Receiver Strategies for GPS L2C Signal Processing

Transcription

1 Receiver Strategies for GPS L2C Signal Processing By SANA ULLAH QAISAR A thesis submitted to The University of New South Wales in partial fulfillment of the requirements for the degree of Doctor of Philosophy School of Surveying & Spatial Information Systems The University of New South Wales Australia March, 21

2 Abstract The central focus of the GPS modernization program is the addition of new navigation signals. L2C is the first modernized GPS civilian signal to become available over the full constellation by the year 216. It has an advanced signal structure designed to meet the demands of new and more challenging application environments. Due to its imminent availability and modern code design L2C is likely to be a widely used GPS signal. A GPS L2C receiver must perform an exhaustive search to acquire the signal, due to the unusually long ranging codes used in L2C, consuming substantial resources at the very first stage of digital processing. Dealing with this problem is particularly important for L2C success in the mass market of low-cost mobile devices such as mobile phones and PDAs, constrained by battery power. This dissertation identifies three different approaches for saving processing resources during the L2C acquisition phase. The first approach focuses on the design of the local replica code to accommodate multiple searches in parallel. Several composite codes are proposed to expedite the L2C search and their acquisition performance is evaluated. In the second approach, down-sampling of baseband signals is investigated, to perform correlation at slower rates, saving searches in the code delay dimension whilst reducing the computations per search. A chip-wise correlation strategy is proposed where one correlation per each chip period is sufficient to accomplish a search without compromising detection performance. In the third approach, partial-period correlations are performed to save searches in the Doppler dimension and their outcomes are combined through a semi-coherent differential processing technique. The detection performance of this approach is shown to be competitive with the full-period correlation. The L2C signal is also the first fully accessible signal to join the legacy L1 C/A signal to serve dual frequency civil users. In this context, two different investigations are carried out in this thesis. First, it is identified that while longer L2C codes might appear a straightforward decision to combat the cross-correlation interference in a dual frequency GPS L1/L2C receiver, in fact L1 C/A is more robust in the Assisted-GPS, warm start and reacquisition scenarios. Secondly, a scheme for improving sensitivity and measurement accuracy of the L1 carrier tracking loop by providing aiding from the L2C PLL is evaluated. A margin of at least 3 db against the effects of radio frequency interference is shown to be achieved by the aided- L1 tracking loop, while such benefits might previously have been obtained though inertial aiding. i

3 Acknowledgements All praises are due to Allah the almighty God, the most Beneficent and the most Merciful. I thank Him for giving me the ability to go well through the rigorous and gratifying times of PhD study. After that, I am grateful to my supervisor Associate Professor Andrew Graham Dempster for providing me the wonderful opportunity of working under his supervision. His passion for research, vision and professional approach were a great help and an inspiration throughout the course of my thesis. Thank you for your consistent guidance and support. I am equally thankful to Professor Chris Rizos who as my co-supervisor and Head of School always ensured the availability of adequate resources for my research. Thanks to both of my supervisors for providing me the opportunity to attend the European Space Agency GNSS Summer School 29 Berchtesgaden, where I was able to discuss my research in more detail with the leading scientists in the area of satellite navigation. Sincere thanks to Associate Professor Fabio Dovis and Tung Hai Ta from Politecnico di Torino, for their contribution to a part of this thesis developed at the University of New South Wales in a collaboration between the two institutions. Working with them was an excellent learning experience. I express my gratitude to the U.S. Institute of Navigation (ION) for appreciating my student paper and awarding me a sponsorship to present the paper at the 22nd International Technical Meeting of the ION Satellite Division 29. I cannot omit to thank my colleagues: Peter Mumford, Nagaraj Shivaramaiah, Omer Mubarak, Faisal Khan, Jinghui Wu, Asghar Tabatabaei, Éammon Glennon, Kevin Parkinson, Usman Iqbal, Bilal Amin and all the other members of the Satellite Navigation and Positioning group for their open technical and moral support to overcome any difficulties during the PhD period. The Australian Research Council is gratefully acknowledged for financing this research under the Discovery Project DP Finally, I feel proud to acknowledge the patience and continuous prayers of my wife, my son, my parents and all other family members for my success. ii

4 Table of Contents Abstract... i Acknowledgements... ii Table of Contents... iii List of Figures... vii List of Tables... xii Abbreviations... xiii 1. Introduction Global Positioning System GPS Modernization The L2C Signal L2C Research Overview Thesis Motivation and Objectives Thesis Contributions Thesis Structure List of Research Publications and Relevant Thesis Contents Background Introduction Overview of GPS Technology L2C Signal Structure Advantages of the New Signal Design L2C Acquisition Signal Acquisition Basics L2C Acquisition Load GPS L2C Receiver Replica Code Modification Down-Sampling Approach Segmented Correlation Processing L2C Post-Correlation Differential Combining CL Acquisition L2C Self Interference L2C Tracking Tracking Loop Basics L2C Combined Data/Pilot Tracking Aided Tracking Loops L2C as Aiding Source iii

5 Table of Contents 3. L2C Data Acquisition Apparatus Introduction L2 Up-Converter Hardware Realization Hardware Testing & Data Verification L2C Acquisition Results Dual Frequency L1/L2C Data Summary L2C Replica Code Design Introduction L2C Signal and System Model L2 CM Replica Code Designs Return to Zero CM (RZ CM) Code Return to Zero Extended CM (RZ ECM) Code Non Return to Zero CM (NRZ CM) Code Non Return to Zero Twin Carrier CM (NRZ TCM) Code Non Return to Zero Dual Channel CM (NRZ DCM) Code Non Return to Zero Folded CM (NRZ FCM) Code Performance Evaluation Code Recovery Function Phase Offset Loss Cross-Correlation Noise Probability of Detection Mean Acquisition Time Summary and Recommendations Down-Sampling Strategies for L2C Correlators Introduction Direct Down-Sampling Approach Anti-Aliasing Filter Signal Power Loss SNR Loss Autocorrelation Side Lobes Phase Offset Loss Non-Integer Down-Sampling Factors FFT Correlation Hardware Chip-Wise Down-Sampling System Architecture Correlator Output Acquisition Results iv

6 Table of Contents Power Consumption and Circuit Size Summary Post Processing of Segmented L2C Correlations Introduction Post-Correlation Differential Combining Partial-Period CM Correlation Architecture Differentially Coherent Combining Residual Carrier Phase Larger Span Differentially Coherent Combining Generalized Differentially Coherent Combining Differentially Semi-Coherent Combining Computational Complexity Performance Analysis Best Case Worst Case Receiver Operating Characteristics Coherent Integration Period CL Code Acquisition Overall Recommendations Summary Cross-Correlation Protection in L1 & L2C Signals Introduction Performance Metric Worst Cross-Correlation Cumulative Probability Sampled Code Sequences Code Observation Period Effect of Relative Doppler Offset Multiple Code Epochs Critical Doppler Window Signal Search Space Likelihood of Critical Doppler Window Overall Performance Comparison Navigation Data Transitions Non-Coherent CL Combinations Summary L2C-Aided L1 Carrier Tracking Introduction v

7 Table of Contents 8.2 L2C Tracking Replica Code Design Data and Pilot Tracking Channels Combined Data/Pilot Carrier Tracking L2C PLL Performance Aided Carrier Tracking Internal Aiding Architecture Performance Analysis of Aided Tracking Loop Aiding Noise Sensitivity Analysis Summary Conclusions Acquisition Load in L2C Receivers L2C Local Replica Code Design Down-Sampling of Baseband Signals Partial-Period Correlations Dual Frequency GPS L1/L2C Receivers Cross-Correlation Interference Aided L1 Carrier Tracking Recommendations for Future Work Appendix A A.1. Probability of False Alarm A.1.1 Conventional Differentially Coherent Combining A.1.2 Generalized Differentially Coherent Combining A.1. Probability of Detection A.1.1 Differentially Coherent Combining A.1.2 Generalized Differentially Coherent Combining Appendix B References vi

8 List of Figures Figure 1.1. Spectral contents of the L2 broadcast from modernized GPS satellites 2 Figure 1.2. a. GPS constellation status, February 19, 21 6 b. L2C satellite availability Figure 2.1. Basic principle of GPS signal transmission with L1 C/A signal example 11 Figure 2.2. A high level block diagram of GPS receiver 12 Figure 2.3. L2C code structure containing same CM but different CL 2 ms 13 segments in the CL period Figure 2.4. Cross Ambiguity Function of simulated noiseless L1 C/A signal 15 (top) Across the considered search grid (bottom) In the correct Doppler and delay bins Figure 2.5. Basic correlation scheme employed for signal acquisition in GPS 16 receivers Figure 2.6. Massively parallel correlators architecture used in parallel search 17 strategies Figure 2.7. Frequency domain parallel search architectures 18 a. FFT in the delay dimension b. FFT in the Doppler dimension Figure 2.8. Basic L2C replica symbols (2 chip periods) 22 Figure 2.9. A generic implementation of differentially coherent post correlation 26 combining. Each value of n corresponds to a different version Figure 2.1. Illustration of a near-far scenario. Both desired autocorrelation peaks 28 (PRN-1, blue) and interfering peaks (PRN-7, red) exceeding the threshold (solid grey line around the box) Simulation parameters: C/A code, TT=1ms, ff ss =5.7143MHz Figure A GPS carrier tracking phase locked loop 3 Figure Basic replica code choices for L2C tracking 32 Figure Contributions of various error sources to total phase jitter, 3 rd order L1 33 C/A PLL, TT =2ms, CC NN =3dBHz, Jerk stress=.25g/s Figure A Doppler aided phase locked loop in GPS receiver 34 Figure 3.1. Illustration of L2 up-conversion approach used for the hardware design 36 Figure 3.2. L2 up-converter hardware developed for L2C data collection 37 Figure 3.3. Hardware setup for L2C data acquisition using up-converter hardware 39 with: a. GP215 L1 RF front-end b. NordNav (Rxx-2) software GPS receiver L1 front-end Figure 3.4. Acquisition result of real L2C signal recorded through the up-converter 4 coupled with GP215. A separation of 1 chip period between the CM and CL codes can be confirmed Figure 3.5. Acquisition result of real L2C signal recorded through the up-converter 41 coupled with NordNav L1 front-end, confirming a separation of 1 chip between the CM and CL codes Figure 3.6. On-board L2 up-converter design used in Namuru V2 GPS L1/L2C receiver 41 vii

9 List of Figures Figure 3.7. Hardware setup for dual frequency L1/L2C data acquisition with 42 Namuru-V2 board Figure 3.8. Tracking result of real dual frequency L1/L2C data recorded with the 43 Namuru-V2 board using the L2 up-converter Figure 4.1. a. Received L2C code, mm 74, NN pp = b. Considered designs of local replica code for L2C acquisition Figure 4.2. L2C code recovery function of considered reference codes 49 Simulation data: PRN-1 code sampled at MHz Figure 4.3. Worst acquisition loss as a function of search step, in considered 5 reference codes Simulation data: PRN-1 code sampled at MHz Figure 4.4. Cross-correlation performance of considered L2C reference codes, 51 PRN-1 and PRN-7 codes sampled at MHz Figure 4.5. L2C correlation system considered for detection probability analysis 52 Figure 4.6. Average probabilities of L2C detection with considered reference 56 codes, PP ffff = 1 3, MM=1 (- theory, + simulation) Figure 4.7. L2C mean acquisition times with considered reference codes for 57 average probabilities case, PP ffff = 1 3, MM=1 (-theory, +simulation) Figure 4.8. Relative Speed-Sensitivity tradeoff levels offered by considered L2C 58 replica codes Figure 5.1. A direct down-sampling approach for performing correlation at slower 61 rates Figure 5.2. a. L2C code spectrum indicating the 2 MHz bandwidth occupied by the 62 main lobe b. Spectral representation with ambient noise Figure 5.3. L2C signal power loss due to pre-correlation filtering 63 Figure 5.4. Effect of anti-aliasing filtering on L2C signal 64 a. Autocorrelation function b. Worst autocorrelation-margin loss Figure 5.5. Worst phase-offset loss in L2C acquisition for the two reference 65 sampling frequencies when using a. RZ CM replica code b. NRZ CM replica code Figure 5.6. Characterization of L2C acquisition loss due to sampling jitter 67 (a) As a function of down-sampling factor for ff ss = MHz (b) As a function of original sampling frequencies for ff NNNN = 1.23 MHz Figure 5.7. Direct down-sampling FFT based correlation architecture 7 Figure 5.8. Altera Stratix DSP Development Board used for hardware implementation of direct down-sampling FFT correlation architecture 7 Figure 5.9. Real L2C SVN 53 acquisition results 71 (a) Full rate correlation processing, η= db Direct down-sampling approach (b) without filter (η=23.523db) and (c) with filter (η=27.296db) Figure 5.1. Chip-Wise down-sampling correlation architecture 72 Figure Possible phases (starting points for the samples accumulation process) 73 of incoming L2C code sampled at MHz Figure All possible phases of the received and replica codes over 2 chip periods, f s =5.714 MHz 73 viii

10 List of Figures Figure Generic structure of the received (top) and replica (bottom) L2C codes, 74 over 2 chip periods Figure CW correlator output for 6 (ff ss =5.714 MHz) consecutive phases of the 75 received L2C signal a. Noiseless simulated signal b. Real signal, CC NN :4 db-hz Figure Comparison of real L2C SVN-48 CAF obtained with full-rate and CW 76 correlation Figure Comparison of full-rate and CW L2C correlators for a full CM period 77 scan a. Power consumption b. Circuit size Figure 6.1. A partial-period CM correlation architecture 8 Figure 6.2. DC combining scheme for segmented CM correlation 81 Figure 6.3. Generalized DC combining scheme for segmented CM correlation, NN= MM nn 1 84 Figure 6.4. A DSC combining scheme for segmented CM correlation, phase 86 dependence has been removed by applying absolute operation prior to final summation across all spans, NN= MM nn 1 Figure 6.5. Detection performance of non-coherent post processing technique 88 considering correct search cell, PP ffff = 1 3, --:Theory, :MC simulations Figure 6.6. Detection performance of considered post correlation processing 89 techniques for the best case ( ff=), TT=1ms, MM=2, PP ffff = 1 3 Figure 6.7. Detection performance of considered post correlation processing 9 techniques for the worst case ( ff = 1 TT), TT=1ms, MM=2, PP ffff = 1 3, due to phase dependence GDC has the worst performance Figure 6.8. Receiver operating characteristic (ROC) curves for the worst case as 91 function of the span-size, (a) GDC technique suffering from the phase loss (b) DSC combining technique with a consistent improvement Figure 6.9. Performance comparison of the DSC combining technique with various 93 combinations of TTand MM a. Probability of detection b. Mean acquisition time, ff=, PP ffff = 1 3 Figure 6.1. Detection performance comparison of DSC combining for segmented 95 (TT=2ms) CL correlations (*) with straight coherent (TT CCCC -ms) correlation (-) Figure Detection probability of Non-coherent CM combining, TT=2ms, ff= 96 Figure 7.1. Worst cross-correlations in C/A, CM and CL codes for all individual 99 codes pair Figure 7.2. Cross-correlation performance comparison of C/A, CM and CL chip 1 sequences over the corresponding full code periods Figure 7.3. Cross-correlation performance comparison of original C/A chip 11 sequence with synchronous (5 samples per chip) and asynchronous (5.714 sample per chip) sampling Figure 7.4. Graphical illustration of the relative Doppler offset concept: Difference in Doppler frequencies of the local and interfering satellite signals 13 ix

11 List of Figures Figure 7.5. Figure 7.6. Figure 7.7. Figure 7.8. Reference correlation system considered for the cross-correlation analysis Offset carriers of 5 Hz and 1 Hz respectively taking exactly opposite and the same phase across 1ms intervals of the product of the local and the interfering spreading codes Cross-correlation behavior of C/A and CM codes both observed over 2ms, in response to relative Doppler offset. (a) Over a relative Doppler offset range of ±5KHz (b) Over the relative Doppler offset range of to 1 Hz Simulation results showing the status of signal search space in dual frequency GPS L1/L2C receiver in the absence of Near-Far problem based on simulations. Desired L1 (CA) and L2 (CM) peaks are well above the corresponding CC peaks Figure 7.9. Simulation results showing the status of search space in GPS L1/L2C 11 receivers in the event of Near-Far problem. Desired L1 (CA) and L2 (CM) have a similar level as the corresponding CC peaks. Narrow search range illustrates the expected scenarios in assisted acquisition Figure 7.1. Test sites selected for computation of relative Doppler offset 111 distribution Figure Distribution of relative Doppler offsets computed for each test location 112 a. Sydney, b. Paris, c. Singapore, d. Brasilia and e. Toronto Figure Cumulative probability of relative Doppler offsets for the test locations 113 a. Sydney, b. Paris, c. Singapore, d. Brasilia and (e) Toronto Figure Overall cross-correlation performance comparison of C/A & CM codes, 114 both observed over 2ms, in the assisted acquisition scenario Figure Cross-correlation performance of C/A and CM code, both observed 116 over 2 ms in the presence of data bit transition at all possible locations Figure Cross-correlation performance of CM and CL code with non-coherent 117 integrations, TT=2ms Figure 8.1. a. E-L (.5 chip correlator spacing) DLL discriminator response to 12 different L2C tracking replica codes b. Multipath error for different L2C tracking replica codes using.5 chip correlator spacing Figure 8.2. Basic L2C PLL implementations using a CM or CL coupling 121 Figure 8.3. Illustration of a combined data/pilot L2C PLL implementation, αα and ββ 122 are the appropriate scaling factors required for the combinations Figure 8.4. Thermal phase jitter comparison in different L2C PLL implementations 123 Figure 8.5. L2C carrier tracking jitter as a function of loop bandwidth, using pilot channel (a) Contribution to total jitter by various error sources (b) combined effect of error sources, TT=2ms, CC NN =3 db-hz, Oscillator specification as given in Table x

12 List of Figures Figure 8.6. Positioning accuracy of standalone and differential GPS showing that the performance of dual frequency receivers can be degraded to that of the single frequency GPS receiver by the RFI Figure 8.7. A direct L2 to L1 feeding implementation 129 (a) Architecture (b) Effect of ionosphere induced frequency shift on real signal tracking Figure 8.8. An L2 to L1 carrier loop aiding implementation 13 (a) Architecture (b) Tracking results of real signals Figure 8.9. L2C-to-L1 carrier aiding architecture considered for the analysis 131 Figure 8.1. Performance comparison of unaided (BB LL =1Hz) and aided (BB LL =1,2,5,1 133 Hz) tracking loops for the scenario described by Table 8.1 and Table 8.2, showing an improvement of 3 db in the tracking sensitivity, BB LL,LL2 =1Hz Figure Performance comparison of unaided (BB LL =1Hz) and aided (BB LL =1Hz) 134 tracking for different loop bandwidths of L2 PLL over the considered range of dynamic stress using the specification given in Table8.1 and Table 8.2 Figure Performance comparison of unaided (BB LL =1Hz) and aided (BB LL =1Hz) tracking over the considered range of dynamic stress using the specification given in Table 8.1 and Table Figure A.1. Figure A.2. The conditional probability density functions versus the histograms (obtained by 5, simulation runs) of the conventional differentially coherent combining The conditional probability density functions versus the histograms (obtained by 5, simulation runs) of the generalized differentially coherent combining xi

13 List of Tables Table 1.1. Overview of L2C research classification with example publications 4 Table 2.1. Comparison of key signal parameters in L1 and L2C 14 Table 3.1. Details of COTS parts used in the L2 up-converter hardware 38 Table 5.1. Summary of direct down-sampling analysis for the sampling frequency of MHz 69 Table 5.2. Table 6.1. Summary of direct down-sampling analysis for the sampling frequency of MHz, a. NN = 1 to 8, b. NN = 9 to 16 Computational complexity comparison of all considered differential combining schemes with full period coherent correlation.{ }: original correlation load, ( ): Extra computations Table 6.2. Computational complexity comparison of all considered differential combining schemes with full period coherent integration for the example of ff ss =5.714 MHz, TT=1ms, MM=2 and KK=19, ( ): Extra computations 87 Table 6.3. Performance improvement in DSC combining over the conventional DC and NC combining techniques 89 Table 6.4. Performance comparison of DSC combining technique for various combinations of TT and MM with the coherent 2ms integration 93 Table 6.5. Detection performance of DSC combining for segmented CL acquisition 95 Table 6.6. Overall recommendations for L2C search using segmented correlations and post correlation processing 97 Table 7.1. ECEF coordinates of test sites 111 Table 7.2. Percentage of relative Doppler offsets observed for each test location 112 Table 7.3. Satellite PRN selected for experiments 112 Table 7.4. Relative Doppler offsets obtained for the experiments 112 Table 8.1. L1 and L2C tracking parameters considered for the analysis 133 Table 8.2. Specifications of non-thermal error sources considered for the analysis 133 xii

14 List of Abbreviations AC ACF AWGN BPSK C/A C/No CAF CC CDMA CDO CDW CL CM CNAV COTS CW CWI DC DSC DSSS FEC FFT FPGA GDC GLONASS GNSS GPCDD GPS IF IGEB JPO L1 L1C Autocorrelation Autocorrelation Function Additive White Gaussian Noise Binary Phase Shift Keying Coarse Acquisition Carrier to Noise Ratio Cross Ambiguity Function Cross-Correlation Code Division Multiple Access Critical Doppler Offset Critical Doppler Window Civil Long Civil Moderate Civil Navigation Commercial Off the Shelf Chip Wise Continuous Wave Interference Differentially Coherent Differentially Semi-Coherent Direct Sequence Spread Spectrum Forward Error Correction Fast Fourier Transform Field Programmable Gate Array Generalized Differentially Coherent (Russian) Global Navigation Satellite System Global Navigation Satellite System Generalized Post Correlation Differential Detector Global Positioning System Intermediate Frequency Interagency GPS Executive Board Joint Program Office Link-1, Frequency: MHz L1 Civilian Signal xiii

15 List of Abbreviations L2 L2C L5 LE LNA MAI M-Code MCS NC NCO NRZ NRZ DCM NRZ FCM NRZ TCM P(Y) PDF PLL PNT PRN RF RFI ROC RTK RZ RZ ECM SIC SNR SV SVN TDM Link-2, Frequency: MHz L2 Civilian Signal Link-5, Frequency: MHz Logic Element Low Noise Amplifier Multiple Access Interference Military Code Master Control Station Non Coherent Numerically Controlled Oscillator Non return-to-zero Non Return-to-Zero Dual Channel CM Non Return-to-Zero Folded CM Non Return-to-Zero Twin Carrier CM Precision encrypted military code Probability Density Function Phase Locked Loop Position, Navigation and Timing Pseudorandom Noise Radio Frequency Radio Frequency Interference Receiver Operating Characteristics Real Time Kinematics Return-to-zero Return-to-Zero Extended CM Successive Interference Cancellation Signal to Noise Ratio Space Vehicle Space Vehicle Number Time Division Multiplexed xiv

16 Chapter 1 Introduction In a world that travels and communicates faster than ever, the need for precise location and navigation has never been greater. Several nations have started developing new Global Navigation Satellite Systems (GNSS) such as the European Galileo and the Chinese Compass (Hofmann-Wellenhof, et al., 27). The existing Global Positioning System (GPS) and Russian Global Navigation Satellite System (GLONASS), at the same time, have initiated modernization plans to offer new services and enhanced performance Global Positioning System GPS is a constellation of over 24 U.S. Government satellites providing position, navigation and timing (PNT) services to civilian and military users on a continuous (allweather, anytime), worldwide basis without a direct user charge. The GPS is managed by the National Space-Based Positioning, Navigation, and Timing Executive Committee, supported by the PNT Executive Secretariat (PNT, 29). Over the years, GPS guided munitions have hit their mark, minimizing collateral damage and today nearly every piece of U.S. and allies military equipment uses GPS. On the civil side, GPS has become embedded in our daily life; examples include automobile navigation, aircraft landing, emergency rescue services, financial transactions and precision farming GPS Modernization Through the modernization program the U.S. Government continues to improve GPS accuracy, integrity and robustness, supporting the growing GPS dependence by commercial industry while protecting national security and foreign policy interests. The original GPS spacecraft transmit a civilian coarse acquisition (C/A) code on L1 ( MHz) and an encrypted precision military code P(Y) on both L1 and L2 1

