closest to the previously estimated delay, otherwise the original version of the estimator is used. The above-mentioned modifications improved the performance of all three estimators, however, for the sake of clarity we include a detailed description of modifications and the corresponding performance results in the Appendix.

35 Code Synchronization in GNSS Carrier Tracking In order to maintain continuous signal tracking, and hence ensure the validity of the resolved (or estimated) integer ambiguities, a high sensitivity carrier phase tracking loop is needed [44]. After the correct code phase is acquired by the tracking loop, a phase and/or frequency locked loop (PLL/FLL) can be employed to track the phase and the carrier frequency, respectively. A very commonly used phase locked loop is known as Costas loop [7] and it is preferred because its performance does not depend on the phase shifts caused by the data bits [51]. Frequency locked loops are used to adjust the frequency of the carrier. In general, for a given signal power level, Costas PLL loops provide the most errorfree data demodulation in comparison with FLL. [15]. However, a well designed receiver starts tracking with the more robust FLL operated wide band, since it is less sensitive to errors and noise. Then, gradually, it switches to a wideband PLL and finally when the tracking is stable, to a narrow band PLL [49].

36 Chapter 4 Research Methodology This chapter describes the research methodology which was followed in order to investigate the complex problem of code delay estimation in multipath and low CNR environment. In every dynamically varying system there is a number of estimation problems where the aim is to characterize the different system parameters. In our case, the system is a satellite communication channel and the estimation of the code delay in multipath and low CNR environment is the problem to be solved. When dealing with complex problems, such as the above-mentioned, the method of Divide and Conquer (DaC) can be of great use. In computer science, DaC is an important algorithm design paradigm. It s principle is based on recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. In order to apply the DaC method in our case, we need to decompose the complex problem into smaller parts. To do so, we identify as the first sub-problem the actual (or the main) problem which is the delay estimation of the line-of-sight signal. Then, we have two conditions which impose restrictions to the environment (space) in which the code estimation will take place. These conditions are the presence of multipath and the low CNR environment and they can be recognized as two sub-problems, defined as multipath mitigation and CNR estimation sub-problems, respectively. The way in which the initial problem is decomposed into sub-problems, and the way in which the sub-solutions are combined to form the solution to the original problem, are depicted in Fig The original problem is encircled by a solid red line, while each of the three subproblems are encircled by a dashed line. The solutions to subproblems are combined in order to form the solution to the initial problem, called. This global solution 25

37 Research Methodology 26 Figure 4.1: Divide and Conquer methodology is encircled by a solid black line. When a decomposition process is taking place, the connecting arrows appear in solid line while the flow of the sub-solution composition is depicted in dashed arrows. How will we deal with the above-mentioned subproblems will be described in detail in the next chapter. Regarding the performance evaluation method, we used computer simulations. In particular, we chose Monte Carlo type of simulation in order to represent in the most realistic way the random nature of a communication channel. We compared the performance of with a set of other code delay estimators in terms of Root Mean Square Error (RMSE), Absolute Mean Error, STandard Deviation (STD) and Mean Time To Lose Lock (MTLL). We also evaluated the impact of various channel parameters in the delay estimators performance. In addition, we decided to evaluate the performance of the proposed CNR estimator (which represents our solution to the subproblem of CNR estimation) individually, because the estimator can be used in different problems (other than code delay estimation in low CNR) and therefore it is a separate contribution on its own. The performance is tested in various channel profiles and evaluated in terms of success rate of accurate CNR level detection (in %).

38 Chapter 5 Novel Contributions This chapter describes the novel approaches employed in order to cope with the subproblems, which were presented in the previous chapter. Moreover, it presents the main contributions of this thesis, which consist of a CNR estimator and a code delay estimator, called. 5.1 CNR Estimation The need for estimating the carrier to noise ratio is undoubtedly present in all types of communication channels. CNR estimators for GNSS signals are rather scarce in the literature, and the existing ones require heavy computations at the receiver (see Chapter 3). This section introduces a novel indoor/outdoor identifier, based on the Level Crossing Rate (LCR), which is built from the non-coherent averaged Absolute value of the correlation function (Acf). By difference with the previous estimators, this identifier is an on-off CNR estimator, meaning that it tries to distinguish the low signal levels from the high signal levels, with the purpose of differentiating between indoor and outdoor scenarios. Discussion on the CNR border between indoor/outdoor environments can be found in the scientific community. Particularly, in [87] the authors considered this border to be about 155 dbm, or approximately equal to db/hz. In [23] the indoor environment is characterized by CNR values less than 20 db/hz, while in [] it is stated that the indoor acquisition requires successful signal detection at typically 20 db/hz CNR level. Based on the above references we chose as the indoor/outdoor border the level of 20 db/hz to be used in our research. 27

