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ION Southern California Section Meeting Software GPS Receivers: Some Recent Developments & Trends Chun Yang Sigtem Technology, Inc. San Mateo, CA (650) 312-1132 chunyang@sigtem.com June 25, 2008 1 Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis • Standardization 2 Software GPS Receivers: Definitions • Typical Architecture of GPS Receivers in Use Today RF IC Baseband IC/Microprocessor Application Platform ANT Down- Processor ADC Correlators Signal Data Processor LNA Converters (BPF, AMP, Processor - Demodulation Application - Positioning I/O I/O Mixers) Code/Carrier - Acquisition Software Generators - Tracking - Interface Power Supply RAM ROM ~GHz ~MHz ~kHz ~Hz 3 Software GPS Receivers: Definitions • Software GPS Receivers: from IF samples to position fix, all implemented in software on a general purpose computer RF IC General Purpose Processor Application Platform ANT Down- Processor Processor ADC DMA LNA Converters (BPF, AMP, Software for Software for I/O I/O Application I/O Mixers) - Acquisition - Code/Carrier Software - Tracking Power Generation - Demodulation Supply - Correlation - Positioning RAM ROM ~GHz RAM ROM ~Hz Several As close to RF Hundreds Total signal bandwidth as possible ~ Tens MHz Several RF channels, e.g., L1, L2, L5 4 Software GPS Receivers: Definitions Tools for Algorithms Evaluation Historical Hardware Receiver Simulator Development Post-Processing of Recorded IF Samples of Software Real-Time Research/Commercial Receivers Receivers Software-Configured Hardware Correlator Software Defined - Configurable Code Generators & NCOs Radio - Sequential Repeated at Very High Speed (>> fs) (SDR) Software-Implemented Correlators: - Time-Domain Sum of Products (XOR, I&D, LUT) - FFT-Implemented Correlation (Acquisition, Tracking) 5 State of the Art SW GNSS Receiver Example • NavX-NSR by IfEN & University FAF Munich • 1st Interactive GPS/Galileo Software Receiver - Triple-Frequency RF Front-End with USB (312.5 Mbps) - 30% of CPU on 2 Intel Xeon 5140 Processors Tracking 18 Satellites - 85% Computation Time for Correlation - GUI for Results and Runtime Control of Channel Configuration, Signal/Code Structure, Processing Algorithms, & Receiver Parameters M. Anghileri, T. Pany, D.S. Güixens, J.H. Won, A.S. Ayaz, C. Stöber, I. Krämer, D. Dötterböck, G.W. Hein, and B. Eissfeller, 6 “Performance Evaluation of a Multi-frequency GPS/Galileo/SBAS Software Receiver,” ION-GNSS’07, Ft. Worth, TX, September 2007 State of the Art SW GNSS Receiver Example Search Strategy: - All resources used to acquire and track a satellite - Extract information from the signal to correct large errors of the PC clock - With timing, calculate approximate satellite position from almanac or ephemeris Acquisition: - FFT-implemented correlation - Two levels of acquisition (high-power first) with interference cancellation - Coherent and non-coherent integration - Time and Doppler search space reduced for weak signals and re-acquisition Tracking: - Mixed FLL and PLL for carrier, rate-aided DLL for code - Frequency error discriminator: mixture of 2-quadrant and 4-quadrant atan2’s Optimized reference waveform (S-curve shaping technique): - Weighted combination of several replicas to achieve a pre-specified S-curve Bit synchronization: - Kalman filter tracking of carrier phase, Doppler, and Doppler rate errors - MLE of bit edge positions - Forward error corrections & Viterbi decoder Navigation Solution: - Single-epoch least squares solution - Kalman navigation filter optimized for car navigation - Pseudoranges, carrier phase and Doppler as well as height and clock fixing 7 M. Anghileri, T. Pany, D.S. Güixens, J.H. Won, A.S. Ayaz, C. Stöber, I. Krämer, D. Dötterböck, G.W. Hein, and B. Eissfeller, “Performance Evaluation of a Multi-frequency GPS/Galileo/SBAS Software Receiver,” ION-GNSS’07, Ft. Worth, TX, September 2007 State of the Art SW GNSS Receiver Example Programming Features: - An object-oriented programming approach with C++ - Classes grouped into modules with well-defined input and output data streams - UML diagram design before implementation - Maximum reuse of source codes - Common algorithms and data structures are implemented as base class (abstract class) - Particular features are then specified in derived classes (inheritance) - Codes optimized with assembler instructions - Multi-threading for better real-time capability Performance: - Code measurement accuracy: better than 30 cm - Carrier phase measurement accuracy: better than 1 mm - In-door positioning capability: FLL operates on signals down to 10 dB-Hz Need a Software Receiver Standard? M. Anghileri, T. Pany, D.S. Güixens, J.H. Won, A.S. Ayaz, C. Stöber, I. Krämer, D. Dötterböck, G.W. Hein, and B. Eissfeller, “Performance Evaluation of a Multi-frequency GPS/Galileo/SBAS Software Receiver,” ION-GNSS’07, Ft. Worth, TX, September 2007 8 Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis • Standardization 9 Recent Developments & Trends • GPS Signal’s Channel Impulse Response vs. Correlation • Correlation: Vital Role in DS-SS CDMA Receivers - Despread (processing gain) for signal detection - Identify which satellite the signal originated from - Provide timing (code/carrier phase) to construct measurements - Enable data demodulation for navigation message - Performance-limiting mix-in point for interference, multipath, etc. - Data compression from MHz to kHz (intensive) - Its implementation distinguishes HW vs. SW receivers ±Tc Code-dependent ±Tc Code structure-dependent Affected by effective bandwidth BPSK ±Ts BOC(s,c) 10 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Uploaded GPS Satellite Navigation Data Bits A Atomic PRN Code Carrier Power Transmit Clock Generation Modulation Amplification Antenna Transmit Shaping Filter h t(t) Local Clock Signal Signal Receiver Receive User & Data Digital Front-end Antenna Processors B Samples Digital Receiver Receive Shaping Filter h r(t) 11 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Uploaded GPS Satellite Navigation Data Bits Propagation Channel A Atomic PRN Code Carrier Power Transmit Clock Generation Modulation Amplification Antenna Ionosphere Transmit Shaping Filter h t(t) Propagation Channel Troposphere Impulse Response hp(t) Local Clock Environment Direct Signal Signal Signal Receiver Receive User & Data Digital Front-end Antenna Processors B Samples Multipath Signals {ai, ti, i = 1, …, M} Digital Receiver Receive Shaping Filter h r(t) 12 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Uploaded GPS Satellite Navigation Data Bits Propagation Channel A Atomic PRN Code Carrier Power Transmit Clock Generation Modulation Amplification Antenna Ionosphere Transmit Shaping Filter h t(t) Propagation Satellite Signal Channel Impulse Response h(t) = hr(t)*hp(t)*ht(t) Channel Channel Transfer Function H(f) = F{h(t)} and h(t) = F -1{H(f)} Troposphere Impulse (* Convolution, F Fourier Transform, F -1 Inverse Fourier Transform) Response hp(t) Local Clock Environment Direct Signal Signal Signal Receiver Receive User & Data Digital Front-end Antenna Processors B Samples Multipath Signals {ai, ti, i = 1, …, M} Digital Receiver Receive Shaping Filter h r(t) C. Yang and M. Miller, “Novel GNSS Receiver Design Based On Satellite Signal Channel Transfer Function/Impulse Response,” 13 Proc. of ION-GNSS’05, Long Beach, CA, Sept. 2005 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Dirac Delta Function (Flat Infinite Spectrum) Ideal 14 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Dirac Delta Function (Flat Infinite Spectrum) Ideal Ideal Correlation with Spectrum Limited to f s/2 Conventional Correlation Correlation with Spectrum Function Limited to feff ±Tc = 1/f c 15 Recent Developments & Trends • GPS Signal’s Channel Impulse Response Dirac Delta Function (Flat Infinite Spectrum) Ideal Normalized Correlation Impulse with Spectrum Limited to f s/2 Response Normalized Correlation (Generalized with Spectrum Limited to f eff Correlation) Ideal Correlation with Spectrum Limited to f s/2 Conventional Correlation Correlation with Spectrum Function Limited to feff ±Ts = 1/f s ±Teff = 1/f eff ±Tc = 1/f c 16 Recent Developments & Trends • What is a GPS signal channel impulse response? - From the output