17 Chapter 1 Introduction L2C M P(Y) Frequency (MHz) Figure 1.1. Spectral contents of the L2 broadcast from modernized GPS satellites ( MHz) L-band frequencies. In March 1996, a Presidential Decision Directive stated the first national GPS policy and established the Interagency GPS Executive Board (IGEB) for enhancing the GPS capabilities. A White House press release on March 3, 1998 announced an IGEB decision to implement two new civil signals, namely L2C (Link-2 Civil) and L5 (Link-5: MHz). Around the same time, that is 1997 and 1998, the GPS Joint Program Office (JPO) investigated the design of a new military (M) signal for use on L1 and L2 frequencies. Furthermore, cooperation with the European Galileo led to a common design of another civil signal at the L1 frequency named L1C. Regarding the space segment, new satellite series designated Block IIR-M, Block IIF and GPS-III are being developed to carry these new signals. In general, these modern satellites incorporate more precise clocks, can deliver more power and include on-station re-programmable processors. Similarly, the ground control stations have been subjected to modernization including upgrading ground antennas and receivers, replacing mainframe computers with distributed architectures and enabling new command and control capabilities for new satellites The L2C Signal L2C is the first modernized GPS signal, initially broadcast by SVN-53 (the first Block IIR-M satellite in space), in September 25. Primarily, there were two expectations from 2

18 Chapter 1 Introduction the second, after L1 C/A, GPS civil signal. First, it shall provide the opportunity to support dual frequency operations, when combined with the legacy L1 C/A signal, such as removing ionospheric errors and enhancing receiver robustness and secondly it should be a valuable host for single frequency GPS applications which have been served by only L1 C/A signal. To meet these requirements, the L2C design team developed a signal structure markedly different from the L1 C/A signal (Fontana, et al., 21; Stansell, 21). In particular, the new L2C signal offers the following points of interest. Having a second civil code on L2 eliminates the need for complex and patent protected semi-codeless processing used for L2 measurements while improving the quality of dual frequency measurements at the same time. The overall L2C code chipping rate is restricted to 1.23 MHz as in L1 C/A code to avoid spectral contamination from the new military M code as shown in Figure 1.1 and to allow synchronous operations with the legacy L1 C/A code. The L2C signal consists of two inter-multiplexed components. A data component modulated by CM (moderate) code and a data-less component (also known as a pilot code) namely CL (long) code, where the data-less signal component can improve the signal tracking performance by at least 6dB. Longer code periods are selected to achieve superior cross-correlation characteristics in order to overcome some limitations of the legacy C/A code. The CM code period is synchronized with navigation data boundaries removing the need for bit synchronization once the signal is acquired L2C Research Overview The advent of the second, after L1 C/A, fully accessible L2C signal was an exciting opportunity for GNSS receiver designers. Developing new systems and upgrading existing ones to avail benefits of the new signal was a natural response to L2C s arrival. The research on L2C, to date, can be classified into three domains. First, considering single frequency GPS L2C receivers, a number of researchers assessed the new signal 3

19 Chapter 1 Introduction Single Frequency GPS L2C Receiver Dual Frequency GPS L1/L2C Receiver L2C Signal Quality Assessment Performance assessment of new signal design: potential benefits and implications in L2C receivers Signal acquisition algorithms (Stansell, 21) (Fontana, et al., 21) (Enge, 23) (Tran, 24) (Dempster, 26) (Psiaki, 24) (Cho, et al., 24) (Yang, 25) (Ziedan, 25) (Moghaddam, et al., 26) L1 assisted L2C signal acquisition Joint L1/L2C signal processing (Ledvina, et al., 25) (Lim, et al., 26) (Yang, 25) (Gernot, et al., 28a) Comparison with C/A & P code (Simsky, et al., 26) (Sükeová, et al., 27) Signal tracking algorithms (Tran and Hegarty, 22) (Psiaki, et al., 27) (Muthuraman, et al., 28) Ionospheric corrections (Rizos, et al., 25) (Fujisawa, et al., 28) (O Keefe, et al., 29) RTK positioning (Pany, et al., 24) Space based receivers (Meehan, et al., 26) RF interference rejection Table 1.1. Overview of L2C research classification with example publications indicates thesis contributions for each of the corresponding research category design to identify potential benefit and implications for the receiver as well as suggested new processing algorithms. Second, in the context of dual frequency GPS L1/L2C receivers, available L2C signals are utilized for ionospheric corrections and improving the performance of real time kinematic (RTK) receivers. The L1/L2C inter-frequency operations to improve the overall robustness of the receiver e.g. tracking loop aiding are also investigated. Third, several research organizations conducted independent tests to measure the quality of received L2C signals in terms of signal to noise ratio and multipath and compared it with that of the C/A and P code. It is also shown that L2C is eminently usable as a signal for space-based science receivers. Table 1.1 presents a picture of overall L2C research contributions. A detailed discussion of previous L2C research with additional relevant references is provided in Chapter Thesis Motivation and Objectives Besides the interest of acquiring the capabilities of working with the new signal, the following requirements drove the research presented in this thesis. 4

20 Chapter 1 Introduction One of the reasons for the limited chipping rate selected for L2C compared to other new civil signals was to save power and hence the L2C receiver was thought to be a favorite for battery operated hand held devices such as mobile phones and PDAs (Fontana, et al., 21). Unfortunately, where the new signal design offers several benefits, due to longer ranging codes, it puts an extensive search load on the receiver leading to increased power consumption. Novel correlation schemes are therefore required to cut down the search computations and hence the power consumption. One of the objectives of this thesis is to develop such new L2C signal search systems with minimal sensitivity loss, if any, to meet the power efficiency requirement of next generation mobile devices. The main purpose of having much longer L2C codes is to achieve extra protection against the self interference or cross-correlation which was considered insufficient in the legacy L1 C/A signal. However, due to continuous satellite motion and possible receiver dynamics the self interference behavior might change significantly leading to situations where in fact extended C/A code will be a preferred choice to resist cross-correlations rather than L2C codes. Comparison of self interference behavior in L1 and L2C signals to identify the right signal choice for preventing cross-correlation, under different operating conditions is another point of interest of this thesis. In the context of a standalone dual frequency GPS L1/L2C receiver, due to ionospheric corrections, the positioning accuracy can be improved ten-fold when compared to the single frequency GPS receiver. Unfortunately, in the presence of radio frequency (RF) interference this performance level tends towards that of a single frequency GPS receiver. However, collaboration between two signals of different frequencies, hosted by the same receiver, can be established to combat the RF interference to maintain higher positioning accuracy. Part of the thesis aims to develop and evaluate a coupling system that takes advantage of the modern L2C design to achieve a margin against the RF interference whilst improving the measurement accuracy. 5

21 Chapter 1 Introduction Allocated slot A D E 2 C Orbital plane 2 B Number of L2C satellites F IIA IIR IIR-M (a) Year (b) Figure 1.2. (a) GPS constellation status, February 19, 21 (b) L2C satellite availability The current GPS constellation status and the L2C population growth, shown in Figure 1.2, indicate its early availability, before any other new GPS civil signal. In other words, L2C research has more immediate application in industry than for other signals which provides another source of motivation for this thesis Thesis Contributions This research on L2C was carried out from August 26 through to March 21. The following main contributions are described by the thesis. A detailed analysis of L2C code design in the context of acquisition performance and identification of various replica code structures for efficient signal acquisition. Investigation of low rate correlations for L2C acquisition through down-sampling of baseband signals and development of a Chip-Wise (CW) correlation strategy for performing L2C acquisition at the code chipping rate without compromising detection performance. An analysis of post correlation processing for L2C acquisition through partialperiod correlations and development of a differentially semi-coherent (DSC) 6

22 Chapter 1 Introduction combining technique for improving the L2C acquisition sensitivity as compared to conventional post processing approaches. This research is conducted in collaboration with researchers from Politecnico di Torino, Italy. A detailed assessment of multiple access interference (MAI) in L1 and L2C signals for identification of right code/frequency to combat the Near-Far problem in dual frequency GPS L1/L2C receiver, under various operating conditions. Sensitivity and performance analysis of L1 carrier tracking loop when aided by the L2C phase locked loop in dual frequency GPS L1/L2C receivers for identification of protection margin against the RF interference. A combination of theoretical analysis, simulations and real data experiments is applied for validation of various investigations carried out in the thesis. In terms of research publications, the contributions along with their corresponding thesis contents are listed in section Thesis Structure The remainder of the thesis is organized into eight chapters as follows. Chapter 2 provides the necessary technical background required to comprehend the discussions in following chapters. The relevant previous work is discussed and thesis contributions, in the context of required L2C research, are justified. Chapter 3 describes the L2 up-converter hardware developed for obtaining real L2C data required for authentication of various investigations carried out in the thesis. Acquisition and tracking results that verify the integrity of collected data are also discussed. Chapter 4 to Chapter 6 focus on the issue of signal acquisition load in GPS L2C receivers. Chapter 4 presents analysis of various designs of L2C replica code in terms of standard acquisition performance parameters. Strengths and potential application scenarios for each design are identified and some recommendations for search strategies are made. Chapter 5 first discusses the direct down-sampling of baseband signals for L2C acquisition and the chip-wise correlation approach to minimize the signal search in code 7

23 Chapter 1 Introduction delay dimension is then presented. Chapter 6 addresses the Doppler search load in L2C acquisition. Various post-correlation processing techniques for partial-period based L2C acquisition are evaluated. The differentially semi-coherent combining scheme for segmented L2C correlations is then presented. Chapter 7 is devoted to assessment of multiple access interference in L1 and L2C signals. The impact of various factors on the ability of the two signals to prevent the Near-Far problem is evaluated and acquisition strategies based on relative strengths of the two signals are recommended. Chapter 8 provides performance analysis of aided-l1 carrier tracking in dual frequency GPS L1/L2C receivers. The benefits offered by the aiding (L2C) tracking loop and sensitivity gain of the aided tracking loop are evaluated. Concluding remarks and some recommendations for future work are given in Chapter 9. 8

24 Chapter 1 Introduction 1.8. List of Research Publications and Relevant Thesis Contents Publications Qaisar S. U. and A. G. Dempster, "Receiving the L2C signal with Namuru GPS L1 receiver", IGNSS Symposium on GPS/GNSS, Sydney Australia, 27, paper 53. Thesis Contents Covered Chapter 3 Qaisar S. U. and A. G. Dempster, "Assessment of L2C replica code design for efficient signal acquisition", IEEE Transactions on Aerospace & Electronic Systems, accepted for publication, 29. Chapter 4 Section 5.3 Qaisar S. U., N. C. Shivaramaiah, A. G. Dempster and C. Rizos, "Filtering IF samples to reduce the computational load of frequency domain acquisition in GNSS receivers", in proceedings of 21st International Technical Meeting of the Satellite Division of the U.S. Institute of Navigation ION GNSS, Savannah GA, 28, pp Chapter 5 Qaisar S. U., N. C. Shivaramaiah and A. G. Dempster, "Exploiting the spectrum envelope for GPS L2C signal acquisition", in proceedings of European Navigation Conference ENC-GNSS, Toulouse France, 28, paper 38. Qaisar S. U., T. H. Ta, A. G. Dempster and F. Dovis, "Post detection integration strategies for GPS L2C signal acquisition", in proceedings of IGNSS Symposium on GPS/GNSS, Gold Coast Australia, 29, paper 45. Ta T. H, S. U. Qaisar, A. G. Dempster and F. Dovis, "Partial differential post correlation processing for GPS L2C signal acquisition, IEEE Transactions on Aerospace & Electronic Systems, 29, under review. Chapter 6 Qaisar S. U., N. C. Shivaramaiah and A. G. Dempster, "Evaluation of undersampling in GNSS correlators for efficient parallel acquisition", GPS Solutions, 29, under review Qaisar S. U. and A. G. Dempster, "Crosscorrelation performance assessment of GPS L1 and L2 Civil codes for signal acquisition", IET Radar Sonar & Navigation Journal, accepted for publication, 21. Qaisar S. U. and A. G. Dempster, "Cross-correlation performance comparison of L1 & L2C GPS codes for weak signal acquisition", in proceedings of International Symposium on GPS/GNSS, Tokyo Japan, 28. Chapter 7 Qaisar S. U. and A. G. Dempster, "An analysis of L1-C/A crosscorrelation and acquisition effort in weak signal environments", in proceedings of IGNSS Symposium on GPS/GNSS, Sydney Australia, 27, paper 17. Qaisar S. U., "Performance analysis of Doppler aided tracking loops in modernized GPS receivers", in proceedings of 22nd International Technical Meeting of the Satellite Division of the U.S. Institute of Navigation ION GNSS, Savannah GA, 29, pp Chapter 8 The paper won both Student Sponsorship and Best Presentation Award for the GNSS Receiver Algorithms Session A3 at the ION GNSS 29 Conference. 9

25 Chapter 2 Background 2.1 Introduction This chapter provides a basis for technical understanding of the potential and challenges associated with the GPS L2C signal, in the frame of this thesis. In the beginning, a basic technical description of GPS is provided. The remainder of the chapter is divided among four main topics: signal design, acquisition, self-interference and tracking. For each of these topics, in the perspective of L2C signal, the following discussion structure is adopted. i. A brief technical introduction ii. Description of technical challenges and/or potential benefits iii. Discussion on relevant previous research iv. Identification of research opportunity or gap v. Description of thesis contribution to address the research gap 2.2 Overview of GPS Technology The Global Positioning System (GPS) consists of three segments namely the space segment, user segment and control segment. The space segment consists of spacecraft, flying at an altitude of about 2,2 Km, equipped to radiate navigation signals. The control segment is a global network of monitoring stations which collect location information from GPS satellites and send it to the master control station (MCS) which models this information as a function of time and sends predictions of behavior to the satellites over the uplink. The MCS also maintains other necessary parameters such as orbital information and atmospheric data. A GPS receiver, on the other hand, is in the user segment. It decodes the navigation messages received from satellites to determine its location, velocity and the accurate time. The receiver computes satellite position and transmit-time from three or more independent signals to compute its position in three 1

26 Chapter 2 Background dimensional space under the trilateration principle. A fourth signal is usually required to remove the clock bias common to all measurements. Signals transmitted by GPS satellites are essentially square waveforms that modulate a high frequency sinusoidal carrier. The square waveforms are constructed by mixing the navigation message {+1,-1} with a relatively high rate periodic chip sequence {+1,-1} such that each message symbol is effectively replaced by one or more periods of chip sequence. This mixing process distributes the energy of original navigation signal over a wide band of frequencies, bringing its power spectral density (PSD) at the receiver to a level below even that of the noise. This characteristic of direct sequence spread spectrum (DSSS), originally developed for secure military communication, protects against jamming because the signal acquires frequency diversity. Navigation data 5 bits/s Spreading code RF carrier 1.23M chips/s GHz Figure 2.1. Basic principle of GPS signal transmission with L1 C/A signal example The spread sequence is then mixed with the sinusoidal carrier, as illustrated in Figure 2.1. GPS employs Code Division Multiple Access (CDMA), whereby each space vehicle (SV) is distinguished by a unique chip sequence or pseudorandom noise (PRN) code. All of these code spread signals use the same carrier. Details on DSSS and CDMA, in the context of GNSS, can be found in Holmes (1998) and Misra and Enge (26). At the receiver, first the RF signal is down converted to an intermediate frequency (IF) by the RF front-end hardware. Replicas of the known transmitted chip sequence and the IF carrier are locally generated and mixed with the received satellite signal to achieve synchronization between the satellite and local signals. 11

27 Chapter 2 Background RF F.END ACQ. LOGIC TRACK. LOGIC Recovered data Replica code IF replica carrier Figure 2.2. A high level block diagram of GPS receiver The initial synchronization phase is known as signal acquisition. As shown in Figure 2.2, the acquisition block is followed by the tracking logic which maintains the signal synchronization with a higher precision for continuous extraction of the navigation message. The signal acquisition and tracking blocks remain the focus of discussion for the most of this chapter. 2.3 L2C Signal Structure The L2C signal is composed of two ranging codes, namely L2 CM (moderate) and L2 CL (long). The L2 CM code is 2 milliseconds long and contains 123 chips while the L2 CL code has a period of 1.5 seconds, containing chips. The CM code is modulo-2 added to data (i.e. it modulates the data) and the resultant sequence of chips is timemultiplexed with CL code on a chip-by-chip basis. The individual CM and CL codes are clocked at khz while the composite L2C code has a frequency of 1.23 MHz. Code boundaries of CM and CL are aligned and each CL period contains exactly 75 CM periods. This time multiplexed L2C sequence modulates the L2 ( MHz) carrier (IS GPS 2 D, 26). The original L2 CNAV data rate is 25 bits per second but a half rate convolutional encoder is employed to transmit the data at 5 symbols per second (the same symbol rate as for L1 C/A code). Consequently, each data symbol matches the CM period of 2 milliseconds. Figure 2.3 illustrates the L2C code structure over a CL code period. Unlike other new GPS signals such as L5, L2C is limited to a single bi-phase signal component rather than two signals in quadrature as it must share the L2 frequency with the new military M-code and the legacy P(Y) code. 12

28 Chapter 2 Background 2 ms 1.5 s CM+CL 1 CM+CL 2 CM+CL 3 CM+CL 74 CM+CL MHz 246 chips CM chips CL chips Figure 2.3. L2C code structure containing same CM but different CL (2ms) segments in the CL period Advantages of the New Signal Design Stansell (21) and Fontana, et al. (21) contributing to the signal development phase, explain decision motives and potential benefits of each feature of the L2C design. For instance, as mentioned in Section 1.3, incorporating the data-less code (CL) improves the tracking threshold by 6 db by allowing the use of a phase locked loop as opposed to a Costas loop. The slower (compared to any other GPS signal) clock rates of individual CM and CL codes will reduce the power consumption without affecting the code measurement accuracy if carrier-to-code loop aiding and advance gated multipath mitigation techniques are considered. Although the L2C power devoted to the data channel is half the total, its data recovery threshold performance is 5 db better than C/A. This is because the Forward Error Correction (FEC) applied to navigation data offers 5dB gain in the data recovery thresholds and cutting the data rate in half, i.e. from 5 Hz (bits per second) in L1 C/A to 25 Hz in the L2C signal improves data recovery threshold another 3 db. Hence even after the initial 3 db loss due to power split between the data and pilot channel, the data recovery threshold is 5 db better. Also, the longer L2C codes are expected to offer better cross-correlation performance than the 1 millisecond long C/A code. Other key signal parameters of L1 and L2C are compared in Table 2.1, indicating that after a long history with only the L1 C/A civil signal, L2C is an entirely different signal and must be dealt with care. At this point, it is worth mentioning that most of the L2C advantages only manifest themselves once the signal is acquired (Dempster, 26). 13

29 Chapter 2 Background Signal L1 L2C *Min. received power (dbw) Ranging code C/A CM CL Chipping rate (MHz) Code period (chips) Code period (ms) Navigation data rate (Hz) FEC No Yes No Table 2.1. Comparison of key signal parameters in L1 and L2C. * Measured at 3-dBi linearly polarized antenna The L2C acquisition, however, will suffer the effects of having longer codes, having a time multiplexed signal structure and being 1.5 db weaker than the L1 signal. 2.4 L2C Acquisition Signal Acquisition Basics Signal acquisition is the first stage of digital processing in a GPS receiver. Hence a signal must be acquired before it can be tracked and used. A desired satellite signal present at the IF stage of receiver is usually modeled as: rr(tt) = 2PP kk dd kk (tt ττ kk )cc kk (tt ττ kk ) cos 2ππ ff IIII + ff DD,kk tt + φφ kk + nn(tt) (2.1) where PP kk is the received signal power (subscript kk identifies received satellite signals whereas local replica signals will be identified by subscript ii), dd kk (tt) = ±1 denotes navigation data symbols, cc kk (tt) is the spreading code while ττ kk represents the phase or delay of the received code and ff IIII is the IF carrier frequency. Due to continuous satellite motion and possible receiver dynamics, the signal frequency suffers from the Doppler Effect, incorporated as ff DD,kk. Also, φφ kk denotes the carrier phase and nn(tt) is the thermal noise in the receiver, modeled as additive white Gaussian noise (AWGN) with two-sided power spectral density of NN 2. Signal acquisition is the process of finding the correct code delay and Doppler frequency (often simply denoted Doppler ) to match the desired signal in order to establish synchronization between the received and local signals. Hence an uncertainty range in 14

30 Chapter 2 Background Relative carrier Doppler (Hz) Replica code delay (samples) Figure 2.4. Cross Ambiguity Function of simulated noiseless L1 C/A signal (PRN-1) Across the considered search grid (top). In the correct Doppler and delay bins (bottom) both Doppler and delay dimensions needs to be searched. Each Doppler/delay trial combination is referred to as a cell and hence a bi-dimensional grid of cells constitutes the search space. A bin on the other hand refers to the individual Doppler or delay window. Each cell trial collects a certain amount of signal energy which conforms to a specific pattern across the search grid maps this pattern for the L1 C/A signal example over a search space of ±3kHz and ±2chips in the Doppler and code delay dimensions respectively, around the correctly matched point. As observable in Figure 2.4, in the code delay dimension, the energy pattern is a triangular cross-section centered at the correct cell, corresponding to the code s autocorrelation function, and it is a Sinc function in the Doppler dimension. In the literature this energy pattern is also known as cross ambiguity function (CAF), given as (Stein, 1981): 15

31 Chapter 2 Background T I IF signal Carrier Generator 9 o f D,i Code Generator τ i S Post-correlation Processing H D s < ν > H 1 T Q Figure 2.5. Basic correlation scheme employed for signal acquisition in GPS receivers TT SS = 1 TT rr(tt)cc ii (tt ττ ii ) eejj2ππ ff IIII +ff DD,ii dddd (2.2) where cc ii (tt) is the local replica code and ff DD,ii and ττ ii represent the Doppler estimate and code delay of the cell under trial, respectively. In other words, the acquisition process is equivalent to evaluating the CAF on a grid of discrete points. Figure 2.5 illustrates the basic arrangement employed for signal acquisition. For each cell trial, the received satellite signal at the IF stage is mixed with two orthogonal sinusoids for generating the in-phase (II) and quadrature (QQ) components. This is followed by correlation with local replica code over the coherent integration period TT and the correlator output SS = II + jjjj is evaluated as (Scharf and Friedlander, 1994): SS = PP kk 2 R( ττ) sin(ππ ffff) ee jj2ππ φφ + nn ππ ffff II (tt) + nn QQ (tt) (2.3) where R( ττ) is the autocorrelation function, assuming a perfect autocorrelation function (ACF) triangle, given as (Parkinson and Spilker, 1996): TT R( ττ) = 1 TT cc kk (tt ττ kk )cc ii (tt ττ ii )dddd 1 ττ, ττ 1, ττ > 1 (2.4) where ττ = ττ kk ττ ii is the relative code delay between incoming and local codes, ff denotes the difference in carrier frequencies of incoming and local signals while nn II (tt) and nn QQ (tt) are the noise contributions in the II and QQ components respectively and φφ is the carrier phase difference between the incoming and replica signals. 16