39 Novel Contributions Level Crossing Rate Concept This sections presents the conceptual basis of the novel indoor/outdoor identifier, as well as a step-by-step description of its characteristics. The LCR at a certain level a is computed as the number of crossings (both from below and from above) of level a. Assuming that the time samples of the normalized correlation function R (τ, f D )/max(r (τ, f D )), with R (τ, f D ) given in eq. (2.12) are denoted by R i and that they are taken at sampling instants τ i, i = 1,2,..., then: LCR(a) = card { i (R i a R i+1 > a) } (R i+1 a R i > a), (5.1) where card is the cardinality of a set and is the union operator. Additional insight on this can be gained from Fig.5.1, where the Acf of the received sine BOC(1,1)-modulated signal is drawn, together with the LCR at level a = 0.2 (here, LCR(0.2) = 4). The channel in Fig.5.1 is single-path static, where CNR is set to 30 db/hz, the oversampling factor N s (i.e., the number of samples per BOC interval) is equal to 10 and the values for noncoherent (N nc ) and coherent (N c ) integration are 2 and 20, respectively. 1 1 path static channel, CNR=30dB/Hz Non coherent Acf crossings at level Times axis Figure 5.1: Averaged LCR for 1-path static channel (N nc = 2, N c = 20). We define the AcfLevel as a vector [0.01 : 0.01 : 1] which divides the Acf in equally spaced stripes of 0.01 width (or resolution). The resolution was chosen in such a way that the computational time would be kept at a reasonable level. In Fig. 5.1 these levels are

40 Novel Contributions 29 represented with parallel green dashed lines to the times axis (for better readability, only the range [0.01 : 0.01 : 0.1] was depicted with its real resolution). Based on Fig. 5.1, an intuitive observation is that in lower Acf levels, the total number of crossings is likely to be higher than in higher Acf levels, due to the noise impact. Having this initial observation in mind, the basic idea was to compute the number of crossings for each value of the AcfLevel and examine how the Level Crossing Rate varies in terms of CNR. To implement this, we produced Nrand = 0 different random Acf realizations for each CNR value of the vector [10 : 5 : ] db/hz and we computed the LCR for each realization. We used 1-path static channel, sampling rate N s = 10, noncoherent integration length N nc = 2 blocks, and coherent integration length N c = 20 ms. Then, we computed the averaged LCR over Nrand and for each CNR. The averaged LCR information is depicted in Fig. 5.2 for CNR values 10 db/hz to db/hz with step of path Static channel, Nnc=2, Nc= CNR=10 CNR=20 CNR=30 CNR= LCR Acf level Max in 20 db/hz Figure 5.2: Averaged LCR for 1-path Static channel (N nc = 2, N c = 20). From Fig. 5.2 we observe that there are certain characteristics of the LCR curve which are dependent on the CNR. Such characteristics are: the position of the maximum LCR in the AcfLevel, the area enclosed by the LCR curve, and number of a levels that result in LCR = 0. The last characteristic describes how much higher from the time axis the Acf is placed, due to the noise impact. We also notice that all of the characteristics act in inverse to the CNR manner, meaning that when we increase the CNR, the position of the maximum LCR in the AcfLevel-axis, the area enclosed by the LCR curve and the number of a levels that result in LCR = 0 decrease. Based on the above mentioned observations, it became obvious that these three characteristics act as potential CNR identifiers.