of a signal generator at satellite to the output of ADC at receiver - Encompass satellite, propagation, receiving environment, and receiver front-end • What are its benefits vs. conventional correlation? - Better timing accuracy, less sensitive to multipath, same operation for all codes • How to obtain a channel impulse response? - System identification (parametric, non-parametric, richness of excitation) - Inverse filter (phase-only and variants) - Wiener filter • When to outperform (what are limiting factors)? - Equivalent bandwidth of signal, propagation, transmitter, and receiver - Sampling rate - Signal to noise ratio (SNR): at input vs. processing loss - Computational loading 17 Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis • Standardization 18 Recent Developments & Trends • Frequency-Domain Baseband Signal Processor Forward Transformation - Signal Spectrum GPS RF Shift for ADC FFT Front-End Doppler Removal Correlation Power Detection Df IFFT Inverse Dt Transformation Delay-Doppler Map Code Complex Replica FFT Conjugate Sequences 19 Forward Transformation - Replica Recent Developments & Trends • Frequency-Domain Baseband Signal Processor Forward Transformation - Signal Pseudo Spectrum Full/Zoom Narrowband GPS RF Extended Quadrature Shift for ADC FFT Interference Front-End Buffer Sampling Doppler Suppression Removal GPS Signal Carrier Parameters Doppler Complex Correlation Detection Df Full or Parameter DFT for ms-Alignment Partial or Extraction Residual Data Bit Sync Pruning Doppler Interpolation IFFT Inverse Dt Transformation Delay-Doppler Map Code Complex Replica FFT Conjugate Sequences 20 Forward Transformation - Replica Recent Developments & Trends • Frequency-Domain Baseband Signal Processor Forward Transformation - Signal Pseudo Spectrum Full/Zoom Narrowband GPS RF Extended Quadrature Shift for ADC FFT Interference Front-End Buffer Sampling Doppler Suppression Removal GPS Signal Carrier Parameters Doppler Complex Correlation Detection Df Full or Parameter DFT for ms-Alignment Partial or / Extraction Residual Data Bit Sync Pruning Doppler Interpolation IFFT Inverse Dt Transformation Delay-Doppler Map Code Phases Code Doppler Code Complex Replica Resampling FFT Conjugate Sequences 21 Forward Transformation - Replica Recent Developments & Trends • Frequency-Domain Baseband Signal Processor Multipath Mitigated Composite Signal Correlation Correlation Signal s(t) Spectrum S(f) Spectrum FFT IFFT Multipath Estimation Replica Replica Multipath r(t) Spectrum R(f) Transfer FFT * Function Autocorrelation Spectrum Parametric Signal Correlation Transfer Multipath Multipath Spectrum Spectrum Function Parameters Mitigation Non-Parametric 22 Recent Developments & Trends • Generalized Frequency-Domain Correlator (GFDC) s(t) S(f) Incoming Signal Fourier Spectrum c(t) Samples Buffer Transform Filtering U C(f) Delay-Doppler Inverse Map of Peak Detection Spectrum Complex & Parameters Fourier Filtering W Generalized Extraction r(t) R*(f) Transform Correlations Code Replica Fourier Spectrum Samples Buffer Transform Filtering V Conjugate Generalized Frequency-Domain Correlator (GFDC) Frequency-Domain Baseband Signal Processor 23 Recent Developments & Trends Two Types of Filtering: Applied to Individual Frequency Bins Involving the Entire Spectrum Examples of Filtering: • Spectrum Excision of Narrowband Interference • Spectral Filtering to Reduce Additive Noise • Spectrum Segmentation of Multiple Codes • Spectrum Translation for Residual Doppler Removal with Feedback Conventional Correlation Impulse Response • Spectrum Windowing/Filtering Phase-Only Correlation Symmetric Phase Only Square-Root Normalized Amplitude-Compensated Make One of Your Own …24 C. Yang, M. Miller, and T. Nguyen, “Symmetric Phase-Only Matched Filter (SPOMF) for Frequency-Domain Software GPS Receivers,” ION Journal: Navigation, Vol. 54, No. 1, Spring 2007 Recent Developments & Trends • Phase-Only Correlation BPSK BOC Adaptive Waveforms: Correlation in Acquisition Phase-Only in Tracking C/A-Code to Achieve Performance of P-Code In Accuracy and Multipath Same Operation for Both BPSK- and BOC-Codes 25 