32 Chapter 2 Background T Sτ 1 f D,i T Sτ 2 IF signal Carrier Generator T Sτ 3 9 o j T Sτ N Code Generator τ 1 τ 2 τ 3 τ N Figure 2.6. Massively parallel correlators architecture used in parallel search strategies Equations (2.3) and (2.4) explain that a perfect match between desired and local signals maximizes the correlator output while any mismatch causes a loss, corresponding to the energy pattern discussed above. The complex correlator output SS is processed further to construct the decision statistic (or decision variable DD ss ) which is compared with a predefined threshold vv to declare the presence (HH 1 hypothesis) or absence (HH hypothesis) of desired signal in a particular cell. Typically an absolute ( ) or squared-absolute ( 2 ) operator is applied on SS to generate II 2 + QQ 2 and II 2 + QQ 2 as decision variables, respectively. However, as the desired signal gets weaker, the coherent integration period has to be increased up to the length of data bit. After that, the single correlator output sample becomes insufficient for signal detection. A number of such samples (SS 1, SS 2, SS 3 SS MM ) are thus collected and combined together to construct the decision variable for the purpose of improving signal to noise ratio, in order to detect the desired weak signals. Search Strategies There are two fundamental strategies of signal search, which can be termed as serial and parallel. The serial search is a time domain strategy, where each search cell is examined one by one, using the classical correlation scheme, shown in Figure 2.5, and the search is terminated as soon as the signal is found. This strategy consists of several techniques such as fixed/variable dwell time, single/multiple trials per cell and full/partial period code correlation; a structured classification of serial search strategies is provided in 17

33 Chapter 2 Background f D,i IF signal Carrier Generator FFT IF signal FFT S 9 o j IFFT S Code Generator τ i Code Generator FFT ( )* (a) (b) Figure 2.7. Frequency domain parallel search architectures (a) FFT in the delay dimension (b) FFT in the Doppler dimension Kaplan and Hegarty (25). The serial search can take a long time for larger uncertainty ranges, however it remains a popular choice for its low power consumption, low cost and reuse of the correlation circuit by the tracking stage. In the parallel search strategy, on the other hand, multiple search cells are simultaneously tested to speed up the acquisition process. This approach often relies on the frequency domain for decisions, unless massively parallel correlators are employed, where each of the replica code delay is tested by a separate correlator as shown in Figure 2.6. The frequency domain parallel search strategy can be further classified into two main categories. First, where for each Doppler bin, all code delays are simultaneously tested. This is realized by multiplying the spectrum of the received satellite signal, after carrier mixing, with complex conjugate of spectrum of the replica code and returning the result back to the time domain, as shown in Figure 2.7a. An FFT algorithm is generally used for spectral translations here. Also referred to as FFT in delay dimension, this realization is based on the well known Convolution-Product Fourier transform pair (Nee and Coenen, 1991; Tsui, 2). In the other parallel strategy, for each code delay, the FFT of the product of received signal and replica code is computed as illustrated in Figure 2.7b. The correct code delay, in this case, identifies the input carrier frequency and hence the associated Doppler (Akos, 1997). This implementation is also known as FFT in the Doppler dimension. On the negative side, parallel searches increase the implementation complexity and cost. Hybrid search methods which scan a group of cells together at a time by employing few parallel 18

34 Chapter 2 Background correlators have also been studied (Malik, et al., 29; Povey, 1998). The frequency domain search is usually applied in software receivers and a time domain search is preferred in hardware receivers. One of the main parameters that determine the amount of effort required for signal acquisition is the PRN code period. A longer code period requires more code delays to be trialed in order to scan the entire code. It also increases the search space in the Doppler dimension as each Doppler bin is roughly 2 3TT Hz (Kaplan and Hegarty, 25), where TT is the coherent integration period typically set to one or more code periods. A longer TT thus means smaller Doppler bin separation and hence more bins to cover a given search space. Moreover, a longer code requires more computations per each cell trial further increasing the power consumption. Also, a longer code will occupy more memory if FFTs of replica codes are stored or longer registers if codes are to be generated on-the-fly. To summarize, a longer code period increases the search time and demands more resources during the signal acquisition phase. Acquisition Performance The decision statistic DD ss is a random variable characterized by the probability density function (PDF). The type of PDF depends on how the decision statistic is constructed. For instance, DD ss = II 2 + QQ 2 = yy, under the hypothesis HH, is a central χχ 2 (chi-square) distribution with 2MM degrees of freedom, where MM refers to the number of complex correlator output samples being combined, whose PDF is: pp (yy) = 1 yy exp 2σσ2 2σσ 2, yy (2.5) In contrast, under hypothesis HH 1, when the test statistic is greater than the threshold, the PDF of test statistic has a non-central χχ 2 distribution given by: pp 1 (yy) = 1 2σσ 2 exp yy + PP kk 2σσ 2 II PP kkyy σσ 2, yy (2.6) where II ( ) is the zero-th order modified Bessel function. The two statistics that are of most interest for the signal detection process are the single-dwell false alarm probability and single-dwell detection probability respectively given by: 19

35 Chapter 2 Background PP ffff = pp (DD ss ) dddd (2.7) vv PP dd = pp 1 (DD ss ) dddd (2.8) vv For a given PP ffff, a higher PP dd indicates better acquisition performance. Besides PP dd, mean acquisition time is the other parameter used to measure the acquisition performance. It is the average time taken to acquire the signal over a given search space. Considering a single-trial (Yes/No) strategy, the mean acquisition time is given as (Holmes, 1998): TT = 2 + (2 PP dd )(qq 1) 1 + KK pppp ffff 2PP dd MMMM (2.9) where qq is the entire uncertainty region to be searched, KK pp is the penalty factor for time lost due to false alarms. An efficient acquisition strategy targets PP dd and qq to minimize the mean acquisition time TT. For example, shorter coherent integration periods decrease qq by reducing searches in the Doppler dimension. 2.5 L2C Acquisition Load In a dual frequency GPS L1/L2C receiver, L1 C/A is the shortest available code and hence it becomes a natural choice for satellite acquisition under normal operating conditions. Once the L1 C/A signal is acquired, the relationship between L1 and L2 frequencies can be used to estimate the Doppler on L2. Since the L1 and L2C codes are transmitted synchronously, once the C/A (1ms) signal is acquired, CM (2ms) boundaries can be located by trialing 2 possible delays (Dempster, 26). Also, Lim, et al. (26), used hardware counters to identify the L1 data boundary instead and then switch over to L2 CM directly. In addition to having a shorter period, C/A code has an advantage of 4.5 db better acquisition sensitivity. This is because as mentioned in Section 2.3.1, the L2C signal is 1.5 db weaker than L1 and another 3 db will be lost due to its TDM structure which requires zero-padding to be applied to the replica code. 2

36 Chapter 2 Background GPS L2C Receiver Considering single frequency GPS L2C receivers, the primary challenge in signal acquisition is to cope with the unusually long code periods. The L2 CM code being 75 times shorter than CL code is the obvious choice for initial signal acquisition, unless the signal environment is compelling to use the CL code. Once the CM code is acquired, a quick search in 75 delay bins, at the most, will find the CL code boundary. However, the CM code itself is longer than any other GPS civil codes designed so far and it therefore requires extensive processing resources for its acquisition. As mentioned earlier, longer codes not only increase the search size but also the computations per search. This translates into higher computation complexity and consequently more power consumption which is in particular a major constraint in the mass market of hand held battery operated mobile devices such as mobile phones and PDAs. In general, different approaches have been adopted to reduce the L2C signal acquisition load Replica Code Modification Conventionally, the receiver generates a replica code identical to the original spreading code in order to exploit the original code s correlation characteristics. However it is possible to adopt a local code design different from that of the original spreading code to speed up the signal acquisition. One method for composing such codes is to add several versions of the code each with a different delay. Such a composite code approach, however, has no control over the resulting cross-correlations. Another approach for constructing such codes is to superimpose several folded segments of the original code. In Moghaddam, et al. (26), Hyper codes are introduced for efficient acquisition of L2 CL codes. Here the local replica code is generated by addition of adjacent partial CL code segments which are considered to have reasonable orthogonal characteristics. This however increases the correlation noise m-fold, where m is the number of components in a Hyper code. Similar folding approaches are discussed in Lee, et al. (28), Li, et al. (28) and Yang (25) to deal with longer codes, all at the expense of significant rise in the correlation noise floor. 21

37 Chapter 2 Background Of all GNSS signals designed to date, the TDM structure is unique to L2C where two chip-sequences of different period co-exist in alternate time slots while realistically only one of them can be acquired over a full period at a time because only one of them is modulated by the navigation message. The undesired chips in that case cause extra crosscorrelation and bring more noise in the correlation process. A good strategy for this situation is to pad zeros in alternate chips of the local replica code (Dempster, 26). These extra zeros will remove half of the correlation noise including both crosscorrelation and thermal noise components. 1.5 chips 1. CM 2. CM CM 3. CM Figure 2.8. Basic L2C replica symbols (2 chip periods) Tran (24) identified three basic choices of replica code for L2 CM acquisition, shown in Figure 2.8. Considering a half chip code search step, the worst timing error in the first choice is.25 chips while it is zero in the second and third choices. Also, the second design allows larger (one chip) code search steps at the cost of increased correlation noise. Dempster (26) discussed the first two choices, called return-to-zero (RZ) and non-return-to-zero (NRZ) versions of the CM code, in the context of autocorrelation function and cross-correlation noise. However, the TDM nature of L2C can also be exploited to accommodate multiple simultaneous searches in both code delay and Doppler dimensions without causing an overlap. A part of this thesis (Chapter 4) is dedicated to characterizing several designs of L2C replica code in terms of their code recovery function, worst-case correlation loss, cross-correlation interference, detection probability and mean acquisition time. These designs provide more efficient ways of performing the signal search, each offering a unique level of trade-off between the acquisition sensitivity and search speed, suited to different applications. 22

38 Chapter 2 Background Down-Sampling Approach There have been a number of research attempts to reduce the data size required for GPS signal acquisition. Namgoong and Meng (21) propose to drop the sampling rate of IF samples to twice the chipping rate of the modulating code in the context of DSSS receivers. An interpolation filter is employed such that its timing is controlled by the contents of a Numerically Controlled Oscillator (NCO) register, which adjusts the data frequency to match the local code sampling frequency of exactly two samples per chip. Dempster (28) has shown that quadrature bandpass sampling (QBPS) can have reduced minimum required sampling rate and a larger range of available sampling rates than for bandpass sampling, when applied to multi-band GNSS receivers. In a proposal by Sajabi, et al. (26), the L1 C/A code sampled at 5 MHz is sub-sampled to have 496 samples in 1ms. The FFT algorithm is then applied on 1 consecutive input data blocks of 496 samples each. The first half (248 samples) of each FFT output is multiplied by the corresponding local code FFT outputs. Hence the processing in subsequent multiplication and inverse FFT operations is reduced by half. However the complexity of this technique grows as the sampling rate gets higher. Similarly Alaqeeli, et al. (23) and Starzyk and Zhu (21) suggested that 1ms C/A data can be averaged to 124 samples to fit it into 1K FFT block. This however requires the entire acquisition operation to be attempted as many times as maximum number of samples in the chip period, in order to resolve the code phase ambiguity. Other FFT-based fast acquisition techniques are discussed in Akopian (25) and Tsui (2). In this thesis (Chapter 5), down-sampling of baseband L2C signals is investigated to reduce the computational complexity of signal acquisition. A chip-wise downsampling approach which transforms each group of samples covering a code chip into one sample, is evaluated. For long sampled L2C codes, this provides a huge saving in the correlation processing load. The samples aggregation process, when supported by a specific replica code design, also ensures to retain the original signal to noise ratio (SNR) and hence the signal detection probability is not affected. 23

39 Chapter 2 Background Segmented Correlation Processing To exploit the circular convolution in FFT processing, the satellite signal must be correlated over a full code period. For longer L2C codes sampled at conventional sampling rates, it requires large, expensive and power intensive FFT blocks. Most of the research on L2C acquisition algorithms has relied on parallel processing in the frequency domain. As far as reducing the acquisition load is concerned, Psiaki (24), Yang (25) and Ziedan (25) have all mainly adopted the following strategy for L2C acquisition. Both the incoming signal and replica code are divided into the same number of shorter (than full period) segments of equal lengths. Each replica code segment is zero padded to double its length. Each of the incoming signal segments is joined with its following segment to construct double-length segments. Each of the double-length incoming signal segments, after carrier removal through circular shifting of the spectrum, is correlated with a corresponding zero-padded replica code segment using an FFT (in the delay dimension). Segmented responses are combined coherently via another FFT (in the Doppler dimension). Although the FFT implementation performs circular convolution, the double-length zeropadding combination adopted here turns that into linear correlation by discarding the second half of each segmented computation. The main idea of this acquisition strategy is to reduce the search space in the Doppler dimension by using shorter signal segments according to say the 2 3TT Hz Doppler-bin separation criterion mentioned above, where TT in this case also represents the size of segments being correlated. Shorter FFTs also save computation as compared to straight correlation for the same search range. However, the drawback is that for each of the segmented correlations, half of the computations are discarded effectively causing a substantial loss of acquisition resources. Secondly, the FFT operation in the last step is repeated as many times as the number of data samples in a segment, in order to estimate the residual carrier. Moreover, for finer estimates of 24

40 Chapter 2 Background residual carrier, the number of FFT points must be increased by appending zeros. Again all this will consume extra time and power. In Chapter 6, a time-domain segmented correlation approach is considered for saving computations compared to FFT processing. In this approach, the responses of segmented correlations are combined through post-correlation differential processing techniques. A differentially semi-coherent combining of segmented correlation responses for L2C acquisition is introduced. In this technique, the residual carrier phase is arrested just before the final accumulation stage, providing a performance gain over conventional differential processing, in the presence of carrier frequency error. A background of post-correlation differential processing techniques along with relevant research contributions is provided in the following section L2C Post Correlation Differential Combining As mentioned in Section 2.4.1, as a desired signal gets weaker, the single correlator output sample SS becomes insufficient for signal detection and hence a number of such samples (SS 1, SS 2, SS 3 SS MM ) are collected and combined together to construct the decision variable DD ss for increasing the signal to noise ratio. A common combining approach is to apply squared-absolute operation on every post-correlation sample and then add them all up to construct a decision variable given as: MM DD ss = SS kk 2 kk=1 (2.1) Due to the squared-absolute operation, applied to remove the phase dependence, the coherence across samples is lost and that is why it is known as non-coherent combining. The differentially coherent combining is another popular approach where each of the correlator output samples is mixed with the conjugate of its preceding sample and the outcomes are then integrated as illustrated in Figure 2.9. The decision variable for this case is given as: MM DD ss = RRRR SS kk SS kk 1 (2.11) kk=2 25

41 Chapter 2 Background Σ M-n Re{ } D s T 2T 3T... MT nt ( )* Figure 2.9. A generic implementation of differentially coherent post correlation combining. Each value of n corresponds to a different version Since the signal component from one sample to the next remains highly correlated while the noise is temporally uncorrelated, the post correlation averaging in this case becomes more effective than for straight non-coherent combining (Zarrabizadeh and Sousa, 1997). Differentially non-coherent is another similar form of combining, where phase dependence of individual combinations is removed prior to summation as given by the following decision variable: MM DD ss = SS kk SS kk 1 kk=2 (2.12) Numerous studies have been conducted to evaluate the potential of post correlation combining schemes for GNSS signal acquisition such as Yang, et al. (27) and Schmid and Neubauer (24). Also, Borio (28a) investigated differentially coherent signal combining for acquisition of composite GNSS signals characterized by data and pilot components in phase quadrature to each other, such as Galileo E1, E5a/b and GPS L5. Similarly Ta, et al. (28) studied differential joint data/pilot strategies of Galileo E1 signal acquisition. In a research proposal by Shanmugam, et al. (27), the idea of differential coherent combining is extended to samples separated by different distances (or delays) and a generalized post correlation differential detector (GPCDD) is introduced for GPS L1 C/A signal acquisition. In GPCDD, the outputs of several versions of differentially coherent combining, each based on a different delay between samples, are integrated together to construct the decision variable given as: MM 1 MM DD ss = SS kk SS kk nn (2.13) nn=1 kk=2 26

42 Chapter 2 Background This combination arrangement provides additional processing gain at the cost of extra add and multiply operations. However, the performance of GPCDD is limited by two factors; the navigation data transitions and the residual carrier signal. A bit transition between the samples being combined prevents a receiver from collecting the entire available signal energy. Similarly, a residual carrier leads to a different phase for each version of differentially coherent combining and their coherent summation can cause a substantial loss. An FFT (in the Doppler dimension) is employed to estimate the residual carrier frequency in order to avoid this problem but again, as mentioned in Section 2.5, it requires a number of power hungry FFT correlations. The fact that L2 CM code is synchronized with CNAV symbols can be exploited to overcome the data transition problem in GPCDD if, for example, 2 partial-period code correlations are integrated via differential processing, instead of using fullperiod code correlation. Chapter 6 provides details on this approach when the L2C partial-period correlations are combined through the differentially semi-coherent processing mentioned above CL Acquisition Direct acquisition of CL code, on the other hand, offers much higher sensitivity to weak signals as it does not restrict the coherent integration period to the data bit length of 2 milliseconds but it requires a massive search using highly precise and stable oscillators to generate closely spaced Doppler frequency estimates and to avoid oscillator drift (Dempster, 26). However, once the CM code has been acquired, the estimates of Doppler frequency, carrier phase and rate of Doppler can be refined to assist for longer coherent integration of the CL code (Psiaki, 24; Ziedan, 25). Similarly, Yang (25) suggested cascaded FFT to deal with the Doppler Effect on CL code acquisition. It is shown in Chapter 6 that combining the CL segmented correlation responses through the differentially semi-coherent processing is far significant, in terms of the acquisition load, than an equivalent straight coherent correlation of the CL code. 27

43 Chapter 2 Background Normalized correlation value Relative carrier Doppler (Hz) Replica code delay (samples) Figure 2.1. Illustration of a Near-Far scenario. Both desired autocorrelation peaks (PRN-1, blue) and interfering peaks (PRN-7, red) exceeding the threshold (solid grey line around the box) Simulation parameters: C/A code, TT=1ms, ff ss =5.7143MHz Joint L1/L2C acquisition strategies have also been studied. Gernot, et al. (27) investigated the possibility of joint L1/L2C acquisition to improve the overall detection capability compared to using only one signal. Several ways of coherent, non-coherent and differentially coherent processing are considered for combining the output of L1 and L2C channels. Some of these combinations are reported to outperform the L1 C/A noncoherent acquisition. 2.6 L2C Self Interference The signal acquisition becomes more challenging as the desired signal gets weaker. The detection threshold is gradually dropped to accommodate weaker signals. Trouble starts when energies from unwanted satellites, usually remaining well below the detection threshold, might now exceed it and consequently the receiver might lock on to the wrong signal. These energies of unwanted satellites, collected in the acquisition process, are known as self interference, cross-correlation or multiple access interference. This phenomenon where strong cross-correlation can prevent the acquisition of a desired weak signal is also known as Near-Far problem (Madhani, et al., 23). Indoor environments, urban canyons and pseudolite installations are often likely to cause such situations for a 28

44 Chapter 2 Background GPS receiver. Figure 2.1 illustrates the cross-correlation impact on signal acquisition using an L1 C/A signal example. The conventional approach to deal with this problem is to mitigate the cross-correlation and then acquire the desired signal. Successive Interference Cancellation (SIC) is one such technique where known strong components are gradually removed from the received signal in order to detect the weak component (Moshavi, 1996). Other approaches of cross-correlation mitigation are discussed in Glennon and Dempster (27), Glennon and Dempster (25), Madhani, et al. (23) and Morton, et al. (27). However, if possible, the best approach for dealing with the Near-Far problem is to have a larger crosscorrelation margin in the signal design. The cross-correlation margin (or protection) is the difference between the highest-value (peak) of autocorrelation and cross-correlation functions. For example, the L1 C/A code has a cross-correlation protection of approximately 24 db for the codes alone or 22 db including possible Doppler offsets (Parkinson and Spilker, 1996). The longer L2 CM and CL codes claim to extend the cross-correlation margin to approximately 28 db and 45 db respectively (Fontana, et al., 21; Tran, 24; Tran and Hegarty, 22). However, these figures can be achieved only if the satellite signal is observed coherently over intervals of 2 milliseconds and 1.5 seconds respectively, without considering the Doppler Effect. The relevant questions to ask here are: what if (for comparison) the L1 C/A signal is coherently observed over the same time period? And, what if, being more realistic, there is a relative Doppler offset between the local and interfering signals? In a dual frequency GPS L1/L2C receiver, L1 C/A, L2 CM and L2 CL are the code choices available to combat the Near-Far problem. The published cross-correlation protection figures of these codes (C/A 22 db, CM 28 db and CL 45 db) are not sufficient to determine the right code choice for various acquisition scenarios. In this thesis (Chapter 7), the two signals are therefore assessed for their cross-correlation performance under different scenarios in order to get answers for the above mentioned questions. It is shown that the cross-correlation performance of multiple 29

45 Chapter 2 Background C/A periods is strongly dependent on the relative carrier Doppler between local and interfering signals and consequently it is far superior to that of the single C/A period. It is concluded that the C/A code is more robust to the Near-Far problem in the assisted acquisition mode (including warm, hot and A-GPS receiver starts) while L2 CM is the best choice only for the cold start scenario. 2.7 L2C Tracking Tracking Loop Basics Coarse estimates of code delay and carrier frequency found in the acquisition phase are handed over to the tracking circuit which refines these estimates and achieves a much closer synchronization with the satellite signal. The aim of a tracking loop is to maintain this synchronization for continuous extraction of the navigation message until the signal is lost. A receiver basically hosts two inter-connected tracking loops; one for tracking the IF Signal I&D I&D I Disc. Q Prompt code 9 NCO Loop Filter Figure A GPS carrier tracking phase locked loop carrier phase, known as the phase lock loop (PLL), and the other one to track the code delay, termed the delay lock loop (DLL). Because of shorter period of the input carrier signal, carrier tracking loops are more challenging to maintain than the DLL, in particular in dynamic and weak signal conditions. A Costas loop, insensitive to data bit transitions, is commonly used for carrier tracking. The Frequency Lock Loop (FLL) is an alternative carrier tracking system which provides an approximate frequency for carrier wipe-off. Often, a well designed receiver starts tracking with a FLL and switches over to the Costas loop once the tracking loops are closed. The phase lock loop remains the subject of rest 3

46 Chapter 2 Background of the discussion here. A generic PLL implementation is shown in Figure The key PLL blocks include a discriminator which determines the phase difference or error between the actual and local signals, a loop filter that removes some of the noise in error measurements and the carrier NCO which provides the updated replica carrier signal. For the purpose of analysis, a PLL is generally modeled as a linear feedback control system where the plant represents NCO, the system transfer function represents loop filter and the controller is the error reading system which includes the correlation circuit and the discriminator, highlighted in Figure More comprehensive discussion on tracking loop modeling can be found, for example, in Misra and Enge (26). The bandwidth of the loop filter, commonly known as loop noise bandwidth, is a critical parameter as it not only determines the amount of noise appearing in the measurements but also the range of signal dynamics that can be tracked by the loop. Tracking Loop Errors Due to the presence of thermal noise, oscillator phase noise, oscillator vibrations and platform dynamics, a phase lock loop is unable to generate accurate estimates of the desired carrier frequency. The tracking error contributed by each of these error sources is measured in terms of phase jitter and their expressions for different loop orders are derived in Kaplan and Hegarty (25). The performance of a PLL is measured as variance of the total 1-sigma phase jitter, which for the two-quadrant arctangent discriminator, is given as: σσ φφ = σσ tt 2 + σσ vv 2 + θθ AA 2 + θθ dd 3 15 (2.14) where σσ tt 2, σσ vv 2, θθ AA 2 and θθ dd are the variance of phase jitter due to thermal noise, platform vibration (when the oscillator is installed in an environment where it is subjected to mechanical vibrations), clock error (modeled as Allan variance) and the dynamic stress caused due to abrupt platform motion, respectively. The 15 o threshold is compliant to model a PLL as a linear feedback system. For phase errors above 15, the navigation signals might still be tracked and decoded, at the expense of performance degradation. 31