41 Novel Contributions LCR-Based CNR Identifier The next step of our research was to examine thoroughly the behavior of the candidate identifiers in different channel profiles and search for the most reliable one. In Fig. 5.3, we show the variation of the three potential identifiers versus CNR, for three channel profiles which have been widely used in our studies (See Chapter 6). The results are based on averaging of 0 random channel instances for each profile. The examined channels are: 1-path static, multipath static with randomly varying number of paths (uniformly distributed between 2 and 5), and multipath Nakagami-m fading channel with randomly varying number of paths (uniformly distributed between 2 and 5) and Nakagami-m factor equal to In the static channel, the paths were in-phase, while in the fading channel the phases varied uniformly between 0 and 2π. The Nakagami distribution (known also as m-distribution) is widely used for modeling the fading characteristics of mobile radio communications [14, 65]. In particular, channels that obey to Nakagami fading are used to best model the satellite-to-indoor mulipath propagation [52, 53]. Based on the extensive simulations, it became clear that the first characteristic, meaning the position â of the maximum LCR in the AcfLevel (lower plot in Fig. 5.3) is the most promising because it is affected the least by the various channel profiles (static versus fading, single-path versus multipath): â = arg max a LCR(a). (5.2) Before we evaluate its performance, we need to take into account the relationship of â with the integration times, both coherent and non-coherent. This necessity comes from the fact that the CNR is higher after integration than before coherent and non-coherent integration, therefore this dependency needs to be taken into account. The CNR values given here are those obtained before coherent and non-coherent integration and they correspond to 1 khz bandwidth. In Table 5.1 we present the averaged Acf level of max LCR versus N nc and N c for the fixed CNR value of 20 db/hz (we recall that this value was chosen as the border between the indoor and outdoor scenarios, as explained earlier in this section). The averaging has been made over 0 random Acf realizations and the channel is 1-path static. From the table we notice that the averaged Acf level increases when we increase the non-coherent integration time while it decreases when increasing the coherent integration time. We remark that we examined the N nc /N c influence for multipath static channel as well, and as expected from the lower plot of Fig. 5.3, the values were quite similar. Therefore, we can rely on the values from Table 5.1 in order to choose the indoor/outdoor threshold. The proposed algorithm has the following steps:

42 Novel Contributions 31 Averaged Acf level of max LCR Averaged Acf level of max LCR, Nnc=2, Nc=20 1 path Static 2 to 5 path Static 2 to 5 path Nakagami Averaged Area Enclosed by Averaged LCR Averaged Area Enclosed by Averaged LCR, Nc=2, Nnc=20 1 path Static 2 5 path Static 2 5 path Nakagami CNR in db/hz CNR in db/hz 2.5 Averaged Num. of Acf Levels with LCR = 0, Nc=2, Nnc=20 1 path Static 2 5 path Static 2 5 path Nakagami Averaged Num. of Acf Levels with LCR = CNR in db/hz Figure 5.3: Averaged CNR Identifiers for three different channel profiles. Table 5.1: Averaged Acf level of the max LCR (â) versus N nc and N c for 1-path static channel and CNR=20 db/hz. N c = N nc =

43 Novel Contributions Compute the correlation function R (τ, f D ) between the incoming signal and the reference code (in baseband domain) at a certain estimated Doppler shift f D (given, for example, from the acquisition time) and for several time delays, within a certain window around the estimated coarse delay from the acquisition time. In our simulations, we used window lengths of 4 chips for single path channels and 8 chips for multipath channels. Normalize this correlation function via its maximum value and form the cost function J: J = R (τ, f D )/max(r (τ, f D )). 2. Compute the instantaneous LCR(a) levels of J, for a = [0.01 : 0.01 : 1]. 3. Find out â sim (the averaged Acf Level of max LCR), based on the instantaneous (simulations-based) LCR. 4. If â sim â with â given in Table 5.1, decide that we are in indoor scenario (i.e., that CNR is below 20 db/hz). If â sim > â, decide that we are in outdoor scenario. 5.2 Multipath/Noise Mitigation The problem of multipath mitigation has been widely discussed in the literature (see Chapter 3) and the case of closely-spaced paths is very challenging. The results of our research on the multipath problem are based on the observation that the presence of the Line-Of-Sight (LOS) path is significantly related to the continuity of the Acf. In particular, we noticed that the existence of the LOS path is indicated by the presence of a Discontinuity Point (DP). In contrast with the previously implemented algorithms (i.e., PT()), which assume only peaks to be candidates for LOS path, our approach does not relate the estimated delay to a local maximum but it allows any positive DP (p-dp) to be candidate for the true delay. It is important to clarify that by positive DP we refer to any discontinuity point that forms a convex angle, while negative DP (n-dp) refers to a concave angle. Naturally, the local maximum and the local minimum points are particular cases and they belong to the p-dp and n-dp groups correspondingly. In the Fig. 5.4 we show some of the most often encountered DPs in the Acf. The upper part of the figure contains the p-dps while the lower part contains the n-dps. Intuitively, we could consider a p-dp as the result of a closely-spaced multipath environment, where the additive paths are not necessarily visually distinguishable. In the left plot of Fig. 5.5, we see the Acf of the received signal for a 3-path Nakagami-m fading channel while in the right plot we have zoomed in the top of the main lobe and marked the most visible DPs. From the right plot of the Fig. 5.5, it is obvious that the true LOS delay (p-dp1) does not correspond to a local maximum but to a positive discontinuity