C. Yang, M. Miller, and T. Nguyen, “Symmetric Phase-Only Matched Filter (SPOMF) for Frequency-Domain Software GPS Receivers,” ION Journal: Navigation, Vol. 54, No. 1, Spring 2007 Recent Developments & Trends • Generalized Frequency-Domain Correlator (GFDC) Symmetric Phase-Only 3 Pairs of Curves: With and Without Multipath Matched Filter (SPOMF) ▪ Conventional Correlation Signal + Noise + Multipath Conventional Correlation Signal + Noise ▪ Impulse Response Signal + Noise + Multipath Impulse Response (SCIR) Signal + Noise ▪ Symmetric Phase-Only Signal + Noise + Multipath Signal + Noise Infinite Bandwidth 26 Fixed Relative Strength a = 0.2 Same Noise at Each Delay Recent Developments & Trends • Frequency-Domain Baseband Signal Processor Narrowband L1 C/A-Code L1, L2 or L5 Full Spectrum Single Band Antenna, Spectrum Narrowband per Band RF Front-End & ADC Segmentation L1C-Code Narrowband L1/L2 or L1/L5 50 Msps 24 MHz Spectrum L2C (CM & CL) Complex L1, L2 Dual-Band Antenna, Screening RF Front-End & ADC DFT/FFT for Spike 50,000 Excision Wideband Complex P(Y)-Code Spectrum DFT/FFT Filtering per 1 ms Triple-Band Antenna, Split-band RF Front-End & ADC M-Code L1, L2 and L5 L5 Spectrum Wideband Incoming Signal FFT Only Done Once Filtering L5 (I5 & Q5) But Used for All Codes for All Satellites! Spectrum Segmentation = Ideal Bandpass Filtering 27 Recent Developments & Trends • Block-Repeated Iterative Processing Block 1 Block 2 Block 3 ▪ ▪ ▪ Block M ▪ ▪ ▪ Block N Time Parameter 1 Parameter 2 Parallel Processing ▪ ▪ ▪ Parameter N Sequential Processing Parameter 1 Parameter 2 ▪ ▪ ▪ ▪ ▪ ▪ Parameter N Sequential Parameter 1 Parameter n+1 ▪ ▪ ▪ Parameter N-n+1 Parallel ▪ ▪ ▪ ▪ ▪ ▪ Processing Parameter n Parameter 2n ▪ ▪ ▪ Parameter N • Multipath Mitigation Parameter 1 Parameter 2 Block ▪ • Near-Far Interference Cancellation Repetitive ▪ Processing ▪ • Iterative Approximation to Nonlinearity Parameter N 28 • Successive Removal of High Dynamics Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis Strong-Weak (Near-Far) Problem S-Curve-Shaping • Standardization 29 Recent Developments & Trends • Strong-Weak Signal (Near-Far) Problem: Cause & Effect - Masking of Weak Signals by Strong Signals - Non-orthogonality (Cross-Correlation) between Codes Ideal Case (Orthogonal) Constructive Destructive as y as y as y s: Strong Noise Cloud Non Signal (as) Orthogonal w: Weak Signal (aw) s s s y: Received Signal aw w aw w aw w Weak Signal Weak Signal None of Strong Signal Cross-Correlation Cross-Correlation Projection (w/o Weak Signal of Strong Signal of Strong Signal Cross Correlation) Out of Noise (i.e., Projection) (i.e., Projection) 30 Recent Developments & Trends • Strong-Weak Signal (Near-Far) Problem: Signal Models Amplitude Vector Unit Amplitude Matrix Number of Correlation Samples Strong Signals Weak Signals 31 Recent Developments & Trends • Strong-Weak Signal (Near-Far) Problem: Removal • Cancellation: - Signal Domain [Madhani et al., 2001] - Correlation Domain [Norman & Cahn, 2004] •Adaptive Orthogonalization with Constraints [Glennon & Dempster, 2007] Equivalent • Signal Subspace Projection [Morton et al., 2007] • Unnormalized Oblique Projection [Behrens & Scharf, 1994; Thomas et al., 2004] Constrained Optimization for Adaptive Replica 32 Recent Developments & Trends • Successive Interference Cancellation (SIC) - Signal Domain Iteration [Madhani et al., 2001] 33 Recent Developments & Trends • Successive Interference Cancellation (SIC) - Correlation Domain Iteration [Norman & Cahn, 2004] 34 Recent Developments & Trends • Adaptive Orthogonalization with Constraints [Glennon & Dempster] C/A-Code: - Max correlation = 1023 - Max cross correlations = -63 and +65, each @ 12.5% (-24 dB) - Typical cross correlation = -1 @ 75% (-60 dB) Cross-correlation due to imbalance of 64 out of 1023 chips Idea: rebalance the code via modifying 32 chips Procedure: - Calculate the total cross correlation (cc) between 2 sequences - Get indices of chips: sign of chip cc = sign of sequence cc - Sign-reverse some selected indices to eliminate cc Complexity: multiple strong signals, data bit, residual Doppler 35 Recent