47 Chapter 2 Background L2C Tracking Choices Due to data modulation on the L2 CM code only, a receiver cannot directly use a composite CM/CL replica to track the L2C signal because the sign relationship between CL and CM is disturbed by the data; rather the data and pilot codes must be independently tracked. For each of the data and pilot channel, RZ versions of replica code, shown in Figure 2.12, are the best option, for their noise rejection and sharp autocorrelation peak characteristics. If only one of the two codes is to be tracked, L2 CL is the straightforward choice as being data-less it allows for the use of a coherent discriminator (pure PLL) with extended linear range (Tran and Hegarty, 22). Moreover, as mentioned earlier, the coherent integration time does not need to be limited to the data bit length. On the other hand, combining the outcome of data and pilot channels for more robust tracking has been an active research area. 1. CM 2. CL Figure Basic replica code choices for L2C tracking L2C Combined Data/Pilot Tracking For channels operating on the same frequency (e.g. data and pilot channels in GPS L2C and L5 signals), the output of individual channels has been combined in the following ways. Spilker and Van Dierendonck (21) proposed to combine (non-coherently) the coherent integration output of L5 data and pilot channels at the code discriminator. Similarly, Muthuraman, et al. (27) proposed differential combinations of L2C data and pilot channels at the discriminator level. All of the above combination schemes aim to increase the signal energy available for tracking and hence to improve tracking robustness. In another approach, the measurements of independent data and pilot channels are combined to reduce the tracking error. For example, Hegarty (1999) proposed to run independent discriminators on data and pilot channels and then combine their outputs using weights that are inversely proportional to their output variances, in the context of the L5 signal, achieving performance improvement in weaker signal range. 32

48 Chapter 2 Background RMS phase jitter (degrees) Doppler Estimation Doppler Aiding Rx. Clock Wideband Noise Dynamic Stress Vibration Single-sided PLL bandwidth (Hz) Figure Contributions of various error sources to total phase jitter, 3 rd order L1 C/A PLL, TT =2ms, CC NN =3dBHz, Jerk stress=.25g/s Also, Tran and Hegarty (22) applied the above optimal weights technique for tracking the L2C signal. For such combinations, to avoid the use of any irrelevant information from the data discriminator (having a limited linearity region), Julien (24) proposed a method that checks the consistency between the data and pilot discriminator outputs before combining them. Muthuraman, et al. (28) investigated the use of coherent discriminators on both L2 CM and L2 CL channels and proposed Kalman filter based combining. On the other hand, for any tracking combination across different frequencies, the ionospheric and Doppler effects must be addressed carefully. Gernot, et al. (28b) proposed a Kalman filter based combined L1/L2C tracking scheme where the outputs of L1 and L2 discriminators are combined by estimating the total electron count (TEC) variations in the signal path. Ries, et al. (22) discuss the possibility of L1/L5 joint tracking by aiding the L1 tracking with the L5 carrier NCO using pilot channel, assuming the ionospheric drift to be less than 5 Hz. Similarly Megahed, et al. (29) evaluated the performance of a Kalman filter based combined L1/L5 tracking scheme. 33

49 Chapter 2 Background Aided Tracking Loops Figure 2.13 plots all of the individual jitters given in Equation (2.14), as a function of loop bandwidth, for the given set of parameters. An interesting observation here is that except for thermal phase jitter, all other errors grow as the loop bandwidth is reduced. It can also be observed that towards smaller loop bandwidths, dynamic stress is the dominant source of error, posing a restriction on the minimum loop bandwidth. In aided tracking loops, the dynamic stress is dealt with by an out-of-loop source and consequently, the tracking loop is able to operate at much narrower bandwidths, rejecting most of the thermal noise and hence improving the tracking accuracy and robustness. The external source provides Doppler estimates to be included in the NCO updates in the aided tracking loops as shown in Figure However, the external Doppler estimates are associated with an error due to limitations of the aiding source. Consequently, the dynamic-stress jitter of an aided tracking loop is replaced by the Doppler estimation error, as shown in Figure 2.13 (Gebre-Egziabher, et al., 23). IF Signal I&D I&D I Disc. Q Prompt code 9 NCO Loop Filter Doppler Aid Figure A Doppler aided phase locked loop in GPS receiver Doppler assistance has long been used for carrier-to-code loop aiding. The typical code loop bandwidth, with Doppler aiding from carrier loop is around.5 to 1 Hz, depending on the application (Van Dierendonck, 1996). Gebre-Egziabher, et al. (25) investigated the PLL aiding using an inertial navigation system (INS) to combat RF interference and report 4 db-hz RFI margin to have been achieved using a set of tactical grade moderate quality inertial sensors. Christopher, et al. (24), Chiou (25) and Chiou, et al. (27) 34

50 Chapter 2 Background analyzed the performance of inertial-aided FLL and PLL carrier tracking loops in a GPS receiver. The traditional L1 to L2 loop aiding has been used for semi-codeless tracking of P(Y) code for improving the SNR in the L2 PLL (Woo, 1999) L2C as Aiding Source Dual frequency GPS L1/L2C receivers will be a simple means for improving the positioning accuracy to sub-meter level once the two civil signals become available over the full constellation. This is because with two frequencies the ionospheric delays (the largest source of positioning errors) can be estimated more accurately and then removed from the position solution. However, the RF interference pushes this performance level back to that of single frequency standalone GPS receiver, posing a serious threat for dual frequency GPS L1/L2C commercial receivers (Enge, 29). In this context, an internal aiding system can be established where an RFI-affected tracking loop can be aided by the unaffected one. In addition, since in this case, the two loops are hosted by the same receiver (i.e. the effects are experienced by the same antenna), the vibration and clock error estimates can also be provided by the aiding source. Hence the only errors left in the destination (aided) loop are its own thermal phase jitter and the Doppler estimation error from the aiding source. Part of this thesis (Chapter 8) presents the sensitivity and performance analysis of internally-aided carrier tracking loops in a dual frequency GPS L1/L2C receiver. Slower dynamics due to relatively low carrier frequency and the data-free channel make the L2C PLL a natural choice of aiding source operating at wider loop bandwidth to absorb non-thermal errors while the L1 PLL can be set to operate at a much narrower loop bandwidth. The analysis however remains relevant for any other pair of GNSS signals. The results of this analysis reveal that for an L1 PLL aided by the L2C PLL in a dual frequency GPS L1/L2C receiver a 3 db or higher RFI margin can be achieved. 35

51 Chapter 3 L2C Data Acquisition Apparatus 3.1 Introduction In the initial phase of this thesis, an apparatus was developed by the author for collecting the real L2C and dual frequency L1/L2C data from Block IIR-M satellites, before an explicit GPS L2 front-end was commercially available. The real data was required for the authentication of the approaches and algorithms developed in the thesis. The apparatus comprises an L2 up-converter hardware that shifts the GPS L2 band to the L1 frequency, allowing the L2C signal to be processed by an L1 RF front-end. The up-converter has also been used for dual frequency L1/L2C data collection. Mixing signal (L1-L2) Frequency mixer L2 BPF L2 signal L1 RF Front-End L1 Band Figure 3.1. Illustration of L2 up-conversion approach used for the hardware design 3.2 L2 Up-Converter Since L1 and L2C signals have similar power levels, same code chipping rate and thus the same spectral width, an L2C front-end can be almost identical to the L1 front-end except that it needs to work with a different carrier frequency thus requiring a modification to the filters and mixers of the L1 front-end. However, another approach for designing the L2C RF front-end is to shift the L2-band to the L1 frequency and then process the L2C signals with a L1 front-end. 36

52 Chapter 3 L2C Data Acquisition Apparatus 1MHz clock to L1 front-end Frequency mixer Local oscillator L2 bandpass filter MHz 2dB LNA L2 signal from the antenna 19dB LNA MHz Figure 3.2. L2 up-converter hardware developed for L2C data collection The approach taken for this spectrum translation is to filter the L2-band, up-convert it to the L1 frequency and then feed it to an L1 RF front-end, such as suggested in Ledvina, et al. (25). The up-conversion is accomplished by mixing the L2 signal with a signal whose frequency equals the difference between L1 and L2 frequencies i.e MHz, as illustrated in Figure Hardware Realization The up-converter has been implemented using commercial off-the-shelf (COTS) parts as far as possible in order to reduce costs and minimize design risks. A labeled photograph of the L2 up-converter hardware is shown in Figure 3.2. The first component (from the right) on the L2 up-converter board is a 2 db low-noise amplifier (LNA) that compensates for the insertion losses in the subsequent components, i.e. L2 band-pass filter and the frequency mixer. This is followed by the L2 filter whose job is to pass a 2 MHz wide signal centered at the L2 frequency; hence any image signals are rejected here. The 2 MHz filter bandwidth will also allow the processing of the military P(Y) code. On the left side of the L2 up-converter board, a frequency synthesizer generates the mixing signal with a frequency of MHz. This results in a difference of 687 Hz in the nominal intermediate frequency, which is balanced by adjusting the frequency of replica carrier signal. A 19 db amplifier is placed after the frequency synthesizer to provide the prescribed power level to the 37

53 Chapter 3 L2C Data Acquisition Apparatus COTS Part Manufacturer Model Reference 2 db LNA Mini Circuits ZEL 1217 LN (Mini-Circuits, 29c) 19 db LNA Mini Circuits ZFL 5 HLN (Mini-Circuits, 29b) L2 GPS BPF CTS CER4A (CTS, 29) Frequency Mixer Mini Circuits ZX5-42MH (Mini-Circuits, 29a) Local Oscillator Analog Devices ADF (Analog-Devices, 29) Table 3.1. Details of COTS parts used in the L2 up-converter hardware kkkkkkkkkkkk mixing signal. The two signals at MHz and MHz are combined together in the frequency mixer (a passive device). The output of the frequency mixer is the L2C signal spectrum, centered at the L1 frequency. Table 3.1 lists details of the RF components used in the up-converter hardware Hardware Testing & Data Verification The individual RF components and the entire up-converter hardware were initially tested with an RF generator. Next, the L2 up-converter hardware was independently coupled with two different L1 RF front-ends (a Zarlink GP215 chip and a NordNav software GPS receiver Rxx-2 L1 front-end) and the real L2C data was recorded using a Leica AT 54 L1/L2 dual band antenna for each case. The standard Zarlink GP215 L1 front-end chip provides a net bandwidth of 1.9 MHz which is wide enough to capture the main lobe of the C/A spectrum while enabling the front-end to sample at 4/7 = MHz. The nominal L1 frequency is down-converted to MHz, but due to aliasing in the baseband a MHz image is selected for the IF processing. The final output of the GP215 is 2-bit IF samples (Zarlink, 29). On the other hand, the standard NordNav Rxx-2 software GPS receiver L1 front-end has a (-3dB) bandwidth of 2. MHz, an intermediate frequency of MHz and provides IF samples at a rate of MHz (NordNav-Technologies-AB, 27). This front-end is capable of providing multiresolution (1-bit, 2-bits and 4-bits) IF output samples. 38

54 Chapter 3 L2C Data Acquisition Apparatus Dual-band L1/L2 antenna RF output GP215 L1 RF front-end L2 Up-Converter CPU 1 MHz clock Namuru GPS L1 Receiver (a) Dual-band L1/L2 antenna 1 MHz clock L2 Up-Converter CPU RF output NordNav GPS L1 front-end (b) Figure 3.3. Hardware setup for real L2C data acquisition using up-converter hardware with: (a) GP215 L1 RF front-end (b) NordNav (Rxx-2) software GPS receiver L1 front-end The 4-bit resolution was selected for recording the data during the testing of L2 upconverter. Figure 3.3 illustrates the setup used for L2C data collection. As shown in the figure, the GP215 chip, in this case, is hosted by a GPS L1 receiver called Namuru (Mumford, et al., 26). The L1 front-end in each case (GP215 or NordNav Rxx-2) is phase-locked to the same 1 MHz reference oscillator that drives the required mixing signal in the frequency synthesizer. The output of the L1 front-end is transferred to a computer and logged there for later processing L2C Acquisition Results The integrity of collected L2C data samples is verified by performing a correlation with the replica signals for the acquisition of CM and CL codes, using the conventional correlation architecture shown in Figure 2.5 and engaging the return-to-zero (RZ) version of the local replica codes. Figure 3.4 shows the acquisition result for the GP215 coupling over a search space of ±4 TT and ±2TT cc in the Doppler and code delay dimensions respectively, where TT = 2 milliseconds is the coherent integration period used for signal acquisition and TT cc =1/ is the L2C code chip period. 39

55 Chapter 3 L2C Data Acquisition Apparatus Absolute correlation output x Relative carrier Doppler (Hz) CM 3136 CL Replica code delay (samples) 3122 Figure 3.4. Acquisition result of real L2C signal recorded through the up-converter coupled with GP215. A separation of 1 chip period between the CM and CL codes can be confirmed Considering the CM result, the locations of nulls of the Sinc function at integer multiples of 5 Hz (1 TT) are consistent with 2 millisecond coherent integration period. After the CM acquisition, correct CL delay was searched by trialing all 2 millisecond CL segments one by one. Figure 3.4 verifies a separation of one chip period (approximately 5 samples as the sampling rate is MHz) and a correlation pattern match between the two codes, along the entire considered range of relative carrier Doppler. The data was recorded from a Block IIR-M satellite (PRN-17) flying at an elevation of approximately 85 degrees with a clear sky view and the acquired signals had a carrier to noise ratio of approximately 45 db-hz which is typical performance of the Zarlink GP215 for an L1 signal acquired in the same scenario. Similar observations can be made for the NordNav Rxx-2 coupling (having a different sampling frequency, IF and data sample resolution). The data for this case was recorded at a different time from a different satellite (PRN-12) having about the same elevation i.e. 85 degrees. As shown in Figure 3.5, the absolute values of acquisition peaks in this case are approximately 3 times higher than with GP215, compliant with the relationship between sampling frequencies of the two front-ends (the ratio of sampling frequencies of the NordNav front-end to the GP215 is 2.865). The locations of nulls, one-chip (16 samples, as the sampling rate is MHz) spacing between CM and CL acquisition results along the entire range of relative carrier Doppler and the same CC NN level of approximately 45 db-hz are also confirmed for this case. 4

56 Chapter 3 L2C Data Acquisition Apparatus Absolute correlation output 5 2 x Relative carrier Doppler (Hz) CM CL Replica code delay (samples) 479 Figure 3.5. Acquisition result of real L2C signal recorded through the up-converter coupled with NordNav L1 front-end, confirming a separation of 1 chip between the CM and CL codes 3.3 Dual Frequency L1/L2C Data The up-converter design approach discussed above was later adopted in the 2 nd version of the Namuru (V2), which is a dual frequency GPS L1/L2C receiver (Mumford and Parkinson, 29). The Namuru V2 consists of two GP215 L1 RF front-ends. One of the two front-ends is coupled with an on-board L2 up-converter to facilitate the L2 signal processing. As shown in Figure 3.6, the on-board up-converter uses an Analog Devices ADF436D-7 for generating the local mixing signal of MHz. This is followed by the Mini Circuits matching transformer (TCM4-6T) to provide the appropriate power level for the mixing signal and Mini-Circuits MCA1-24 double balanced mixer for spectrum translation. On the other side of the up-converter, the L2 signal is filtered by a 2 MHz wide L2 ceramic bandpass filter followed by the Avago SiGE LNA (MGA ) which counteracts for the losses in the image reject filter and the mixer MHz Frequency mixer L2 BPF LNA MHz Level matching balum MHz Figure 3.6. On-board L2 up-converter design in Namuru V2 GPS L1/L2C receiver 41

57 Chapter 3 L2C Data Acquisition Apparatus Dual-band L1/L2 antenna RF output Zarlink GP215 L2 Up-Converter CPU 1 MHz clock Zarlink GP215 Figure 3.7. Hardware setup for dual frequency L1/L2C data acquisition using the Namuru V2 board with L2 up-converter The L1 and L2 data samples provided by the corresponding RF front-ends are transferred to a CPU via a USB port. Unfortunately, the on-board L2 up-converter has issues of data loss and remains under investigation to date. However, the discrete L2 up-converter developed by the author has been coupled with one of the L1 front-ends to successfully record the real dual frequency L1/L2C data from the Block IIR-M satellite (PRN-7), required for experiments in the aided carrier tracking analysis conducted in the thesis. In this case, the two Zarlink GP215 chips are driven by the same 1 MHz oscillator on the frequency synthesizer board, as shown in Figure 3.7. The dual frequency data was transferred directly from the front-ends to the PC via USB port in two separate files. The recorded L1/L2C data was tracked for 1 seconds with independent C/A, CM and CL tracking loops to prevent any ionosphere-induced biases on the two frequencies. The tracking results are depicted in Figure 3.8. Stable power levels at the prompt correlator output for each tracking loop verify the operation of up-converter as well as the synchronization across the two front-ends of the Namuru V2 receiver. Note that the CNAV message on the L2 signal was turned off at the time of data recording, however, the NAV message on the L1 frequency could be successfully tracked. Having known delays of received CM and CL codes, a chip-by-chip composite L2C replica code was also constructed to perform the joint CM/CL tracking. As shown in Figure 3.8, the prompt correlator output in this case attains a power level twice that of the individual CM and CL code tracking. 42

58 Chapter 3 L2C Data Acquisition Apparatus Propomt correlator output CM/CL C/A CM CL Time (seconds) Figure 3.8. Tracking result of real dual frequency L1/L2C data recorded using the Namuru V2 board with L2 up-converter 3.4 Summary L2 up-converter hardware is developed for obtaining L2C IF data samples through an L1 RF front-end. The up-converter is tested with two different L1 RF front-ends and the L2C codes transmitted from Block IIR-M satellites were successfully acquired from the recorded data. The up-converter is also employed for dual frequency L1/L2C real data collection using a dual front-end GPS receiver board. The acquisition and tracking results of real data collected through the up-converter verify its design and hardware implementation. The up-converter has been used for collecting a variety of real datasets used in various analyses conducted during the thesis development. 43

59 Chapter 4 L2C Replica Code Design 4.1 Introduction The problem of the huge acquisition load in L2C receivers was discussed in Section 2.5. It was also described in Section 2.3 that the TDM structure of the L2C signal incorporates two different codes in two separate channels provided by alternate time slots. Since realistically only one of the two codes (when observed over respective full code periods) can be acquired at a time, because data modulates only one of them, the local replica code targets only alternate chips of the incoming L2C code, wasting half of the signal observation time. However, this time duration can be utilized in several ways to design more efficient L2C replica codes which reduce the L2C acquisition load. In this chapter, six designs of L2C replica code are assessed. The acquisition performance of these designs is evaluated in terms of code recovery function, self interference, detection probability and mean acquisition time. Acquisition sensitivity, search capability and potential application scenarios of each replica code design are identified. Finally, some recommendations are made that can be applied for developing acquisition strategies in GPS L2C receivers. 4.2 L2C Signal and System Model The L2C signal received from the k th satellite, at the IF stage of receiver, can be modeled as: rr(tt) = 2PP kk [dd kk (tt ττ kk )cccc kk (tt ττ kk + mmtt cccc ) + cccc kk (tt ττ kk )] cos 2ππ ff IIII + ff DD,kk tt + φφ kk + nn(tt) (4.1) where cccc kk (tt) and cccc kk (tt) represent the CM and CL code components respectively, TT cccc denotes the CM period (2 ms) and mm 74 is an integer that gives the number of CM epochs in the current CL epoch while all other parameters remain the same as 44

60 Chapter 4 L2C Replica Code Design defined in Section The CM code component in Equation (4.1), being shorter than the CL component, remains the receiver s target for signal acquisition in most of the operating scenarios as mentioned in Section For the analysis presented in this chapter, L2 CM acquisition is therefore considered; the analysis however remains valid for the L2 CL code acquisition. The received L2C signal is mixed with local replicas of code and two orthogonal carriers generating the in-phase (II) and quadrature (QQ) components, expressed as: TT II = rr(tt) cccc ii (tt)cos 2ππ ff IIII + ff DD,ii tt dddd (4.2) TT QQ = rr(tt) cccc ii (tt)sin 2ππ ff IIII + ff DD,ii tt dddd (4.3) where cc mm,ii (tt) is the local CM replica code and ff DD,ii represents the locally generated carrier Doppler estimate. Equations (4.2) and (4.3) are evaluated as: II = PP kk 2 CC kk,ii ( ττ) cos(2ππ φφ) sin(ππ ffff) + nn ππ ffff II (tt) (4.4) QQ = PP kk 2 CC kk,ii ( ττ) sin(2ππ φφ) sin(ππ ffff) + nn ππ ffff QQ (tt) (4.5) where CC kk,ii ( ττ), in general, represents the correlation between received and local replica code sequences as a function of relative code delay ττ = ττ kk ττ ii. For the particular case of CM code acquisition, over one code period, CC kk,ii ( ττ) can be given as: TT CC kk,ii ( ττ) = [cccc kk (tt ττ kk + mmtt cccc ) + cccc kk (tt ττ kk )]cccc ii (tt ττ ii ) dddd (4.6) 4.3 L2 CM Replica Code Designs The generic replica (or reference) code for CM acquisition can be modeled as: cc ii (tt) = cccc ii αα (tt) + cccc ii (tt) (4.7) 45

61 Chapter 4 L2C Replica Code Design where cccc ii αα (tt) and cccc ii (tt) are the two constituent components, such that one of these two components, at a time, recovers the desired signal while the other one may reduce the noise floor (enhancing the acquisition sensitivity) or it may facilitate signal search (increasing the search speed) at the cost of minor rise in the noise floor. Different code structures are realized by different definitions of cccc ii αα (tt) and cccc ii (tt). For all designs of reference code, cccc ii αα (tt) is given as: NN cc 1 cccc αα cccc ii (tt) = aa ii,nn nn= pp αα (tt nnnn) (4.8) where aa cccc ii,nn {+1 1} refers to CM chips when nn is odd while aa cccc ii,nn = when nn is even, NN cc denotes the number of chips in the coherent observation period i.e. 246 in this case and pp αα (tt) is a rectangular pulse of width αα (in chips) given by: pp αα (tt) = 1, tt αα, ooooheeeeeeeeeeee (4.9) whereas the value of αα (1 αα 2) is determined by the particular design. The definition of the cccc ii (tt) component, on the other hand, is design specific as described in the following section. The following designs of reference code, shown in Figure 4.1, have been investigated Return to Zero CM (RZ CM) Code This design is realized by setting αα = 1 and cccc ii (tt) = in Equation (4.7). Consequently, the reference code alternates between CM chips and zeros, and is hence known as returnto-zero (RZ) CM code Return to Zero Extended CM (RZ ECM) Code In this design, αα and cccc ii (tt) are respectively set to 1.5 and, and hence the reference code alternates between extended CM chips (1.5 times CM chip period) and zeros Non Return to Zero CM (NRZ CM) Code Here αα takes a value of 2 while cccc ii (tt) remains zero, creating a non return to zero CM code running at khz. 46