44 Novel Contributions 33 Figure 5.4: Types of Discontinuity Points. point that particularly belongs to the type (a) of the Fig It is worthwhile to mention that in this example all the three paths are present in the form of p-dps, where p-dp2 and p-dp3 correspond to types (b) and (c), respectively. Although multipath can be considered as a type of noise itself, we need to take also into account other types of noise such as AWGN or receiver noise. So, when it comes to the noise mitigation problem, there are two stages. First, we estimate the noise level for choosing an appropriate approach, depending if CNR is high or low, for the code delay estimation (as described in the previous section). Second, we try to cancel out as much noise as possible, by employing a threshold, Ac f thresh, which reduces further the search space of the candidate p-dps for the LOS delay. Our approach for choosing the threshold level is based on an area ratio. In particular, we define a percentage of area exclusion, ExcPerc, the total area enclosed by Acf, TotArea, the partial area, PartArea(i) which is the area enclosed by Acf and limited by the level i from the AcfLevel vector (as described in 5.1.2), and the current exclusion area at level i, CurExcArea(i), defined as CurExcArea(i) = PartArea(i)/TotArea. Then the Ac f thresh is defined as: Ac f thresh = {Ac f Level(i) CurExcArea(i) ExcPerc & CurExcArea(i + 1) ExcPerc} (5.3) In Fig. 5.6, we see where the Ac f thresh is placed on the non-coherent Acf, for two different CNR values, when ExcPerc = 70%. We remark, that the channel is static and

45 Novel Contributions 34 1 True Path Delays: True Path Delays: p DP p DP Acf 0.5 Acf Time axis Time axis p DP3 Figure 5.5: Autocorrelation function for a 3-path Nakagami-m fading channel (left plot) and the top of the main lobe of the Acf (right plot). the number of paths varies uniformly from 2 to 4, and the spacing between two paths varies also uniformly between 0 and 0.35 chips. We notice that for CNR = 50 db/hz, the threshold is placed high enough to exclude the noise and the sidelobes of the Acf, however the latter (Acf sidelobes) may not be always the case. In the case where CNR = 20 db/hz, the threshold manages to exclude part of the Acf, which could be used for further processing. 1 CNR=20dB/Hz, Exc. Perc.= 70% 1 CNR=50dB/Hz, Exc. Perc.= 70% Non coherent Acf % of the total area enclosed by Acf and limited by Acf thresh Non coherent Acf % of the total area enclosed by Acf and limited by Acf thresh Time axis Time axis Figure 5.6: Placement of Ac f t hresh for CNR= 20 db/hz (left plot) and CNR= 50 db/hz (right plot))

46 Novel Contributions Code Delay Estimation As it was mentioned in Chapter 3, code delay estimators can be divided into two main classes, feedback and feedforward. Here we use the feedforward technique because of its advantages mentioned in [59]. In particular, the method we employ has the novelty of being CNR-dependent, where the distinction is made between low and high CNR levels. In the case of low CNR, we take into account the information from the previous estimation. This is needed because in conditions where noise dominates the signal, methods based on the current Acf only might be insufficient to keep track of the LOS path, and the receiver eventually loses the lock. However, full dependency on the previous delay estimate may also lead to loss of lock, in the case where the initial error (the one coming from the acquisition stage) is big enough. Therefore, methods for reducing the search space, or appropriate windowing of the Acf can boost the performance of a feedforward estimator. In the case where high CNR level is detected, no information from the previous delay is used in order to reduce the impact of the initial error. The signal dominates the error, and techniques based on the current Acf only can be used to estimate the LOS delay. We remark that the accuracy of the CNR-dependent methods is critically dependent on the accuracy of the CNR estimator, as well as on the number of CNR distinction levels (in our case we have one distinction level). However, complexity issues need to be taken into account as a limitation factor to increased accuracy. 5.4 Procedure This section presents the procedure of the algorithm Discontinuity Tracker () which aims to resolve the problem of code delay estimation in multipath, low CNR environment. is the output of our work led according to Divide and Conquer principle and copes with the three sub-problems, as they were presented in the previous sections. The procedure of is depicted in Fig In the figure, we see that is represented in three blocks, each of which deals with the sub-problems of multipath/noise mitigation, CNR estimation and code delay estimation. The inputs of are the non-coherent Acf, the previous delay, τ, the oversampling factor, N s, the BOC modulation order, N B = 2, and the matrix, Level thresh, that contains the level thresholds for each (N c,n nc ) pair. The output is the estimated delay, τ (we notice that in the figure, the symbol we use for the estimated delay is τ instead of τ and that the symbol ε means belongs to ).