Developments & Trends • Signal Subspace Projection [Morton et al.] Projection onto <S>: - Strong Signal Subspace: <S> = span{s1, s2, …, sM} PS = S(STS)-1ST N N - Recover Strong Signals via Subspace Projection: - Remove Strong Signals: - Detect Weak Signals: 1N mm N1 Projection onto Orthogonal Subspace Equivalent code replica 36 Recent Developments & Trends • Constrained Optimization for Adaptive Replica - Constraints for Adaptive Code Replica : - Correlation with Synthesized Code: To Minimize - Constrained Optimization: Subject to - Solution: Similar to Subspace Projection with R = diagonal “Optimal” – noise minimized 37 Recent Developments & Trends • SINR Maximization for Adaptive Replica - Correlation with Synthesized Code to Find : CC between weak signals ignored Signal Noise + Interference - Optimality: Signal to Interference plus Noise Ratio - Constrained Optimization: Subject to - Solution: 38 Recent Developments & Trends • MSE Minimization for Adaptive Replica [Lacatus et al., 2007] - Signal already synchronized, to improve its reception quality - Optimality: Mean square error (MSE) minimization - Constrained Optimization: Subject to - Solution: - Complexity: R, p 39 Recent Developments & Trends • Signal Subspace Projection [Morton et al.] Success Rate (%) Success Rate (%) Without Removal Success Rate (%) Without Removal Achieve 90% Success Rate 40 Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis Strong-Weak (Near-Far) Problem S-Curve-Shaping • Standardization 41 Recent Developments & Trends • Multipath Error with “E-L” Code Error Discriminator S = Correlator Spacing p = Multipath Delay wrt Direct Path T = Chip Duration q = Bias in Delay Error Discriminator E = Early, P = Prompt, L = Late Ed , Pd , Ld = Direct Signal Correlation Er, Pr, Lr = Multipath Signal Correlation 42 Recent Developments & Trends • Multipath Mitigation Methods at Correlator Narrow Correlator Double Delta Correlator: - Strobe Correlator Number of correlators - Pulse Aperture Correlator Correlator spacing - Gated Correlator Correlator location Multipath Elimination Technique (Slopes) Correlator weighting E1/E2 Tracking Multipath Estimating Correlator (Parametric) High Resolution Vision Correlator Improved Multipath Performance at the Cost of Impulse Response Increased Thermal Noise 43 Recent Developments & Trends • Synthesize Code Error Discriminator (S-Curve Shaping) Incoming Signal R(Dt-4d) S* a-4 R(Dt-3d) VVL S* a-3 R(Dt-2d) VL S* a-2 R(Dt-d) Local Code L S* a-1 Optimal D(Dt) = kDt As narrow R(Dt) P S* a0 Code Error as possible R(Dt+d) E S* a1 Discriminator in tracking d R(Dt+2d) D(Dt) VE S* a2 R(Dt+3d) VVE S* a3 S-Curve R(Dt+4d) S* a4 Code Generator Dt As wide as possible in acquisition Operating Interval (±1 chips) T. Pany, M. Isigler, & B. Eissfeller, “S-Curve Shaping: A New Method for Optimum Discriminator Based 44 Code Multipath Mitigation,” ION-GNSS’2005, Long Beach, CA Recent Developments & Trends • Synthesize Code Error Discriminator (S-Curve Shaping) d = R a N = Alternative Solution Dtj -N Convolution of ai and R(id) -Ld 0 Ld id T. Pany, M. Isigler, & B. Eissfeller, “S-Curve Shaping: A New Method for Optimum Discriminator Based 45 Code Multipath Mitigation,” ION-GNSS’2005, Long Beach, CA Recent Developments & Trends • Synthesize Code Error Discriminator (S-Curve Shaping) Infinite 8 MHz Infinite 8 MHz Linear Region: 0.05 0.2 0.05 0.2 Fit Range: 1.5 2 1.5 2 Resolution: 0.05 0.2 0.05 0.2 Offset: 0 0.02 0.002 0.05 46 T. Pany, M. Isigler, & B. Eissfeller, “S-Curve Shaping: A New Method for Optimum Discriminator Based Code Multipath Mitigation,” ION-GNSS’2005, Long Beach, CA Outline • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis • Standardization 47 Software Communications Architecture (SCA) SCA is Standards for Software Defined Radio (SDR) by JTRS - H/W & S/W specifications - Open architecture framework: how elements of hardware and software operate - Structure and operation: load waveforms, run applications, and networking to an integrated system Applications Core Framework (CF) Operating Environment (OE) Commercial Off-the-Shelf (COTS) Non-CORBA Non-CORBA Non-CORBA Modem