62 Chapter 4 L2C Replica Code Design 2-ms CM 1 CL 1+mNp CM 2 CL 2+mNp CM 3 CL 3+mNp CM 123 CL 123+mNp (a) 1. 2-ms CM 1 CM 2 CM 3 CM CM 1 CM 2 CM 3 CM chips 3. CM 1 CM 1 CM 2 CM 2 CM 3 CM 3 CM 123 CM CM 1 CM 1 CM 2 CM 2 CM 3 CM 3 CM 123 CM 123 f 1 f 2 5. CM 1,1 CM 2,1 CM 1,2 CM 2,2 CM 1,3 CM 2,3 CM 1,123 CM 2, CM 1 CM 5116 CM 2 CM 5117 CM 5115 CM ms (b) Figure 4.1. (a) Received L2C code, mm 74, NN pp =123 (b) Considered designs of local replica code for L2C acquisition. The subscript in chip labels indicates the chip number For design 5, the subscript in chip labels indicates satellite index followed by the chip number Non Return to Zero Twin Carrier CM (NRZ TCM) Code In this structure αα remains 1 while cccc ii (tt) is defined as: cccc ii (tt) = ee jj2ππ ff NN cc 1 cccc aa ii,nn nn= pp αα (tt nnnn) (4.1) cccc where aa ii,nn cccc {+1 1} refers to CM chips when nn is even such that aa ii,nn cccc = aa ii,nn 1 while cccc aa ii,nn = when nn is odd and ff refers to the carrier offset between two components. As shown in Figure 4.1, the two components of this design are identical except that each of 47

63 Chapter 4 L2C Replica Code Design them incorporates a separate carrier. In other words, this design refers to having a replica carrier with two frequency components multiplexed together on a chip by chip basis Non Return to Zero Dual Channel CM (NRZ DCM) Code The value of αα for this case is 1 while cccc ii (tt) is given by: NN cc 1 cccc ii (tt) cccc = aa ww,nn nn= pp αα (tt nnnn) (4.11) cccc where aa ww,nn {+1 1} refers to CM chips when nn is even and equals zero when nn is odd while the subscript ww is used to distinguish between the two satellites (ii & ww) being searched by two components of this design such that ww ii Non Return to Zero Folded CM (NRZ FCM) Code For this design, NN cc is replaced by NN cc 2 in both components, αα = 1 and cccc ii (tt) is: NNcc 2 1 cccc cccc ii (tt) = aa ii,nn pp αα (tt nnnn) (4.12) nn= cccc Here, aa ii,nn cccc cccc = aa ii,nn+1229 for even values of nn while aa ii,nn remains zero when nn is odd. In other words, this code is generated by folding the RZ CM code (design 1) about its middle. As a result, the entire CM code is accommodated in 1 milliseconds. Note that αα=1.5 in the RZ ECM design allows to assess an intermediate performance level in the range between αα=1 and αα= Performance Evaluation The acquisition performance of the considered replica codes is evaluated under the following criteria Code Recovery Function The code recovery function herein refers to the correlation function, given by Equation (4.6), evaluated around the zero relative code delay (i.e. ττ = ) and is denoted as R kk,ii. Figure 4.2 shows the code recovery function of all considered reference codes, having a primary difference in the peak region. The RZ ECM and NRZ CM codes have a flat top 48

64 Chapter 4 L2C Replica Code Design Normalized correlation value NRZ CM RZ ECM RZ CM/NRZ TCM/DCM/FCM Code delay (chips) Figure 4.2. L2C code recovery function of considered reference codes Simulation data: PRN-1 code sampled at MHz of half a chip and one chip respectively while all other codes have a sharp triangular function. The flat tops of RZ ECM and NRZ CM codes allow code search at larger steps without losing the acquisition sensitivity, discussed in more detail later in the chapter. The code recovery functions shown in Figure 4.2 are obtained by correlation of simulated PRN-1 L2C code containing a CM period and first 2 millisecond segment of the corresponding CL code (i.e. mm= ) with the corresponding replica codes, sampled at MHz (such as used in Zarlink GP215 chipsets). In terms of the design parameter αα, the L2C code recovery function can be modeled as: TT R kk,ii ( ττ, αα) = 1 TT [cccc kk(tt ττ kk + mmtt cccc ) + cccc kk (tt ττ kk )]cccc ii (tt ττ ii )dddd 1 ττ, 1 ττ 2 1 ττ, αα TT 2 cc ττ 1 + αα TT cc 1 2, ττ αα TT cc, ooooheeeeeeeeeeee (4.13) where ττ measures the relative code delay in units of chips and TT cc =1-chip refers to the L2C code chip period, that is (1/123) seconds. 49

65 Chapter 4 L2C Replica Code Design Worst-case correlation loss (db) NRZ CM RZ ECM NRZ TCM/DCM/FCM Search step (chips) Figure 4.3. Worst acquisition loss as a function of search step, in considered L2C reference codes Simulation data: PRN-1 code sampled at MHz Note that Equation (4.13) assumes perfect triangle and straight line (for flat region), reasonable for the L2C code recovery function, as observed in Figure Phase Offset Loss The aim of a code search process is to hit the correlation maximum (peak) as closely as possible. This however is strongly dependent on the size of search step. For a given search step, in the best case, the maximum of correlation function will be hit. However, depending on the phase of the received code, the search may step over the correlation maximum and in the worst case an offset of εε/2 chips, from the maximum, will be created, where εε is the size of search step in units of chips. This offset or timing error causes correlation loss and therefore restricts the search step size and hence the search speed. Equation (4.14) defines the correlation loss (in db) of the considered reference codes as a function of εε and αα: R llllllll = 2 log 1 1 εε (αα 1) 2 5, εε αα 1, εε > αα 1 (4.14) Figure 4.3 compares the worst-case correlation loss in each reference code based on simulation results, showing that NRZ CM can offer search steps of up to 1 chip without loss while RZ ECM will do the same job at.5 chip stepping.

66 Chapter 4 L2C Replica Code Design 1 Cummulative probability RZ CM RZ ECM NRZ TCM/DCM NRZ CM NRZ FCM Relative cross-correlation power (db) Figure 4.4. Cross-correlation performance of considered L2C reference codes Simulation data: PRN-1 and PRN-7 codes sampled at MHz These lossless larger steps are due to flat tops of corresponding code recovery function mentioned earlier and can be used to speed up the signal search. All other codes will, however, suffer an acquisition loss, in the worst case, for any search step, corresponding to their triangular code recovery function Cross-Correlation Noise For CM acquisition, the local reference sequence suffers cross-correlation with the CL code component in the received signal i.e. cccc kk (tt ττ kk ), given in Equation (4.1). The crosscorrelation performance of a reference sequence is determined by the margin between its acquisition peak and the highest cross-correlation value. The larger the margin, the better is the cross-correlation performance. Each of the reference codes (PRN-7) is correlated with the composite L2C PRN-1 code (i.e. containing a CM period and first 2 millisecond segment of the CL code as mentioned earlier) and the cross-correlation results are compared in Figure 4.4. The horizontal axis of the figure represents the cross-correlation power with reference to the acquisition peak (i.e. db), while the vertical axis gives the cumulative probability of distribution of the cross-correlation result. A curve towards the left has better cross-correlation performance. In particular, the top region of these curves is of interest, where cross-correlations start to be a problem. This method of evaluating the L2C cross-correlation performance has also been used by Fontana, et al., (21) and 51

67 Chapter 4 L2C Replica Code Design T I IF signal Carrier Generator 9 o f D,i Code Generator τ i T ( ) 2 ( ) 2 Q Σ D s M H < ν > H 1 Figure 4.5. L2C correlation system considered for the detection probability analysis Qaisar and Dempster (29c).The RZ CM code has the best performance because of its zeros placed in its alternate chips. These zeros occupying half of the code, reducing the cross-correlation to half and that is why the NRZ CM code where CM chips occupy the entire code period is approximately 3dB worse, while RZ ECM code with one fourth of the code filled with zeros falls between the two. The NRZ TCM and NRZ DCM have the same level of performance which is slightly worse than RZ ECM but interestingly better than the NRZ CM case. The improvement just mentioned is due to different sequences placed in two components of the local code which will average out more cross-correlation noise compared to when identical sequences are placed in the two components of NRZ CM code. The NRZ FCM code is penalized here for its shorter period as the crosscorrelation performance of CM sub-codes, that is segments of CM code shorter than 2 milliseconds, is proportional to their length (Dempster, 26). For CM acquisition, the cross-correlation margin is on the order of 28 db (Tran, 24), large enough for normal operating conditions. This margin might become insufficient only in cases where the Near-Far problem occurs: where the desired signal is significantly weaker than the interfering signal, leading to false acquisition, which is the subject of Chapter 7. For the remainder of this chapter, the impact of cross-correlation is therefore not considered Probability of Detection With reference to the correlation system, shown in Figure 4.5, the decision statistic DD ss for the hypothesis of a useful L2C signal present with white Gaussian noise, i.e. H 1, is: 52

68 Chapter 4 L2C Replica Code Design DD ss = PP kk 2 R kk,ii ( ττ) cos(2ππ φφ) sin(ππ ffff) 2 + nn ππ ffff II (tt) + PP kk 2 R kk,ii ( ττ) sin(2ππ φφ) sin(ππ ffff) ππ ffff 2 + nn QQ (tt) (4.15) where DD ss 2 σσ nn is a non-central χχ 2 (chi-squared) distribution with 2MM degrees of freedom, where MM is the number of non-coherent integrations and σσ nn 2 is the power of nn II (tt) and nn QQ (tt) noise components each. The single-trial detection and false alarm probabilities of the test statistic DD ss 2 σσ nn are obtained by integrating the corresponding probability density functions beyond the detection threshold which can be computed through inverse chisquare cumulative distribution function for a given PP ffff and MM (Bastide, et al., 25). The noise power σσ nn 2 will depend on the choice of local reference code. Following the approach used in Yao (27), for the RZ CM code, it can be derived as follows. The noise variance at the output of II and QQ channels is expressed as: 2 = VVVVVV nn II (tt)cccc RRRR ii (tt) cos 2ππ ff IIII + ff DD,ii tt + φφ ii dddd (4.16) σσ nn,ii TT 2 = VVVVVV nn QQ (tt)cccc RRRR ii (tt) sin 2ππ ff IIII + ff DD,ii tt + φφ ii dddd (4.17) σσ nn,qq TT where VVVVVV(XX) = EE XX EE(XX) 2 = EE(XX 2 ) [EE(XX)] 2, cccc ii RRRR (tt) is the RZ CM local replica code, ff DD,ii represents the local Doppler estimate while φφ ii denotes the phase of local carrier herein considered to be zero for simplicity. TT EE nn II (tt)cccc RRRR ii (tt) cos 2ππ ff IIFF + ff DD,ii tt dddd TT = EE{nn II (tt)} cccc ii RRRR (tt) cos 2ππ ff IIII + ff DD,ii tt dddd = (4.18) Similarly, 53

69 Chapter 4 L2C Replica Code Design TT EE nn QQ (tt)cccc RRRR ii (tt) sin 2ππ ff IIII + ff DD,ii tt dddd TT = EE nn QQ cccc ii RRRR (tt) sin 2ππ ff IIII + ff DD,ii tt dddd = (4.19) Hence, σσ nn,ii TT 2 2 = EE nn II (tt)cccc RRRR ii (tt) cos 2ππ ff IIII + ff DD,ii tt dddd (4.2) σσ nn,qq TT 2 2 = EE nn QQ (tt)cccc RRRR ii (tt) sin 2ππ ff IIII + ff DD,ii tt dddd (4.21) Considering only the in-phase noise component, for convenience, Equation (4.2) can be solved as: TT nnii (tt)cccc RRRR ii (tt) cos 2ππ ff IIII + ff DD,ii tt dddd 2 = EE TT nn II (ss)cccc RRRR ii (ss) cos 2ππ ff IIII + ff DD,ii ss dddd σσ nn,ii (4.22) Since nn II (tt) is a band-limited White Gaussian Noise, it can be decomposed as (Yao, 27): nn II (tt) = 2[nn 1 (tt) cos(2ππff IIII tt) + nn 2 (tt) sin(2ππff IIII tt)] (4.23) Where nn 1 (tt) and nn 1 (tt) are two independent and identically distributed Gaussian processes with centre frequency ff IIII. Substituting Equation (4.23) into Equation (4.22) and ignoring the higher frequency terms gives: nn 1(tt) sin 2ππff DD,ii nn 2(tt) cos 2ππff DD,ii tt cccc RRRR ii (tt)dddd. 2 = EE TT nn 1(ss) sin 2ππff DD,ii nn 2(ss) cos 2ππff DD,ii ss cccc RRRR ii (ss)dddd σσ nn,ii TT 54

70 Chapter 4 L2C Replica Code Design As nn 1 (tt) and nn 2 (tt) are two independent Gaussian processes with respect to each other, EE[nn 1 (tt)nn 2 (ss)] =, hence the above expression for in-phase noise variance reduces to: 2 σσ nn,ii TT TT = EE 1 2 nn 1(tt) nn 1 (ss)sin 2ππff DD,ii tt sin 2ππff DD,ii ss (4.24) nn 1(tt) nn 1 (ss)cos 2ππff DD,ii tt cos 2ππff DD,ii ss ccmm ii RRRR (tt)cccc ii RRRR (ss)dddddddd TT TT σσ 2 nn,ii = 1 2 NN 2 δδ(tt ss)sin 2ππff DD,iitt + φφ ii sin 2ππff DD,ii ss NN 2 δδ(tt ss)cos 2ππff DD,iitt (4.25) + φφ ii ) cos 2ππff DD,ii ss cccc ii RRRR (tt)cccc ii RRRR (ss)dddddddd where NN 2 is the two-sided noise power spectral density. TT σσ 2 2 nn,ii = σσ nn,qq = NN 4 cccc ii RRRR (tt)cccc RRRR ii (tt) sin 2 2ππff DD,ii tt + cos 2 2ππff DD,ii tt dddd (4.26) = NN 4 cccc ii RRRR (tt)cccc RRRR ii (tt)dddd TT = NN 4 TT 2 = NN TT 8 (4.27) Following the approach used in Bastide, et al. (25) and Yao (27), the expected value of the non-centrality parameter, for this case, can be given as: λλ = 4MMPP kk NN TT R kk,ii( ττ) 2 sin(ππ ffff) 2 ππ ffff (4.28) Considering ττ =, ff = and kk = ii, Equation (4.28) reduces to: λλ = MMPP kk NN /TT (4.29) 55

71 Chapter 4 L2C Replica Code Design Probability of detection RZ CM RZ ECM NRZ CM NRZ TCM/DCM NRZ FCM C/No (db-hz) Figure 4.6. Average probabilities of L2C detection with considered reference codes PP ffff = 1 3, MM=1, TT=2ms (- theory, + MC simulations) Note that the denominator NN /TT in Equation (4.29) represents the noise power in a 1/TT Hz bandwidth, i.e. the total noise power at the correlator output. Depending on the replica code design, different noise power is accumulated in the correlation process. Hence, for the considered designs of replica code, the expression for noise power, in terms of design parameters, can be generalized as: TT σσ 2 nn (αα, ρρ) = NN 4 cccc ii(tt)cccc ii (tt)dddd = (αα + ρρ) NN TT 8 (4.3) where ρρ refers to the pulse width of cccc ii (tt) such that ρρ= for RZ CM, RZ ECM and NRZ CM code while ρρ=1 for all other designs. Also, the generic non-centrality parameter can be given as: λλ αα,ρρ = 4MMPP kk (αα + ρρ)nn TT R kk,ii( ττ) 2 sin(ππ ffff) 2 ππ ffff (4.31) Considering a search grid of uniformly distributed carrier Doppler and code delay in the range of ± 2 3TT Hz and ±1 chip respectively, the average L2C detection probabilities with each of the reference code designs are plotted in Figure 4.6 (using the expression derived for the non-centrality parameters and Equation (2.8), and verified through the Monte Carlo simulations), where the probability of false alarm PP ffff is set to 1 3, MM=1 and 56

72 Chapter 4 L2C Replica Code Design 1 Mean acquisition time (s) RZ CM RZ ECM NRZ TCM/DCM NRZ FCM NRZ CM C/No (db-hz) Figure 4.7. L2C mean acquisition times with considered reference codes for average probabilities case, PP ffff = 1 3, MM=1, TT=2ms (-theory, + MC simulations) TT=2 ms (except for the NRC FM where TT=1 ms). Considering the grid average provides a relatively realistic estimate of the detection performance for each code design. As given by Equation (4.19), the relative difference in detection probabilities of various code choices is due to the difference in their code recovery function R kk,ii ( ττ) and noise power σσ nn 2 which is dependent on αα + ρρ. For the same output of R kk,ii ( ττ), a smaller value of αα + ρρ results in better detection performance. For instance, the RZ CM has the best detection performance with αα + ρρ=1, followed by RZ ECM and NRZ CM with αα + ρρ equal to 1.5 and 2 respectively. Because of the smaller losses at larger offsets, shown in Figure 4.3, the NRZ CM code outperforms NRZ TCM and NRZ DCM, all having the same value of αα + ρρ. Finally, the NRZ FCM has the worst performance as it observes the L2C signal over an interval half of that used by other code designs Mean Acquisition Time As discussed in Section 2.4, the mean acquisition time for single dwell search strategy is given as (Holmes, 1998) : TT = 2 + (2 PP dd )(qq 1) 1 + KKPP ffff 2PP dd MMMM (4.32) where the uncertainty region is dependent on the replica code design, as given by: 57

73 Chapter 4 L2C Replica Code Design Acquisition sensitivity RZ CM RZ ECM NRZ CM NRZ TCM/DCM NRZ FCM Search speed Figure 4.8. Relative Speed-Sensitivity trade-off levels offered by considered L2C replica codes qq = NN ccnn DD εε αα + ρρ (4.33) where NN DD is the number of Doppler bins and represents the integer part of its real number argument such that αα + ρρ =1 for RZ CM and RZ ECM codes while αα + ρρ =2 for all other designs where KK is the penalty factor set to 1 MMMM. Considering a search step of 2 3TT Hz over a Doppler range of ±5 khz and a step of.5 chip to cover 246 chips in the code delay dimension, Figure 4.7 compares the L2C mean acquisition time with all reference code designs for average detection probabilities. It can be observed from Figure 4.7 that for clear sky conditions where the CC NN level is above 35 db-hz, NRZ FCM is the fastest choice, followed by the NRZ group, and then the RZ CM & RZ ECM codes respectively. The RZ FCM and NRZ group here take advantage of a shorter observation period and dual search capacity respectively to speed up the search in the code phase dimension. However, this performance order is changed in the weaker signal range where RZ CM and NRZ CM tend to become better options followed by RZ ECM and then rest of the code designs. This is because the relative difference in corresponding detection probabilities for the lower range of CC NN levels is changed. 4.5 Summary and Recommendations New choices of replica code for L2C acquisition are evaluated. Collectively these designs offer multiple levels of trade-off between the acquisition sensitivity and search speed as 58

74 Chapter 4 L2C Replica Code Design shown in Figure 4.8. Each design provides an improved solution for a different acquisition scenario. The value of the discussed code designs can be summarized as follows: RZ CM offers the best acquisition sensitivity and cross-correlation performance, making it a good choice for weak signal environments. NRZ FCM has the highest acquisition speed and is good for open-sky and warm start conditions. This design saves time in both Doppler and code delay dimensions simultaneously. NRZ TCM would be a good design for scenarios with larger Doppler search spaces such as in the receiver cold start, i.e. in the absence of expected satellite location information. NRZ DCM can reduce the receiver complexity by dropping the number of search channels to half. For the typical half-chip search resolution, NRZ CM and RZ ECM are promising designs due to their superior worst-case acquisition performance. The NRZ CM code can be particularly exploited to prevent phase offset losses in L2C correlators operating at lower frequencies, as discussed in the next chapter. Most of the commercial GPS receivers (e.g. Garmin etrex H) allow the user to inform the unit about its surrounding environment (such as inside buildings or outdoor) at the startup. The receiver can then use this information for adopting a search strategy. Similarly, a receiver would usually check the availability of a priori knowledge to decide whether a cold start or a warm start is required. Also, generally a receiver is able to identify if it has been tracking a cross-correlation peak instead of the true signal. For each of these scenarios, an appropriate L2C replica code can be selected to expedite the signal search in a GPS L2C receiver. 59

75 Chapter 5 Down-Sampling Strategies for L2C Correlators 5.1 Introduction For a given code period, acquisition resources taken by correlators are directly proportional to the sampling frequency (ff ss ) set by the RF front-end which is likely to change from one receiver implementation to another. Conventional sampling frequencies such as MHz (for the Zarlink GP215 front-end) and MHz (for the SiGe SE411 front-end) are several times higher than the code chip rate (ff cc ) while operating at twice the code chip rate is statistically sufficient for the correlation process (Namgoong and Meng, 21). Thus performing correlation on an average ff ss ff cc samples per chip can be considered redundant and resource consuming. Moreover, in the frequency domain, this problem translates to the requirement of larger and more expensive FFT blocks. In this chapter, down-sampling of baseband signals is investigated to reduce the consumption of acquisition resources by L2C correlators. The contents of the chapter are arranged as follows. A direct down-sampling approach is first discussed and the corresponding acquisition losses are characterized. A more efficient, chip-wise (CW) down-sampling strategy that allows L2C correlators to operate at the code chip rate is then presented. The down-sampling strategies are applied for acquiring both real and simulated L2C signals and the results of acquisition are discussed. Finally, the findings of this work are summarized. For all experiments conducted in this research, two industry standard RF sampling frequencies, MHz and MHz are selected as reference. For other sampling frequencies, the reference results will change proportionally. For all acquisition experiments and analysis, the L2C signal is observed over a coherent integration period of 2 milliseconds using the L2 CM code. 6

76 Chapter 5 Down-Sampling Strategies for L2C Correlators 5.2 Direct Down-Sampling Approach A direct approach for data down-sampling is to select every NN th sample from the baseband L2C data stream and delete the rest of the samples. This however can have two implications for the correlator. First, the down-sampling factor NN must adhere to the Nyquist criterion restricting the minimum operating frequency to twice the code chip rate. f s f Ns N T I IF signal Carrier Generator 9 o f D,i Code Generator τ i S Post Correlation Processing D s H < ν > H 1 N T Q Figure 5.1. A direct down-sampling approach for performing correlations at lower rates Secondly, since the phase of the received codes is not known, the down-sampling process may start from different points in a chip in the received and the local replica codes, causing an extra phase offset loss. For the square waveform of received satellite codes, the sampling frequency can be reduced to as low as the code chip rate while preserving the code identity required for the correlation process. In the absence of noise, aliasing caused at this sampling frequency will not affect the correlation output as both incoming and local replica codes will experience identical aliasing effects. Unfortunately, channel noise is present along with the transmitted codes when they are presented to the correlator. In the case of aliasing, this noise is addressed by an anti-aliasing filter. In the following sub-sections, the downsampling range between the original sampling frequency and the code chip rate is evaluated in terms of acquisition losses and correlator operating frequency, in order to identify the effective trade-off region for L2C correlators Anti-Aliasing Filter For a desired correlator operating frequency below the Nyquist rate, both the received and 61

77 Chapter 5 Down-Sampling Strategies for L2C Correlators 1.5 S n (ω) N /2 Normalized magnitude 1.5 Considered Undersampling filtering Frequency (MHz) -2πB 2πB ω (a) (b) Figure 5.2. L2C code spectrum (a) indicating the 2MHz bandwidth occupied by the main lobe (b) Spectral representation with ambient noise local replica codes must be passed through a low-pass anti-aliasing filter before the downsampling phase, as illustrated in Figure 5.1. The L2C code has a line spectrum with an envelope that follows the Sinc function. As shown in Figure 5.2a, the main spectral lobe, typically filtered by the RF front-end, occupies a single-sided bandwidth of 1.23 MHz containing 9 percent of the signal power as in the case of C/A code (Van Dierendonck, 1996). The anti-aliasing filter discussed here will thus remove certain amount of the tail of the main spectral lobe, causing a minimal loss of signal power due to its Sinc shape Signal Power Loss For the baseband GPS L1 C/A signal, the power loss due to pre-correlation filtering is characterized in Van Dierendonck (1996) as: PP = 1 2ππππ SS(ωω)dddd ππ (5.1) where BB is the single-sided spectrum bandwidth while SS(ωω) denotes the power spectral density given by: SS(ωω) = AA2 TT cc 2 ssssss 2 (ωωtt cc 2) (ωωtt cc 2) 2 (5.2) where AA is the signal amplitude and TT cc denotes the code chip period. 62