47 Novel Contributions Multipath/Noise Mitigation Here, we compute the inverse Tangent, invtang(i) for each pair of points of the Acf and then we calculate the differences for every inverse tangent pair. Each tangent difference corresponds to the inner angle, φ i, of a 3-point set. The middle point of each set is a discontinuity point (DP) and from those we keep only the positive ones, posdiscont (p-dps). Then, we compute the Acf threshold ( thresh ) for ExPerc = 70%, below which all the p-dps are discarded. The value of ExPerc is chosen based on the ideal Non-coherent Acf, so as the Acf sidelobes to be excluded. In Fig. 5.7, we see the ideal non-coherent Acf and where the thresh is placed. 1 Exclusion percentage 70% Ideal Non Coherent Acf % of the Total Area is excluded 30% of the Total Area enclosed by non Coh. Acf Time axis [chips] Figure 5.7: threshold based on 70% exclusion of the total are enclosed by the non-coherent Acf Although this value is based only on a single-path static channel, the fact that we are using the proportion (70% exclusion) allows thresh to vary according the current Acf and in this way we try cancel out part of the noise. As part of the future work, ExPerc could be somehow optimized for other channel profiles as well as we could examine the possibility of it being a function of the estimated CNR level. We also remark that this part of the algorithm does not solve the problem of multipath in the strict manner of identifying the paths and rejecting the non-los paths. We approach the problem by trying to include all the paths in our search space (appearing as p-dps), while cancelling out part of the noise. 2. CNR Estimation Here, we want to estimate the CNR level in order to apply different method for code

48 Novel Contributions 37 delay estimation (CNR-dependent). Therefore, we compute the level crossing rate, LCR(a), at each level a taken from the vector Ac f Level = [0.01 : 0.01 : 1] and we find the position, â, of the maximum LCR in Ac f Level. The process is the same as the one presented in Section 5.1, with the difference that here our goal is to distinguish between the CNR level of 30 db/hz. The main reason for choosing this value for Level thresh and not the one for indoor/outdoor distinction (20 db/hz), is that we want to distinguish between bad and good CNR conditions. In addition, the higher the Level thresh is, the smaller the standard deviation of â is. This implies that the accuracy of CNR level distinction is higher when Level thresh is higher. Using a set of preliminary experiments, we found that the value of 30 db/hz is appropriate for our goal; however, there is place for optimization and the possibility of more than one CNR distinction level is for future investigation. We notice that the value of Level thresh is dependent on the pair (N nc,n c ) ([80]) and in Table 5.2 we see the averaged Acf level of max LCR versus N nc and N c for the fixed CNR value of 30 db/hz. The averaging was made over 0 random Acf realizations and the channel was 1-path static. 3. Code Delay Estimation In the last block of, the goal is to estimate the delay of the LOS path. For this purpose, we first detect whether we have good or bad CNR conditions. If â Level thresh, then we use the information from the previous estimate, and the estimated delay, τ, is the p-dp from CandDiscont which is closest to the previous estimate. If high CNR level is detected (â Level thresh ), then Ac f thresh is set high enough to exclude the noise as can be seen in Fig From the p-dps which are above the threshold, we assume that the first one (CandDiscont(1)) corresponds either to the left sidelobe of the LOS path (if Ac f thresh was set higher than the sidelobe) or to the main lobe of the LOS path (if Ac f thresh was set lower that the sidelobe). Here, we take into account that the LOS path is the first arriving path. We also notice that the distance between the left sidelobe and the main lobe is 1 2 N snb. In the future, our plans are to find a method for identifying all the paths, for medium to high CNR levels, and thus, to increase the accuracy of the delay estimation block of.

49 Novel Contributions 38 Figure 5.8: procedure Table 5.2: Averaged Acf level of the max LCR (â) versus N nc and N c for 1-path static channel and CNR=30 db/hz. N c = N nc =