78 Chapter 5 Down-Sampling Strategies for L2C Correlators Power loss wrt infinite bandwidth (db) Theory L2C simulation Single-sided spectrum bandwidth (MHz) Figure 5.3. L2C signal power loss due to pre-correlation filtering. Note a minimal power loss in...the plateau at the right matched by simulations (PRN-1), in the range of interest Since the L2C signal has same spectral specifications as the L1 C/A signal, Equations (5.1) and (5.2) are valid for the L2C discussion here. Equation (5.1) has been evaluated as a function of single-sided spectrum bandwidth and the corresponding signal power loss with reference to the infinite bandwidth i.e. BB =, is plotted in Figure 5.3. This signal power loss appears as an acquisition loss (measured as a drop in the level of acquisition peak) at the correlator output as verified by simulation results shown in Figure 5.3. For simulations, a correlation is performed between the composite L2C PRN-1 code (i.e. containing a CM period and first 2 millisecond segment of the CL code) with a RZ CM local replica code, both sampled at MHz, engaging a software implemented 1-tap FIR filter SNR Loss The white noise experienced in a GPS receiver has a constant spectral density NN 2 as illustrated in Figure 5.2b. The resulting noise power in a two-sided bandwidth 2B Hz is as follows (Van Dierendonck, 1996): PP nn = 2NN BB (5.3) 63

79 Chapter 5 Down-Sampling Strategies for L2C Correlators Absolute correlation value x Relative code delay (chips) (a) Un-filtered 1.23MHz.682MHz.5115MHz Autocorrelation margin (db) Single-sided filter bandwidth (MHz) (b) Figure 5.4. Simulation results showing the effect of anti-aliasing filtering on L2C signal.(a) Autocorrelation function (b) Worst autocorrelation-margin loss For a received L2C code, as shown in Figure 5.2b, the anti-aliasing filtering will thus also remove some of the noise and consequently the effective signal-to-noise ratio (SNR) loss will be smaller than the signal power loss, as in the case of L1 C/A code. Comparing Equations (5.3) and (5.1) also indicates that the effective SNR loss will have a similar behavior as that of the signal power loss Autocorrelation Side Lobes In addition to signal power loss, the anti-aliasing filtering causes the side lobes of the code s autocorrelation function to rise, as shown in Figure 5.4a. The term autocorrelation (instead of correlation) is used here to facilitate the discussion as both the received and local replica codes are equally band-limited. A side-lobe rise will reduce the margin between the autocorrelation peak and the side lobe, degrading the original autocorrelation characteristics. The autocorrelation-margin protects the receiver from locking onto a sidelobe instead of the true acquisition peak. A smaller autocorrelation-margin demands a higher detection threshold, which for a given probability of false alarm will decrease the probability of detection. 64

80 Chapter 5 Down-Sampling Strategies for L2C Correlators Acquisition loss (db) -2-4 fs=5.7143mhz fs= mhz Down-sampling factor (a) Acquisition loss (db) fs=5.7143mhz fs= mhz Down-sampling factor (b) Figure 5.5. Simulation results of worst phase-offset loss in L2C acquisition for the two reference...sampling frequencies when using: (a) RZ CM replica code (b) NRZ CM replica code For the un-filtered L2 CM codes, the average autocorrelation margin is 28 db (Tran, 24). Figure 5.4b plots the worst autocorrelation-margin for the L2 CM code as a function of filter cutoff frequency. The worst case for each filter bandwidth is found by trialing all 32 PRN codes published for the L2C satellite constellation (IS GPS 2-D, 26). It can be inferred from these results that for filter cutoff frequencies as low as two thirds of the Nyquist cutoff (2ff cc 3=.682 MHz), the autocorrelation-margin loss is negligible. However, for filter cutoffs below this value, the autocorrelation-margin has a sharp drop Phase Offset Loss As mentioned above, the direct down-sampling strategy selects every NN th sample from both incoming and local replica codes, reducing their sampling frequency to ff ss NN. The sampling interval is thus increased to NN ff ss. Considering a code search step equal to the sampling interval (which is often the case in GPS receivers), the worst phase mismatch between the received and local replica codes, in units of chips, can be given as: 65

81 Chapter 5 Down-Sampling Strategies for L2C Correlators ττ = NNff cc 2ff ss (5.4) where the down-sampling factor NN is: NN = 1,2,3, ff ss ff cc (5.5) where represents the integer part of a real number argument. From Equations (5.4) and (5.5), it can be deduced that the sampling interval and hence the code search step remains smaller than a chip. Secondly, for a given sampling frequency, higher down-sampling factors push the code phase error to half a chip. It was shown in Chapter 4 that when using the RZ CM replica code, a half a chip code phase error leads to 6 db acquisition loss. Figure 5.5a presents the worst phase-offset loss using RZ CM replica code for the two reference sampling frequencies as a function of corresponding down-sampling factors, based on simulations. To obtain the worst case, simulations consider all 32 PRN codes and all possible phase offsets for a given sampling frequency and down-sampling factor. It can be verified from these results that for higher down-sampling factors, the worst phase-offset loss tends to approach 6 db. On the other hand, as discussed in Section 4.4, the NRZ CM replica code guarantees an all-chip match for the code search steps of up to one chip without an acquisition loss, as shown in Figure 4.3. Hence the 6 db loss mentioned above can be avoided by employing the NRZ CM replica code here. Although it will raise the correlation noise by 3 db, its overall detection performance, for the worst case, will be 3 db better than that of the RZ CM replica code, as discussed in Section 4.4. However, for the asynchronous sampling frequencies such as MHz and MHz, direct down-sampling of baseband L2C samples results in different number of samples in different code chips. For such cases, although the NRZ CM replica code will provide a match for a certain number of samples per each CM chip, some of the local CM samples will experience a mismatch at the same time, corresponding to the phase offset between the received and local replica codes, causing a minor acquisition loss. This mismatch will, however, not occur if the received and local replica codes have the same phase. Figure 5.5b shows that the worst loss in this case remains below.3 db including all down-sampling factors for the selected reference sampling frequencies. 66

82 Chapter 5 Down-Sampling Strategies for L2C Correlators Acquisition loss (db) Down-sampling factor (a) Acquisition loss (db) Sampling frequency/resamplijng frequency (b) Figure 5.6. Characterization of L2C acquisition loss due to sampling jitter (a) As a function of down-sampling factor for ff ss = MHz (b) As a function of original sampling frequencies for ff NNNN = 1.23 MHz Figure 5.5 indicates that overall the phase-offset loss tends to increase for higher downsampling factors; the exact behavior of this loss will however slightly vary with the code s PRN and sampling frequency Non-Integer Down-Sampling Factors A non-inter value of down-sampling factor (NN) can also be considered. However, it will cause an additional loss due to sampling jitter. The sampling jitter would occur because of a non-integer ratio between the original sampling frequency and the new (ff NNNN ) or resampling frequency (ff ss ff NNNN ) as a received data sample may not always align with the new sampling instants. The phase offset caused due to sampling jitter in this case can be given as: ττ ss = ff ss ff NNNN ff ss ff NNNN (5.6) And the acquisition loss due to this phase offset can be expressed as: 67

83 Chapter 5 Down-Sampling Strategies for L2C Correlators NN ss γγ = TT ss nn ff ss ff ss NN ss ff NNNN ff NNNN nn=1 (5.7) Where TT ss is the sampling interval of the original sampling frequency and NNNN represents the total number of samples in the signal observation period after down-sampling. Figure 5.6a shows the acquisition loss associated with down-sampling of an L2C signal sampled at MHz, over the full range of down-sampling factors. Not that this result will replicate over the higher (>1) values of down-sampling factors. Similarly, Figure 5.6b shows the acquisition loss associated with down-sampling an L2C signal to its code chip rate for the considered range of original sampling frequencies. It can be observed from this result that for a desired re-sampling frequency, a higher original sampling frequency allows higher down-sampling factor with smaller loss. It can also be verified from these results that an integer down-sampling factor does not suffer from sampling jitter. Both of the above results were obtained theoretically using Equation (5.7). The entire above analysis is summarized in Table 5.1 and Table 5.2 for the two reference sampling frequencies. Note that the signal power loss given in Table 5.1 and Table 5.2 is measured with reference to the main spectral lobe. Also, the effective SNR loss will be smaller than the signal loss reported in these tables. Overall, these results suggest that a significant reduction in the correlator operating frequency can be achieved at the cost of minor acquisition loss which is acceptable, particularly when not all of the signal power collected by long L2C codes is always required to detect the signal. For example a downsampling factor of 4 in Table 5.2 reduces the operating frequency by 75% against the worst-case total acquisition loss (summing the 3 losses) of.4489 db. Similarly for the relatively higher sampling frequency case (which allows higher down-sampling factors and consequently more savings) of Table 5.1, the operating frequency is dropped by 9%, for a down-sampling factor of 1 at the cost of worst-case total acquisition loss of.2518 db. Note that for smaller down-sampling factors, filtering losses as well as filter implementation cost can be avoided with a minimum saving of 5%. For frequency domain acquisition, these savings can be seen as a reduction in the required FFT size. As an example, consider a baseband L2C signal sampled at MHz, 68

84 Chapter 5 Down-Sampling Strategies for L2C Correlators Down-Sampling Factor Filter cutoff (MHz) Signal power loss due to filtering (db) Autocorrelation-margin loss due to filtering (db) Worst phase-offset (db) Operating frequency reduction - 5% 66.6% 75% 8% Table 5.1. Summary of direct down-sampling analysis for the sampling frequency of MHz Down-Sampling Factor Filter cutoff (MHz) Signal power loss due to filtering (db) Autocorrelation-margin loss due to filtering (db) Worst phase-offset (db) Operating frequency reduction - 5% 66.6% 75% 8% 83.3% 85.7% 87.5% (a) Down-Sampling Factor Filter cutoff (MHz) Signal power loss due to filtering (db) Autocorrelation-margin loss due to filtering (db) Worst phase-offset (db) Operating frequency reduction 88.8% 9% 9.9% 91.6% 92.3% 92.85% 93.3% (b) Table 5.2. Summary of direct down-sampling analysis for the sampling frequency of MHz (a) NN = 1 to 8, (b) NN = 9 to 16 containing approximately samples per CM code period. This will fit into a point Radix2 FFT block. However, a down-sampling factor of 4 will reduce the number of samples in the CM period to which can be accommodated in a point Radix2 FFT at the cost of worst-case total loss of.4489 db, offering a more feasible implementation. Using the well-known n log 2 n growth in FFT processing, where n represents the number of FFT points, this means a saving of about 78% processing per FFT operation. A hardware implementation of FFT-processing for real L2C signal acquisition using direct down-sampling approach is demonstrated, as described in the following section FFT Correlation Hardware Frequency domain acquisition of real L2C signal sampled at MHz having a CC NN level of 4 db-hz is performed, employing a direct down-sampling FFT correlation 69

85 Chapter 5 Down-Sampling Strategies for L2C Correlators f s f Ns IF signal N FFT e j2π(f+fd,i)t IFFT D s Code Generator N FFT ( )* Figure 5.7. A direct down-sampling FFT based correlation architecture architecture illustrated in Figure 5.7, where ff NNNN refers to the new sampling frequency, after down-sampling. A down-sampling factor of 4 and hence a filter cutoff frequency of MHz, as specified in Table 5.1, are used. For hardware implementation a Altera Stratix EP1S25 DSP Development Board equipped with Altera Stratix FPGA device (Altera, 29b), large enough to hold three point Radix2 FFTs is selected (see Figure 5.8). Figure 5.8. Altera Stratix DSP Development Board used for hardware implementation of direct down-sampling FFT correlation architecture A standard Radix2 FFT scheme having an internal precision of 16 bits with fixed streaming architecture, provided by the Altera FFT Megacore function has been considered for implementation. A separate FIFO read control is employed for the downsampling process. FFT outputs are scaled to reduce the bit-width for subsequent processing and the absolute value of the final result is computed with Robertson approximation as used in (Ward, 1996). The acquisition results shown in Figure 5.9 are measured in terms of deflection coefficient, given by Borio (28b): 7

86 Chapter 5 Down-Sampling Strategies for L2C Correlators Normalized correlation outpu Normalized correlation outpu Normalized correlation outpu Code phase (samples) (a) Code phase (samples) (b) Code phase (samples) (c) Figure 5.9. Real L2C SVN 53 (CC NN =4 db-hz) acquisition results (a) Full rate correlation processing, ηη= db Down-sampling factor NN=4 (b) without filter (ηη=23.523db) and (c) with filter (ηη=27.296db) ηη = (EE[DD ss HH 1 ] EE[DD ss HH ]) 2 VVVVVV[DD ss HH ] (5.8) where DD ss denotes the decision variable while HH 1 and HH are the hypothesis of useful signal being present and absent respectively. The effectiveness of anti-aliasing filter can be confirmed by comparing the results of Figure 5.9b (ηη= db) and Figure 5.9c (ηη= db) having a difference of db which can be observed as a drop in the noise floor. The final acquisition result of hardware platform (ηη= db) is found to be competitive (only.239db worse) with the corresponding full-rate correlation processing result of ηη= db, shown in Figure 5.9a. This implementation was a joint effort by the author and his colleague Nagaraj Shivaramaiah. 71

87 Chapter 5 Down-Sampling Strategies for L2C Correlators f s f c T c T I IF signal Carrier Generator 9 o f D,i T c Code Generator τ i T ( ) 2 ( ) 2 Q Σ D s M H < ν > H 1 Figure 5.1. Correlation architecture for chip-wise down-sampling The above analysis led to discovering a more efficient L2C down-sampling strategy which, irrespective of the receiver implementation, reduces the correlator operating frequency to the code chip rate and avoids all of the above mentioned down-sampling losses. The following section discusses this strategy in detail. 5.3 Chip-Wise Down-Sampling In this strategy, the baseband L2C samples across each chip period are accumulated so that each code chip is represented by one sample. This effectively reduces the correlator operating frequency to the code chip rate. The down-sampled code is thus directly correlated with a replica NRZ CM chip sequence and the correlator outputs are combined coherently over the signal observation period TT System Architecture Figure 5.1 illustrates the correlator architecture required for this approach. After removing the carrier from the received signal, baseband L2C samples are integrated for each chip period. The following procedure is adopted for sample accumulation. An index vector is first generated as: where pp is an integer, given by: xx[nn] = (pp 1)ff ss ff cc + 1 (5.9) pp = 1,2,3, NN cc (5.1) 72

88 Chapter 5 Down-Sampling Strategies for L2C Correlators t Figure Possible phases (starting points for the samples accumulation process) of incoming L2C code sampled at MHz CM 1 CL1 CM 1 CL 1 Phase- CM 1 CL 1 CM 2 Phase-1 CM 1 CM 1 CM 1 CL 1 CM 2 CL 1 CM 2 CL 1 CM 2 Phase-2 Phase-3 Phase-4 CM 1 CL 1 CM 2 Phase-5 CM 1 CM 1 CM 1 CM 2 Local phase- Local phase-1 Figure All possible phases of the received and replica codes over 2 chip periods, f s =5.714 MHz Samples enclosed by adjacent indices given by Equation (5.9) are then accumulated. The samples accumulation commences from the first sample received, which also represents the phase of incoming code. If this phase is aligned with the chip boundary, accumulated samples will exactly represent the code chips and correlation of these chips with the reference chip sequence will result in the same signal-to-noise ratio at the correlator output as that achieved at original full sampling rate. However, for a different phase of the incoming code, further investigation is required, as discussed next. Consider a sampling frequency of MHz, leading to 5 or 6 samples per code chip. This means that there can be 6 possible phases of the incoming code and that one of the 6 consecutive phases will indicate the chip boundary with a certain precision set by the sampling instant which may or may not hit the exact chip boundary. Since there is not enough information in the signal, at this stage, to recognize the chip boundary, sample accumulation may start from any one of the 6 possible phases illustrated in Figure

89 Chapter 5 Down-Sampling Strategies for L2C Correlators c k,1 (t) c k,2 (t) c k,3 (t) c k,4 (t) T 1 T c T 2 2T c c i,1 (t) c i,2 (t) c i,3 (t) c i,4 (t) T 1 T c T 2 2T c Figure Generic structure of the received (top) and replica (bottom) L2C codes, over 2 chip periods One solution for such situations is to trial all of the 6 phases one-by-one and the phase with highest acquisition peak will identify the chip boundary without any loss in the SNR. This however does not save acquisition resources except for some FFT size benefits in the frequency domain acquisition (Alaqeeli, et al., 23). For L2C signals, this phase ambiguity problem can be resolved if the NRZ CM replica design is engaged. Figure 5.12 shows all possible phases of the received and corresponding local replica code, over 2 chip periods (as each symbol in the reference NRZ CM code is two chips wide). Note that the local replica code has only two corresponding phases as the code search step is equal to 1-chip. It can be observed from Figure 5.12 that one of the two local phases provides one-chip CM match for all phases of the incoming code. Note that for some cases different CM chips constitute the chip match. For example, when incoming phase-3 and local phase-1 are compared, the total match of CM 1 and CM 2 equals one chip period. This means that regardless of the incoming phase, correlation over two-chips, and subsequently over the entire code period, will generate the same result, except a different cross-correlation value due to a different code delay Correlator Output Consider the generic structure of received and replica L2C codes over 2 chip periods, shown in Figure The two codes are decomposed into four components each, as labeled in the figure, such that TT 1 TT cc and TT 2 = TT 1 + TT cc where TT cc refers to the chip period. Depending on the received code delay, cc kk,1 (tt) and cc kk,2 (tt) may represent the same chip or two different chips (a CM chip and a CL chip). The same is true for cc kk,3 (tt) and cc kk,4 (tt). On the other hand, for simplicity, the replica code delay is considered as zero. 74

90 Chapter 5 Down-Sampling Strategies for L2C Correlators Absolute correlation value Code phase offset (samples) (a) x 1 4 Absolute correlation value x Code phase offset (samples) 8367 (b) phase phase 1 phase 2 phase 3 phase 4 phase 5 x 1 4 phase phase 1 phase 2 phase 3 phase 4 phase 5 Figure CW correlator output for 6 (ff ss = MHz) consecutive phases of the received L2C signal (a) Noiseless simulated signal (b) Real signal, CC NN :4 db-hz For a given relative code delay ττ, the output of conventional correlation (operating at full sampling rate) between the two codes can be expressed as: 2TT cc ( ττ) = cc kk,1 (tt)cc ii,1 (tt) dddd + cc kk,2 (tt)cc ii,2 (tt) dddd CC kk,ii TT 1 TT cc TT 1 TT 2 2TT cc + cc kk,3 (tt)cc ii,3 (tt) dddd + cc kk,4 (tt)cc ii,4 (tt) dddd (5.11) TT cc TT 2 2TT cc ( ττ) = aa ii,1 cc kk,1 (tt) dddd + cc kk,2 (tt) dddd CC kk,ii TT 1 TT cc TT 1 TT 2 2TT cc + aa ii,2 cc kk,3 (tt) dddd + cc kk,4 (tt)dddd (5.12) TT cc TT 2 Note that for the NRZ CM replica code, involved here, cc ii,1 (tt) = cc ii,2 (tt) = aa ii,1 and cc ii,3 (tt) = cc ii,4 (tt) = aa ii,2, where aa ii,1, aa ii,2 {+1 1} represent the corresponding replica chips. Equation (5.12) can be further simplified as: 75

91 Chapter 5 Down-Sampling Strategies for L2C Correlators Relative Code delay (chips) Figure Comparison of real L2C (SVN-48, CC NN :32 db-hz, f s = MHz) CAF obtained with full-rate and CW correlators TT cc 2TT cc ( ττ) = aa ii,1 cc kk,1 (tt) + cc kk,2 (tt) dddd CC kk,ii 2TT cc (5.13) + aa ii,2 cc kk,3 (tt) + cc kk,4 (tt) dddd TT cc Equation (5.13) exactly represents the correlator output in CW strategy (see Figure 5.1) where the incoming code is integrated over each TT cc and then correlated with the corresponding replica chips. Hence the full-rate and CW correlators will generate the same final output. That is why the CW strategy inherits the probability of detection, mean acquisition time and worst-case loss of the NRZ CM reference code, presented in Chapter 4, without any performance degradation. Note that for each correlation trial, since the local replica code is shifted by one chip, the above analysis remains valid for any nonzero delays of the local replica code. Also, due to coherent accumulation of correlator outputs, the presence of a residual carrier will have the same effect as in the full rate correlation. Figure 5.14 compares the L2C acquisition results of CW correlators for 6 (as the sampling rate is MHz) consecutive phases of the received code. 76

92 Chapter 5 Down-Sampling Strategies for L2C Correlators Power consumption (watts) MHz MHz 84.96% 1.23MHz(CW) 94.51% fs Circuit size (LEs) MHz MHz 82.1% 1.23MHz(CW) 93.75% fs (a) (b) Figure Comparison of full-rate and CW L2C correlators for a full CM period scan (a) power consumption (b) circuit size These results verify that the level of acquisition peak is maintained for all of the trialed phases and hence the CW samples accumulation process is independent of the received code phase Acquisition Results A real L2C signal sampled at MHz and having CC NN level of approximately 32 db-hz was subjected to both CW and full-rate correlators. Figure 5.15 compares the acquisition result of the two correlators. It can be observed from this comparison that the distribution of collected signal energy across the considered search space (or the cross ambiguity function CAF) remains closely matched for both cases. The output of two correlators is also measured in terms of deflection coefficient and the values of ηη for the full-rate (18.36 db) and CW (18.32 db) correlators are found to be approximately the same Power Consumption and Circuit Size In order to estimate the magnitude of benefits which can be exploited by employing CW correlators, a massively parallel correlators circuit layout was developed in the Altera QUARTUS-II9 design environment, selecting the Cyclone-II FPGA device (Altera, 29a). 77

93 Chapter 5 Down-Sampling Strategies for L2C Correlators For each sampling frequency, the number of parallel correlators to be included is equal to the number of samples (i.e. delays) in the CM period. Estimates of power consumption and required circuit size in terms of logic elements (LEs: an LE refers to the basic circuit unit on the Altera FPGA devices) reported by the QUARTUS compiler are plotted on in Figure A saving of 8 to 9 percent can be observed from the figure. Due to the parallel correlators architecture, the circuit size savings indicated in Figure 5.16 are contributed not only by having lower operating frequency but also by the reduced number of delay trials requiring fewer correlators. For serial correlator architectures where all code delays are trialed by a single correlator this later contribution can be translated into reduced acquisition time, but power consumption savings would be similar. 5.4 Summary An analysis of baseband data down-sampling for reducing the operating frequency of L2C correlators is presented. It is found that direct down-sampling is an effective way of saving L2C acquisition resources at the cost of minor acceptable losses. A chip-wise down-sampling strategy, that minimizes the operating frequency of L2C correlators without losing the acquisition sensitivity, is developed. The considered down-sampling strategies exploit NRZ CM replica code design to prevent acquisition losses. These down-sampling strategies also allow the use of shorter and less expensive FFT blocks for signal acquisition in the frequency domain. The down-sampling strategies are applied for real signal acquisition on both software and hardware platform and their benefits, in terms of saving processing resources, are demonstrated. 78

94 Chapter 6 Post Processing of Segmented L2C Correlations 6.1 Introduction The techniques for reducing the L2C search space in the code delay dimension were discussed in Chapter 5. This chapter presents an approach for reducing the L2C acquisition load in the Doppler dimension. In this approach, a segmented correlation strategy is employed where the replica CM code period (2 milliseconds) is divided into MM segments of equal length and each of these segments performs an independent partialperiod correlation. Results of segmented correlations are then combined through a differentially semi-coherent (DSC) post correlation combining technique. The DSC combining technique exploits the synchronization of CNAV data symbols with the CM code period to avoid the data bit transition losses that occur with L1 C/A signal and combines together the outcome of several versions of the differentially coherent combining technique to achieve the processing gain. This approach saves searches in the Doppler dimension due to segmented correlations and improves the detection probability when compared to the conventional non-coherent (NC) and differentially coherent (DC) post correlation processing techniques addresses the residual carrier signal issue in the generalized differentially coherent (GDC) technique. The DSC combining approach also provides a more efficient way of acquiring the CL code compared to the straight coherent integration. The contents of this chapter are arranged as follows. A partial-period CM correlation architecture is described at the beginning. Various techniques for post correlation differential processing, in terms of their decision variable and dependence on the residual carrier phase are then discussed. Performance of all considered differential processing techniques is compared with the conventional coherent and non-coherent integration approaches in terms of detection probability, receiver operating characteristic (ROC) curves and mean acquisition time. Acquisition of CL code using the DSC combining technique is then discussed. 79

95 Chapter 6 Post Processing of Segmented L2C Correlations 4ms 2ms Received L2C code S 1 S 2 c 1 c 2 l l l S M c M c 1, c 2, c M S 1, S 2, S M CM replica code segments of length l Output of segmented correlations Figure 6.1. A partial-period CM correlation architecture Key findings of this work are listed in the summary and a theoretical analysis of the false alarm and detection probabilities for the DC and GDC combining techniques, verified through simulations, is provided in the appendix A. This research work was a joint effort by the author and a colleague from Politecnico di Torino, Italy (Tung Hai Ta) under the research collaboration between the University of New South Wales Australia and Politecnico di Torino, Italy. Tung Hai Ta contributed to the assessment of residual carrier phase described in Section 6.2 and developed the theoretical analysis for DC and GDC techniques, provided in the appendix A. 6.2 Post Correlation Differential Combining Partial-Period CM Correlation Architecture Considering a passive matched filtering approach (Shivaramaiah, 25), the concept of partial period (or segmented) correlation as applied to L2 CM acquisition is illustrated in Figure 6.1, where a 4 millisecond block of incoming L2C code (after the received signal has been mixed with the replica carrier) is slid over the static MM segments of replica CM code. Each of the MM replica segments has a length ll = TT CCCC MM, where TT CCCC refers to the CM code period, and hence it performs an independent correlation over a coherent integration period TT = ll. Sliding the entire 4 millisecond block of the received L2C code guarantees that a full 2 millisecond CM code match will occur, including the scenario of received L2C code having a CNAV symbol transition. 8

96 Chapter 6 Post Processing of Segmented L2C Correlations Σ M k=2 S k S k-1 ( )* k={1, 2, 3,., M} D DC Figure 6.2. DC combining scheme for segmented CM correlation The results of individual correlation segments can then be combined through post correlation signal processing techniques. The primary objective of segmentation is to reduce the Doppler search by having shorter coherent integration periods, which also allows processing of larger remaining carrier frequency across individual correlation segments. This is because a given phase error over a shorter integration period allows for a large frequency error, as long as the phase effects are removed by taking the phase amplitude. This carrier frequency error (or the residual carrier) however prevents the receiver from coherent accumulation of segmented correlation results. The differentially coherent combining technique (Schmid and Neubauer, 24) on the other hand is not dependent on the phase of the residual carrier and it can therefore be applied for combining the results of segmented CM correlations while conventionally it combines results of correlations performed over the full code period, such as in the case of C/A code. All of the following post correlation combining techniques are discussed in the context of partial-period CM correlation. Note that a segmented correlation performed in the time domain such as in passive matched filtering architecture can save half of the computations discarded due to zero padding applied in existing FFT-based processing of segmented correlations for L2C acquisition, discussed in Section Differentially Coherent Combining The conventional DC combining scheme as applied for L2C acquisition is shown in Figure 6.2. As shown in the figure, the correlation result of each of the MM segments is multiplied with the complex conjugate of that of its preceding segment and the outcomes are then coherently accumulated to form the decision variable as: 81

97 Chapter 6 Post Processing of Segmented L2C Correlations MM DD DDDD = SS kk SS kk 1 kk=2 (6.1) where SS kk represents the correlation output from the kk tth segment. Each correlation output consists of both the signal (ss) and the noise (ww) components, hence Equation (6.1) can be expressed as: MM = ss kk ss kk 1 kk=2 MM DD DDDD = (ss kk + ww kk )(ss kk 1 + ww kk 1 ) kk=2 MM + ss kk ww kk 1 kk=2 MM + ss kk 1 kk=2 MM ww kk + ww kk ww kk 1 kk=2 (6.2) Residual Carrier Phase As mentioned earlier, in a segmented correlation, the carrier frequency error (caused due to the local oscillator frequency drift or the Doppler Effect) and phase mismatch may change from one correlation segment to the next. In DC combining, since the two consecutive correlation results are to be (complex) multiplied, this change in the residual carrier frequency and phase mismatch becomes an important concern. In order to assess its effect in DC combining, the signal component in Equation (6.2), i.e. ss kk ss kk 1, is sufficient for consideration. The decision variable can thus be given as: MM DD DDDD = 2PP kk PP kk 1 CC kk ( ττ)cc kk 1 ( ττ)dd kk (tt)dd kk 1 (tt)sinc( ff kk TT)Sinc( ff kk 1 TT) kk=2 (6.3) exp{jj[ππ( ff kk ff kk 1 )TT + (φφ kk φφ kk 1 )]} where ττ is the relative code delay between the received and replica code, PP kk and CC kk ( ττ) are the signal power and L2C correlation function for the kk tth correlation segment, and dd kk (tt) = ±1 refers to the corresponding data symbols and eventually the sign of correlation output. Similarly ff kk and φφ kk represent the residual carrier and phase mismatch (between the incoming and local replica carriers) in the kk tth correlation segment, whereas TT stands for the coherent integration period equal to the length of the segment (ll), as already defined. Hence the term ( ff kk ff kk 1 ) refers to the change in the residual carrier frequency from one correlation segment to the next and (φφ kk φφ kk 1 ) represents the 82

98 Chapter 6 Post Processing of Segmented L2C Correlations difference of phase mismatches at the start of each correlation segment. Over the course of CM period (2 milliseconds), it is fair to assume that the frequency error from one segmented correlation to the next, all over the code period, remains relatively constant, that is: ff kk = ff kk 1 = ff (6.4) On the other hand, a phase mismatch at the start of kk tth correlation segment can be given by: φφ kk = φφ kk 1 + 2ππ ff kk 1 TT (6.5) Hence the difference in the corresponding phase mismatches is: φφ kk φφ kk 1 = 2ππ ff kk 1 TT = 2ππ ffff (6.6) Substituting Equation (6.6) and (6.7) into Equation (6.4) gives: DD DDDD = 2PP kk PP kk 1 CC kk ( ττ)cc kk 1 ( ττ)sinc( ff kk TT)Sinc( ff kk 1 TT) MM ee jj2ππ ffff dd kk (tt)dd kk 1 (tt) kk=2 (6.7) Since the CM code boundaries are aligned with CNAV data symbols, for the correct code delay of local replica code, all of the correlation outputs will have the same sign and their post processing will not suffer a data bit transition loss. In other words, for the correct replica code delay, the terms dd kk (tt) and dd kk 1 (tt) in Equation (6.7) will have the same sign. Equation (6.7) can thus be simplified as: DD DDDD = GG kk GG kk 1 ee jj2ππ ffff (MM 1) (6.8) where GG kk and GG kk 1, for a given ff, ττ and TT, are constant terms given by: GG kk = 2PP kk CC kk ( ττ)sinc( ffff) (6.9) GG kk 1 = 2PP kk 1 CC kk 1 ( ττ)sinc( ffff) (6.1) Since for the correct code delay GG kk and GG kk 1 will have approximately the same value, Equation (6.8) can be finally expressed as: 83

99 Chapter 6 Post Processing of Segmented L2C Correlations Span-1 S k-1 GDC Combining ( )* N Σ k=2 S k Span-2 S k-2 ( )* Σ N k=3 Σ D GDC Span-3 S k-n ( )* Σ N k=n+1 Span-(M-1) S k-(m-1) ( )* k={1, 2, 3,., M} Figure 6.3. GDC combining scheme for segmented CM correlation, NN= MM nn 1 DD DDDD = (MM 1)GG 2 (6.11) Equation (6.11) shows that for a stable frequency drift, the differential correlation delivers samples that are all in phase with each other Larger Span Differentially Coherent Combining A span herein refers to the distance (or delay) between correlation segments whose outputs are to be combined. The DC combining scheme discussed above is an example of Span-1. Similarly, Span-2 refers to combining the alternate correlation output samples, i.e. SS kk and SS kk 2. The difference of phase mismatches between two correlation results to be combined in Span-2 can thus be given as: φφ kk φφ kk 2 = 2ππ ff(2tt) (6.12) Following Equation (6.8), the decision variable in this case becomes: DD DDDD = GG kk GG kk 2 ee jj2ππ ff(2tt) ( MM 1) (6.13) 2 84

100 Chapter 6 Post Processing of Segmented L2C Correlations where the function refers to the next higher integer value of a real number argument. For example for nn =3 and MM =2, 2 =7. For a Span-n, Equation (6.13) can be 3 generalized as: DD DDDD = GG kk GG kk nn ee jj2ππ ff(nnnn ) ( MM 1) (6.14) nn Equation (6.14) can be further simplified as: DD DDDD = GG 2 ee jj2ππ ff(nnnn ) ( MM nn 1) = ( MM nn 1)GG2 (6.15) Note that Equation (6.15) remains independent of the residual carrier phase. The final output of different spans can also be combined together to increase the processing gain as discussed in the following section Generalized Differentially Coherent Combining This technique combines the output of all versions of DC combining (i.e. from Span-1 to Span-(MM 1)) coherently (Shanmugam, et al., 27), in order to fully exploit the gain of differential processing, as shown in Figure 6.3. Following Equation (6.15), the decision variable for this case can be given as: MM 1 DD GGGGGG = GG 2 ee jj2ππ ff(nnnn ) ( MM 1) (6.16) nn nn=1 Equation (6.16) shows that the final output is now dependent on the residual carrier phase as the output of individual spans has a different phase and hence a coherent accumulation across all spans, depending on ff and TT, may lead to a processing loss. The equation also indicates that a higher loss might occur as the span-size, i.e. number of spans involved in the combining is increased. Hence this scheme will have a high processing gain only if the residual carrier phase can be accurately estimated Differentially Semi-Coherent Combining The above mentioned phase problem can be resolved if the phase dependence is removed (by applying an absolute operation) prior to final accumulation across all spans, as shown in Figure 6.4. Following Equation (6.16) the decision variable for this scheme can thus be given as: 85

101 Chapter 6 Post Processing of Segmented L2C Correlations Span-1 S k-1 ( )* DSC Combining N Σ k=2 Span-2 N Σ k=3 S k S k-2 ( )* Σ D DSC Span-3 S k-n ( )* N Σ k=n Span-(M-1) S k-(m-1) ( )* k={1, 2, 3,., M} Figure 6.4. DSC combining scheme for segmented CM correlation, phase dependence has been removed by applying absolute operation prior to final summation across all spans, NN= MM nn 1 MM 1 DD DDDDDD = GG 2 ee jj2ππ ff(nnnn ) ( MM 1) nn nn=1 MM 1 DD DDDDDD = GG 2 ( MM 1) nn nn=1 (6.17) (6.18) Equation (6.18) shows that the final output in DSC combining is not dependent on the residual carrier phase. Removing the phase dependence however causes some of the noise averaging benefit to be lost as compared to the GDC combining technique (in the absence of frequency error). Hence this technique can also be seen as a hybrid or semi-coherent approach in which the individual correlation results in each span are combined coherently, whereas the outcome of various spans is collected in a non-coherent fashion, as shown in Figure Computational Complexity The computational load due to extra sum and multiplication operations carried out in all of the differential combining techniques is negligible when compared to the actual 86

102 Chapter 6 Post Processing of Segmented L2C Correlations Strategy Multiplications Sums Coherent (full CM period) NN NN NN NN DC {NN NN} + MM nn 1 {NN NN} + MM 1 nn GDC DSC KK {NN NN} + MM 1 nn nn=1 KK {NN NN} + MM 1 nn nn=1 KK {NN NN} + MM 1 nn nn=1 KK {NN NN} + MM 1 nn Table 6.1. Computational complexity comparison of all considered differential combining schemes with full period coherent correlation.{ }: original correlation load( ): Extra computations nn=1 Strategy Multiplications Sums Coherent (full CM period) DC (19) (19) GDC (6) (6) DSC (6) (6) Table 6.2. Computational complexity comparison of all considered differential.combining schemes with full period coherent integration for the example of..ff ss =5.714MHz, TT=1ms, MM=2 and KK=19, ( ): Extra computations correlation load. Table 6.1 compares the computational complexity for NN samples in the full CM periods where MM and nn, as already defined, identify the number of correlation results to be combined and the span or distance of combination, while KK represents the span size. Considering a sampling rate of MHz (used in Zarlink GP215), TT=1 millisecond, MM=2 and span-size KK = MM 1, as an example, the additional number of add and multiply operations are given in Table 6.2, which shows that the number of additional computations in the differential combining techniques can be neglected. 6.3 Performance Analysis The acquisition performance of the considered differential combining techniques for partial-period CM correlations is compared with that of the non-coherent and coherent acquisition strategies in terms of detection probability and mean acquisition time. For the non-coherent and coherent cases, the simulation results matched the corresponding theory, discussed in Section 4.4, as shown in Figure

103 Chapter 6 Post Processing of Segmented L2C Correlations 1 Detection probability NC (T=1, M=2) Coherent (T=2, M=1) C/No (db-hz) Figure 6.5. Detection performance of non-coherent post processing technique ff=, PP ffff = 1 3, -- Theory, * Monte Carlo simulations Also, for the DC and GDC schemes, simulation results are in good agreement with the theoretical analysis of probability of false alarm and probability of detection provided in the appendix A. For the DSC combining, the results are based on Monte Carlo simulations. For all experiments conducted in this work, correct code delay bin is considered and the RZ CM design is selected for generating the local replica code Best Case A perfect estimate of the received carrier frequency (i.e. ff=) is first assumed to evaluate the relative detection performance of various post correlation processing techniques. Considering PP ffff =1-3, TT=1 and MM=2, the detection performance of NC, DC, GDC and DSC techniques is presented in Figure 6.6. These results show that the coherent integration technique, as expected, has the best performance. Among the others, all of the post correlation differential combining techniques (i.e. DC, GDC, and DSC) perform better than the non-coherent combining. The DC technique based on Span-1 provides the least improvement of 1 db with respect to the non-coherent combining. If all the spans are considered, the performance of GDC combining approaches that of the full period coherent integration. 88

104 Chapter 6 Post Processing of Segmented L2C Correlations Detection probability NC DC DSC(1) DCSC(5) DSC(1) DSC(19) GDC Coh.(CM period) C/No (db-hz) Figure 6.6. Detection performance of considered post correlation processing techniques for the best case ( ff=), TT=1ms, MM=2, PP ffff = 1 3 Combining Strategy PP ffff = 1 3, PP dd = 9%, TT = 1mmmm, MM = 2 Min. detectable C/No (db-hz) Relative PP dd Gain (db) DSC DC NC Table 6.3. Performance improvement in DSC combining over the..conventional DC and NC combining techniques This performance is however only guaranteed when the residual carrier frequency is accurately known (i.e. the best case as considered here). The performance of DSC combining (grouped together in the figure) can be seen as dependent on the span size (i.e. number of spans involved) such that as the span size increases, the detection capability also improves. However, the relative performance improvement decreases as the span size is increased because the gain offered by higher spans (due to fewer samples to be combined) is relatively smaller. For the largest span- size (i.e. 19 in this case), the DSC offers an advantage of more than 1 db over the considered DC combining and more than 2 db over the non-coherent combining technique as given in Table 6.3. Note that for the GDC and DSC combining techniques, the default span-size considered is (MM 1). For any other span-size, the notation adopted for these two techniques is GDC (span-size) and DSC (span-size). 89

105 Chapter 6 Post Processing of Segmented L2C Correlations Detection probability NC DC DSC(1) DSC (5) DSC (1) DSC (19) GDC Coh. (CM period) C/No (db-hz) Figure 6.7. Detection performance of considered post correlation processing techniques for the worst case ( ff = 1 4TT), TT=1ms, MM=2, PP ffff = 1 3, due to phase dependence GDC has the worst performance Worst Case In order to assess the effect of residual carrier on various differential combining techniques, a residual carrier of (1 2TT)/2=25 Hz, where (1 2TT) refers to a typical Doppler search step (Tsui, 2), was introduced in the simulations. Figure 6.7 provides the detection performance comparison for this case. It can be observed from the figure that except for GDC combining technique, all other schemes suffer a performance degradation of 1 db when compared to the best case, as expected for the considered value of frequency error. Note that the coherent integration curve is based on an equivalent 12.5 Hz residual carrier due to TT=2 milliseconds in that case. Due to phase dependence in GDC combining, its performance is far worse than any other technique. The relative improvements of DC combining and the DSC technique (with different span-sizes) however remain the same as in the best case. Hence the detection performance of DSC combining technique remains 2 db better than the NC combining and 1 db better than the DC combining technique, as occurred in the best case Receiver Operating Characteristics A Receiver Operating Characteristic (ROC) curve plots the behaviors of the PP ffff and PP dd of a binary classifier system as its discrimination threshold is varied. 9

106 Chapter 6 Post Processing of Segmented L2C Correlations Span-Size.8.7 Probability of detection Probability of false alarm (a).8.7 Probability of detection Probability of false alarm (b) Figure 6.8. Receiver operating characteristic (ROC) curves for the worst case as function of the span-size, (a) GDC technique suffering from the phase loss (b) DSC combining technique with a consistent improvement; CC NN =3 db-hz, TT=1ms, MM=2 The curve is qualified to consolidate theoretical analysis by Monte Carlo simulations as well as to make performance comparisons among different acquisition strategies. To study the effect of frequency error on the detection performance of the GDC and DSC combining techniques in more detail, simulations were performed to obtain ROC curves for the two techniques. Figure 6.8a shows the ROC curves of GDC combining with different span-sizes for the worst case, i.e. when the residual carrier is 25 Hz, as mentioned earlier. It can be observed from these results that the span-size does not show a correlation with the detection performance. 91

107 Chapter 6 Post Processing of Segmented L2C Correlations Although the exact behavior will depend on the carrier phase difference determined by ff and TT as given by Equation (6.16), it can be inferred from these results that overall, the detection performance gets worse as the span size is increased. On the other hand, for the DSC combining technique, since the phase dependence is removed prior to final accumulation, a consistent improvement in detection performance is achieved as the span size increases. Due to a reliable detection performance in the worst case, the DSC technique can also be seen as a realistically implementable version of the GDC technique which by contrast always requires the exact information about the residual carrier Coherent Integration Period For the analysis of DSC combining technique presented so far, a coherent integration period (TT) of 1 millisecond with 2 correlation segments (MM) has been considered. In order to observe the effect of coherent integration period and thus of having fewer correlation segments, on the performance of DSC technique, several combinations of TT and MM were trialed and corresponding detection probabilities and mean acquisition times were computed through simulations. Figure 6.9a compares the detection performance of selected TT & MM combinations indicating that despite the number of correlation segments being reduced, an increased coherent integration period improves the detection performance. On the other hand, a larger coherent integration period will affect the mean acquisition time as depicted in Figure 6.9b for a Doppler search range of ±5 khz with search steps of 1 2TT and.5 chip in the Doppler and code delay dimensions, respectively. Table 6.4 compares the overall performance of considered TT & MM combinations including the TT=1 and MM=2 case which reflects the full period CM correlation. Considering the 9% detection probability (for a sufficient detection confidence), Table 6.4 presents the minimum CC NN detected in each case and the mean acquisition time required to detect that CC NN. In other words, for a fair assessment, the mean acquisition times of different TT & MM combinations are compared against the same detection probability, i.e. 9%. These results show that the DSC combining technique can achieve significant savings in the mean acquisition time at the cost of some loss in the detection probability. 92

108 Chapter 6 Post Processing of Segmented L2C Correlations Detection probability T=.5ms, M=4 T=1ms, M=2 T=2ms, M=1 T=5ms, M=4 T=1ms, M=2 Coh.(2ms) C/No (dbhz) (a) Mean acquisition time (s) T=.5ms, M=4 T=1ms,M=2 T=2ms, M=1 T=5ms, M=4 T=1ms, M=2 T=2ms, M= C/N (db-hz) (b) Figure 6.9. Performance comparison of the DSC combining technique with various combinations of TT& MM, (a) Probability of detection, (b) Mean acquisition time, ff=, PP ffff = 1 3 TT MM PP ffff = 1 3, PP dd = 9% Min. detectable C/No TT (db-hz) ( 1 3 ) s PP dd loss (db) TT Saving (%) Table 6.4. Performance comparison of DSC combining technique for various..combinations of TT & MM with the 2ms coherent integration 93

109 Chapter 6 Post Processing of Segmented L2C Correlations For example considering the case of TT=1 and MM=2, acquisition time can be reduced by 94.22% with a 1.41 db loss in the acquisition sensitivity, compared to full-code CM correlation. 6.4 CL Code Acquisition Direct acquisition of CL code over the full period is not recommended, as it creates a huge search space and requires a highly precise local oscillator to trial closely spaced Doppler bins due to its long code period (Dempster, 26). However, a partial-period correlation strategy can make the CL code search more feasible. It is obvious that for coherent integration periods shorter than 2 milliseconds CM is a better choice for L2C signal acquisition. This means that for CL code acquisition the coherent integration period must be at least 2 milliseconds. However, for any coherent integration period the entire CL code (1.5 seconds) must be scanned to find the correct code delay. One way to utilize this entire search interval is to perform segmented correlations and then combine their results using, for example, the DSC combining technique. However, for such a long observation period, the assumption of constant residual carrier in different correlation segments to be combined, particularly for larger spans, will not be valid. Consequently, the phase mismatch from one correlation segment to another one will be different. However, an a priori estimate of the rate of change of Doppler (i.e. a carrier phase acceleration) can be included in the computation of local Doppler estimate (Psiaki, 24). Such aiding by an a priori phase acceleration estimate will thus allow the use of the DSC combining technique for longer observation intervals. In order to evaluate the performance of this strategy, a coherent integration period of 2 milliseconds (the minimum value recommended for CL acquisition) was considered and different number of correlation segments (MM) were trialed. Figure 6.1 shows the detection performance of DSC combining for different number of correlation segments. Table 6.5 gives the corresponding minimum CC NN detected for each combination. For each of the DSC performance curves a coherent integration period (TT CCCC ) was determined which provided the same level of detection performance using straight correlation. 94

110 Chapter 6 Post Processing of Segmented L2C Correlations Detection probability dB T M=5, T CL =6 CL =15 M=1, T CL =15 M=75, T M=2, T CL =28 CL =9 M=3, T M=5, T CL =8 CL =38 M=2, T CL = C/N (db-hz) Figure 6.1. Detection performance comparison of DSC combining for: segmented (TT=2ms) CL correlations (*) and straight coherent (TT CCCC ms) correlation(-) MM PP ffff = 1 3, PP dd = 9%, TT = 2mmmm Min. detectable CC NN (db-hz) Table 6.5. Detection performance of DSC combining for segmented CL acquisition For example considering the DSC performance curve for MM=5, a coherent integration period of 6 milliseconds (TT CCCC =6) was required to match this performance. Also, the case of MM=75 where the 1.5 seconds interval is fully utilized, has a performance only 2 db worse than the full CL period correlation. On the other hand, DSC will offer huge saving in the mean acquisition time due to segmentation. This analysis suggests that DSC combining is a significantly effective approach for CL code acquisition as compared to straight coherent correlation. 6.5 Overall Recommendations A typical search strategy adopted in GPS receivers is to start with a coherent integration 95

111 Chapter 6 Post Processing of Segmented L2C Correlations 1 Detection probability M=2 M=5 M=2 M= C/N (db-hz) Figure Detection probability of non-coherent CM combining, TT=2ms, ff= period equal to the PRN code period, and then gradually increase it by integer number of code periods until the length of data bit is reached, and then switch over to non-coherent integrations. The above analysis shows that for signal observation period of up to 2 milliseconds, segmented CM correlations with DSC combining is the best approach. For the CL code acquisition, DSC combining is shown to be a better approach than the straight coherent correlations. However, for signal observation periods greater than 2 millisecond but less than 1.5 seconds, non-coherent integrations of CM code must be considered, as the DSC cannot be directly applied for CM acquisition over these observation intervals due to data modulation. Figure 6.11 shows the detection performance of non-coherent CM integration for TT=2ms different values of MM corresponding to different signal observation periods between 2 millisecond and 1.5 seconds. Table 6.6 shows the minimum detectable CC NN and the corresponding segment size for different techniques, identified in the analysis. In this table, a difference of 2 to 3 db in the detectable CC NN is considered for switching over from one set of parameters to the next. This identifies a sequence of search to be followed in terms of the acquisition parameters and corresponding combining strategy as the desired signal gets weaker. For example, a receiver should start the signal search with TT=1 and MM=2 using DSC technique and, if a desired signal is not detected, it should switch over to the next set of 96

112 Chapter 6 Post Processing of Segmented L2C Correlations PP ffff = 1 3, PP dd = 9% Min. detectable C/No (db-hz) TT MM Code Strategy CM DSC CM DSC CM NC CM NC CM NC CL DSC CL DSC CL DSC Table 6.6. Overall recommendations for L2C search through post processing of...segmented correlations parameters given in Table 6.6, and so forth. It can be observed that DSC combining remains a dominant strategy for the considered CC NN range. 6.6 Summary Post processing of segmented correlation responses, for reducing the L2C acquisition load in the Doppler dimension, is discussed. Acquisition performance of various differential combining schemes for segmented CM correlations is evaluated. A differentially semi-coherent post processing technique is suggested to combine the results of segmented correlations. The DSC combining technique is shown to outperform the conventional differentially coherent and non-coherent combining techniques by 1dB and 2dB respectively. The detection performance of the DSC combining technique is found to be comparable with the full-period correlation for both CM and CL acquisition, with a significant saving in the mean acquisition time. It is demonstrated that for CL code acquisition, the DSC combining offers a more efficient solution than straight coherent correlation. A theoretical analysis (verified through simulations) of probability of false alarm and probability of detection for the conventional DC and GDC combining techniques is provided in the appendix A. 97

113 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals 7.1 Introduction The main purpose of having longer spreading codes in the L2C signal was to achieve extra protection against the strong cross-correlation in the event of Near-Far problem. The other inherent advantages of longer codes are more diffuse line spectrum and the reduced vulnerability to CW interference. This additional protection was desired because the legacy C/A code could not offer more than db of cross-correlation protection. The L2 CM and CL codes extend this figure to db and db respectively, in the worst case (Tran, 24). To achieve this cross-correlation performance, however, requires the coherent signal observation period to be 2 milliseconds (for CM code) and 1.5 seconds (for CL code) as opposed to 1 millisecond for the C/A code. This translates to increased acquisition effort, which naturally leads to the consideration of 2 C/A epochs as an alternative to the CM code and 15 C/A epochs to replace the CL code. The thought becomes more relevant in the context of dual frequency GPS L1/L2C receivers where all the three (C/A, CM and CL) codes are available to combat the Near-Far problem. This chapter provides a cross-correlation performance comparison of the L2C codes with the C/A code in order to recognize the appropriate code choice to overcome the near-far problem in dual frequency GPS L1/L2C receivers, specifically in the coldstart and assisted-start modes. In the case of multiple code epochs, the relative carrier Doppler offset between the local and interfering satellite signals has a significant role as it modulates the periodic product of the local and interfering satellite codes. As a result, some of the cross-correlation noise is averaged out when an accumulation across a coherent integration period several times the fundamental code period is performed. Consequently, the cross-correlation performance of multiple epochs of a shorter code (C/A code in this case) becomes better than an equivalent single code period (a CM code period here). 98

114 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Relative cross-correlation power (db) C/A CM CL Unique satellite pair combinations for 32 PRN codes Figure 7.1. Worst cross-correlations in C/A, CM and CL codes for all individual codes pair The contents of the chapter are organized as follows. The cross-correlation performance metric is first discussed. It is followed by the study of effects of sampling and observation interval on the cross-correlation performance. The impact of relative Doppler offset on periodic cross-correlations is then evaluated. Acquisition strategies based on the relative strengths of the C/A and CM codes identified in the analysis are recommended. The concerns of navigation data transitions and non-coherent integration are also addressed. Finally, the key findings of this work are summarized. 7.2 Performance Metric Worst Cross-Correlation A single worst cross-correlation value is often used to represent the cross-correlation protection (or performance) of a code-group (such as C/A and CM). This worst crosscorrelation is found by trialing all relative code delays for each possible pair of codes in the code-group. Figure 7.1 shows the worst cross-correlation for all codes pair in C/A, CM and CL codes considering the group of 32 PRN codes published for GPS constellation (IS GPS 2 Revision D, 24), for each case. Here, the vertical axis of the figure gives the cross-correlation protection, measured with reference to the autocorrelation (AC) peak. The overall worst cross-correlation for each code (quoted in the introduction) can thus be found by selecting the highest value across all combinations, 99

115 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Cumulative probability C/A CM CL Cross-correlation protection (db) Figure 7.2. Cross-correlation performance comparison of C/A, CM and CL chip sequences over the corresponding full code periods as shown in Figure 7.1. The C/A code is a special case here as it belongs to the Gold Code family having controlled values of cross-correlation and therefore it has a flat response to all satellite combinations. On the other hand, CM and CL codes are generated by having a different initial state of the same feedback shift register and then short cycling it back to the initial state after a desired code length has been achieved. Figure 7.1 shows that for the CM code, individual worst cross-correlation values vary as much as about 4.5 db and therefore a mean value of approximately 28 db is also quoted as the cross-correlation protection figure for the CM code such as given in (Fontana, et al., 21). For the CL code having a longer period, the variation of individual worst crosscorrelations is limited to about 2 db and a mean value of 45 db in this case is also used to represent the cross-correlation protection figure of the CL code, as given in Fontana, et al. (21) Cumulative Probability The Near-Far problem in fact is characterized by not just a single cross-correlation value but rather a range of cross-correlations close to this maximum (worst) value that pose a threat to signal acquisition. A cumulative probability distribution of the cross-correlation values can provide a more comprehensive measure of the cross-correlation performance. 1

116 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals 1 Cumulative probability Without sampling With synchronous sampling With asynchronous sampling Cross-correlation protection (db) Figure 7.3. Cross-correlation performance comparison of original C/A chip sequence with synchronous (5 samples per chip) and asynchronous ( samples per chip) sampling Figure 7.2 compares the cross-correlation performance of the C/A, CM and CL codes as measured by the cumulative probability. The figure plots the cross-correlation result of PRN-1 and PRN-7 chip sequences in each case. The horizontal axis of the figure indicates the cross-correlation protection as measured with reference to the AC peak. Of interest here is the top region of these curves, i.e. say above 9% probability, which represents the range of highest cross-correlations for each case. In other words, it is this region where the cross-correlations start to become a problem. A curve towards the left indicates better cross-correlation performance. In fact, the highest point of these curves represents the worst cross-correlation value for the corresponding codes pair. This assessment approach is also used in (Parkinson and Spilker, 1996) and (Fontana, et al., 21). It is obvious from Figure 7.2 that the CL code has the best cross-correlation performance followed by the CM and C/A codes respectively. A similar relative cross-correlation performance will be observed for any other pair of PRN codes (Dempster, 26). The above discussion of cross-correlation performance assumed unsampled original chip sequences. However, the cross-correlation noise appearing in a receiver is based on the observation of sampled codes modulated by an offset carrier. Hence it is worth addressing the sampling rate, observation period and relative Doppler offset (essentially an offset carrier) here. 11

117 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Sampled Code Sequences The C/A code has controlled cross-correlations and thus was selected to study the effects of sampling on the cross-correlation performance. Figure 7.3 compares the crosscorrelation performance of C/A code with synchronous and asynchronous sampling with that of the unsampled case using the pair of PRN-1 and PRN-7 codes. For the synchronous case where the sampling frequency is an integer multiple of the code chipping rate (containing exactly 5 samples per chip in this case), the worst crosscorrelation is the same, i.e db, as in the unsampled case while the rest of the curve becomes smoother. This is because the individual cross-correlation results here are interpolating between the values in the unsampled case. Similarly the asynchronous sampling where different code chips can have different number of samples (5 or 6 in this case as the sampling rate is MHz), causes even smoother curves to be observed when compared to a synchronously sampled C/A code for the same order of sampling rates. Although the worst cross-correlation in the asynchronous case is slightly higher than those in the synchronous and unsampled cases, the overall performance of synchronous and asynchronous sampling, in the region of interest, remains the same. Also, a performance curve will get smoother as the sampling frequency is increased. The same smoothing effect will be observed for the sampled L2 CM and CL codes Code Observation Period The average cross-correlation performance is directly proportional to the length of code and often the fundamental code period is selected for the cross-correlation performance assessment. The cross-correlation performances of C/A, CM and CL codes discussed above are all based on their respective code periods. The relative performance improvement of L2C codes, shown in Figure 7.2, is entirely due to extended code periods along with the implied increased observation intervals. An observation interval refers to the time period over which the two codes are correlated for a given relative code delay. Hence for a fair comparison, the codes must be observed over the same period. This means, for example, in a comparison with the CM code, the C/A code should be observed over 2 code epochs. 12

118 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Desired Satellite Doppler search range Δf 1,i Δf 2,i Δf 3,i f D,2 f D,3 f D,1 f D,i f D,1, f D,2, f D,3 :Absolute carrier Doppler of interfering satellites f D,i : Locally trialed carrier Doppler Δf 1,i, Δf 2,i, Δf 3,i : Relative Doppler offset Figure 7.4. Graphical illustration of the relative Doppler offset concept: Difference in Doppler frequencies of the local and interfering satellite signals Interestingly, the cross-correlation performance of 2 C/A epochs will remain the same as that for 1 epoch unless the relative carrier Doppler offset, experienced in the receiver, is considered. Thus the cross-correlation protection figures based on only code sequences do not reflect realistic values. For example when a full Doppler range (typically equal to ±5 khz for a static receiver) is considered, the average worst cross-correlation of C/A code drops to 21.6 db (Parkinson and Spilker, 1996). 7.3 Effect of Relative Doppler Offset In signal acquisition, the receiver trials a certain range (or band) of carrier Doppler frequencies to match the Doppler of the desired satellite signal. Each Doppler trial, at the same time, creates an offset with the Doppler of all of the in-view interfering (unwanted) satellites, termed here a relative Doppler offset (see Figure 7.4). As already mentioned, this relative Doppler offset is essentially an offset carrier that modulates the product of the local and interfering codes and can have a strong impact on the cross-correlation performance over multiple code epochs. Considering multiple in-view satellites, the received signal at the IF stage can be modeled as: 13

119 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals T I j,i IF signal Carrier Generator 9 o f D,i Code Generator τ i T ( ) 2 ( ) 2 Q j,i D s H < ν > H 1 Figure 7.5. Reference correlation system considered for the cross-correlation analysis rr(tt) = 2PP kk dd kk (tt)cc kk (tt ττ kk ) cos 2ππ ff IIII + ff DD,kk tt + φφ kk NN 1 + 2PP jj dd jj (tt)cc jj tt jj =1 jj kk ττ jj ) cos 2ππ ff IIII + ff DD,jj tt + φφ jj (7.1) where the subscript jj identifies the interfering satellite (i.e. causing the crosscorrelation) and NN represents the number of in-view satellites and all other parameters have already been defined in Section and Section 4.2. The second term in Equation (7.1) is responsible for introducing the cross-correlation noise in the receiver. With reference to the correlation system shown in Figure 7.5, the above received satellite signal is mixed with the replicas of code and carrier and the cross-correlation noise appearing at the II and QQ channels, can be respectively given as: TT NN 1 II jj,ii = 2PP jj dd jj (tt)cc jj tt ττ jj cos 2ππ ff IIII + ff DD,jj tt + φφ jj jj =1 jj kk cc ii (tt ττ ii ) cos 2ππ ff IIII + ff DD,ii tt + φφ ii dddd (7.2) TT NN 1 QQ jj,ii = 2PP jj dd jj (tt)cc jj tt ττ jj cos 2ππ ff IIII + ff DD,jj tt + φφ jj jj =1 jj kk cc ii (tt ττ ii ) sin 2ππ ff IIII + ff DD,ii tt + φφ ii dddd (7.3) Equations (7.2) and (7.3) can be combined as: 14

120 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Δf j,i =5 Hz Δf j,i =1 Hz 1ms 2 milliseconds Identical products of local and interfering codes Figure 7.6. Offset carriers of 5 Hz and 1 Hz respectively taking exactly opposite and the same phase across 1ms intervals of the product of the local and the interfering spreading codes TT NN 1 II jj,ii + jjjj jj,ii = 1 TT 2PP jj dd jj (tt)cc jj tt ττ jj cc ii (tt jj =1 jj kk ττ ii )ee jj 2ππ ff jj,iitt+ φφ jj,ii dddd (7.4) where ff jj,ii represents the relative Doppler offset between the local and interfering satellite signals described above and φφ jj,ii denotes the difference in phases of the local and interfering carrier signals. Equation (7.4) shows that the Doppler offset carrier, ff jj,ii, modulates the product of the local and interfering codes cc jj tt ττ jj cc ii (tt ττ ii ) in the correlation process Multiple Code Epochs In the case of a signal being observed over multiple code periods, the code product cc jj tt ττ jj cc ii (tt ττ ii ) becomes periodic with respect to the fundamental code period, TT pp, (1 millisecond in the case of the C/A code). The offset carrier takes a certain phase across adjacent periods of the code product. For relative Doppler offsets equal to mm khz where mm is an integer, the offset carrier will have integer number of cycles in each period of the codes product and consequently, the offset carrier will take the same phase across each period of the codes product. Considering the case of 2 C/A code epochs, the offset carrier of 1 khz (having exactly 1 cycle per 1 millisecond of the underlying codes product) is shown in Figure 7.6. In this case, the modulation from one 1 millisecond interval to the next remains relatively constant, and hence the accumulation across 1 15

121 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Cross-correlation protection (db) C/A CM Relative Doppler offset (KHz) (a) Cross-corelation protection (db) Hz C/A CM 97Hz Relative Doppler offset (Hz) (b) Figure 7.7. Cross-correlation behavior of C/A and CM codes both observed over 2ms, in response to relative Doppler offset. (a) Over a relative Doppler offset range of ±5KHz (b) Over the relative Doppler offset range of to 1 Hz millisecond dumps does not provide any averaging benefit. As a result, for these relative Doppler offsets, the cross-correlation performance of multiple C/A periods is the same as that of the fundamental code period. These relative Doppler offsets of mm khz are herein termed critical Doppler offsets (CDO). On the other hand, for non-critical relative Doppler offsets, the offset carrier will take a different phase across different 1 millisecond intervals as illustrated shown in Figure 7.6 for the offset carrier of 5 Hz. In this example, the offset carrier has an exactly opposite phase across adjacent 1 millisecond intervals of the underlying codes product. In this 16

122 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals case, the dump from one 1 millisecond interval to the next will have an opposite sign and consequently an accumulation across 2 dumps will lead to cancellation of virtually the entire cross-correlation. For all other values of relative Doppler offsets between the two extreme cases of 1 khz and 5 Hz discussed above, the cross-correlation will have a relative behavior. To study this effect of relative Doppler offset in more detail, a simulation was conducted where the worst cross-correlation envelope ( II jj,ii + jjjj jj,ii ) of C/A code, when observed over 2 epochs, and the CM code was monitored over a relative Doppler offset range of ±5 khz, while the PRN-1 and PRN-7 codes used for the test were sampled at 5MHz (a synchronous sampling to remove any effects other than the Doppler on the cross correlation performance). Figure 7.7a shows the results of this test, indicating that the worst C/A cross-correlation oscillates between approximately 22 db and 48 db from one critical Doppler offset to the next. This cross-correlation behavior is consistent with the above explanation of phase correlation across 1 millisecond intervals. Figure 7.7 b provides a closer view of these results over one cycle of cross-correlation behavior, i.e. the relative Doppler offsets from to 1 Hz. The figure indicates that the worst C/A cross-correlation basically follows a periodic Sinc function that has its maximum located at the critical Doppler offsets (mm khz) and nulls occurring at every 1 TT=5Hz, where TT is the coherent observation period equal to 2 milliseconds here. For a given TT pp and TT, this cross-correlation behavior can thus be expressed as a function of relative Doppler offset as: C ff jj,ii = SSSSSSSS mm TT pp + ff jj,ii TT (7.5) On the other hand, the theoretical expression for cross-correlation at the correlator output is obtained by solving Equation (7.4) as (Balaei and Akos, 29) (see appendix B for derivation): NN 1 II jj,ii + jjjj jj,ii = 1 TT 2PP jj jj =1 jj kk + ee jj φφ jj,iirr pp jj,ii SSSSSSSS pp TT pp + ff jj,ii TT ll= (7.6) where ll is an integer while RR pp jj,ii is given as: 17

123 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals + RR pp jj,ii = CC ll CC pp ll ee ll= jj2ππ ll TT pp ( ττ) (7.7) where CC ll and CC pp ll respectively represent the Fourier coefficients of the interfering and local replica codes when represented by Fourier series (given in the appendix B). It can be noticed that, as far as the overall cross-correlation behavior is concerned, Equation (7.5) based on the observation of simulation results, and the theory given by Equation (7.6) are in good agreement. The CM code on the other hand has a consistent cross-correlation behavior along the entire test range of relative Doppler offsets as shown in Figure 7.7. This is because it is observed over the single code period and hence the periodic cross-correlations phenomenon does not occur. Although these results consider worst cross-correlation obtained by trialing all relative code delays for each relative Doppler offset, the same relative performance will be observed for any given relative code delay. Hence in the context of cross-correlation behavior in response to relative Doppler offset, the relative code delay is not imperative Critical Doppler Window An interesting point about the results shown in Figure 7.7 is that the C/A code provides better cross-correlation protection than the CM code except for certain segments of the relative Doppler offset range. Simulation results show that this critical range of relative Doppler offsets (called here a critical Doppler window CDW) remains less than 1 Hz about the CDOs. This critical Doppler window will have a specific significance in the signal search space of a dual frequency GPS L1/L2C receiver as discussed in the following section. 7.4 Signal Search Space In the context of the Near-Far problem, locally trialed Doppler frequency and the associated relative Doppler offset are the two key signal search parameters. For each Doppler frequency trial, the receiver comes across a cross-correlation peak based on the associated relative Doppler offset. As long as a desired satellite signal is strong and the detection threshold is well above the cross-correlation peak, it does not cause any harm to 18

124 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Normalized correlation value C/A AC CM AC C/A CC.2 CM CC Doppler search range (Hz) Relative Doppler offset (Hz) Figure 7.8. Simulation results showing the status of signal search space in dual frequency GPS L1/L2C receiver in the absence of Near-Far problem. Desired L1 (CA) and L2 (CM) peaks are well above the corresponding CC peaks the signal acquisition. However, when the desired signal is weak and thus the detection threshold is set low, a cross-correlation peak exceeding the detection threshold might mislead the receiver to a false acquisition. Figure 7.8 shows the status of the search space in a dual frequency GPS L1/L2C receiver for a simulation test scenario where the Doppler of desired L1 signal is set to -15 Hz, and hence the Doppler on L2 can be found as -15 (L2/L1) Hz, whereas the Doppler of the interfering satellite is 8 Hz and a Doppler search range of 5 Hz starting from -28 Hz to 22 Hz is selected. Figure 7.8 shows the locations of the desired L1 and L2 autocorrelation peaks (denoted here as AC) as well as those of the associated worst cross-correlation (CC) threats. Different slopes of the AC functions meeting at the zero local Doppler are in accordance with the relationship between the L1 and L2 frequencies. It can be seen that in this case of strong desired signals, the desired acquisition peaks can be easily distinguished from those of the cross-correlation. Note that for the purpose of cross-correlation performance measurement (in the test scenario), the correlation values of both the desired and the interfering satellites for the L1 signal are independent of those of the L2C signal and the 1.5 db relative power difference between the L1 and L2C signals is therefore not considered here. The simulations consider correlation of PRN-1 and PRN-7 codes sampled at MHz. 19

125 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Normalized correlation value C/A AC CM AC C/A CC CM CC.5 Narrow search range Doppler search range (Hz) Relative Doppler offset (Hz) Figure 7.9. Simulation results showing the status of search space in GPS L1/L2C receivers in the event of Near-Far problem. Desired L1 (CA) and L2 (CM) have a similar level as the corresponding CC peaks. Narrow search range illustrates the expected scenarios in assisted acquisition Figure 7.9 shows the result of another test where the levels of desired signal peaks are similar to those of the cross-correlation interference while everything else remains the same as in the previous scenario described above. Hence in this case the crosscorrelations are likely to cause a false acquisition. This result indicates that an L1 signal search will always experience a critical Doppler window over any Doppler search range of larger than 9 Hz. As discussed above, in this window the L1 cross-correlation level is higher than that of the CM code. Hence if a Doppler search range is larger than 9 Hz, such as in the receiver cold-start, the CM is a better code to deal with the Near-Far problem in a dual frequency GPS L1/L2C receiver. However, for Doppler search ranges smaller than 9 Hz, such as in a receiver warm-start, assisted (A) GPS and re-acquisition scenarios, C/A can be a more effective code to combat cross-correlation interference due to its periodicity in the coherent signal observation interval, in dual frequency GPS L1/L2C receivers, provided the search range does not experience a critical Doppler window. This is because in such scenarios, the receiver has a priori knowledge of the satellite locations through a previous known position, a valid Almanac or an assistance provided by a remote A-GPS server. Compared to the full search range, as illustrated in Figure 7.8, a narrower (less than 9 Hz) Doppler search range is much less likely to experience the critical Doppler window. 11

126 Chapter 7 Cross-Correlation Protection in L1 & L2C Signals Figure 7.1. Test sites selected for computation of relative Doppler offset distribution Location X Y Z Sydney Paris Singapore Brasilia Toronto Table 7.1. ECEF coordinates of test sites ttttttttttttttttttt This finding is quite important because the Near-Far problem occurs mostly in restricted view (e.g. indoor) applications, where A-GPS will be used. In other words, although L2C has a global cross-correlation advantage, L1 C/A is superior in the cases where crosscorrelation is most likely to be a problem Likelihood of Critical Doppler Window In order to estimate the likelihood of a dual frequency GPS L1/L2C receiver experiencing a critical Doppler window when searching over a Doppler range of 9Hz, the following experiments were conducted. Five test locations, evenly dispersed across the globe, were selected for experiments, as shown in Figure 7.1. Table 7.1 gives the locations of test sites in ECEF coordinates. For each test location, the Doppler of all visible satellites above 1 degrees elevation was recorded every 1 minutes over the course of 24 hours, using the almanac data. For each visible satellite, for a search range of 9 Hz (stepping at 2 3TT=33.33 Hz), starting from the correct Doppler, the relative Doppler offset with all other visible satellites was computed. 111