Security I/O Components Components Components Physical RF API Modem Modem Link, Network Security Security Security Link, Network I/O I/O Components Adapter Components Adapter Components Adapter Components Adapter Components MAC API LLC/Network API Security API LLC/Network API I/O API Core Framework IDL (“Logical Software Bus” via CORBA) CORBA ORB & CF CORBA ORB & CF Services Services & Services Services & (Middleware) Applications (Middleware) Applications Operating System Operating System Network Stacks & Serial Interface Services Network Stacks & Serial Interface Services Board Support Package (Bus Layer) Board Support Package (Bus Layer) Black Hardware Bus Red Hardware Bus 48 A Software GPS Receiver Standard? Without Software GPS Receiver Standard - Hardware/software not totally compatible - A stand-alone software GPS receiver per manufacturer, proprietary - Result exchanges using common data format e.g. RINEX (a standard?) - A user has to stick with a manufacturer’s or buys from another With a Software GPS Receiver Standard - Specified to hardware/software functionality components similar to SCA for SDR - we can market a full software receiver, best software components for specific functionalities, common utilities, application specific software components, development tools, … - A user (government buyer) can select and assemble (plug and play) per needs New Business Models: Innovative Small Developers Can Play - Standard compliant platform vendors - Software development tools vendors - Baseband signal/data processors vendors - Applications-specific software vendors Industry-Wide Consortium for Standard Maintenance 49 Summary • Software GPS Receivers: Definitions • Example of a State of the Art Implementation • Recent Developments & Trends - GPS Signal’s Channel Impulse Response - Frequency-Domain Baseband Processor - Online Adaptive Code Replica Synthesis - Semi-Coherent Integration • Standardization 50 Thank you for your attention. Questions? 51 Questions – Enough Throughput for SW RX? • Xeon 5140 Processors - Clock rate of 2.33 GHz and 4 instructions executed per clock tick - 64-bit bus vs. 4-bit samples: 16 samples per transfer from ADC to CPU • Required Throughputs - Sampling rate = 40.96 MHz, Transfer rate = 40.96 MHz/16 = 2.56 MHz - Number of satellites = 18, Number of correlators = 4 (P, E-L for I & Q) - Required data throughput = 18 4 40.96 = 2949.12 MHz • Performance of NavX Implementation - 8 + 8 correlations per 2.5 to 4 clocks (More efficient with more satellite) - 6.4 to 4 correlations per clock, 3.2 to 2 correlations per processor per clock - CPU throughput: Max: 2 Xeon @ 2.33 GHz 3.2 correlations per clock = 10857.8 MHz Min: 2 Xeon @ 2.33 GHz 2 correlations per clock = 9320 MHz - Data throughput / CPU throughput = 2949.12/10088.9 = 29% ~ Claimed 30% - Cannot do multipath mitigation for L2CL (pre-compute double-delta replica) 52 Questions – Frequency-Domain Tracking? • Acquisition - Correlation at (code, frequency): N complex multiplications + N-1 complex additions - Sequential correlations: NcNfN = NfN2 complex multiplications - FFT-implemented correlations: NfNlog2N N/log2N ~ 186, 341 Times Less • Tracking for N = 2048, 4096 - Correlators: 3(N+N)M = 6NM, M = Number of codes - FFT: Nlog2N + 3NM + 5NM = (log2N + 8)NM ~ (19, 20)NM 3.5 Times More • Trade-offs - With a dedicated FFT processor, the computation is about the same - Except for different code replicas, exactly the same for BPSK & BOC - Blurred line between search & tracking: acquire, reacquire, coverage - Narrowband interference suppression - Signal channel transfer function/impulse response - Joint error discriminator & joint tracking loop across signals per satellite - Snapshot of 2 ms of data: delay and Doppler for all codes 53 Recent Developments & Trends • Semi-Coherent Integration Signal movement during integration Area covered Search in Time & Frequency: Search point Area of coverage 1/2Ti= 500 Hz Long Integration Interval: Df Unknown data bits Changes in frequency Search Point ½ Tc ½ ms Dt Correlator IF Samples zn = sn + wn Post-Correlation Despreading Integration Integration with @ 1 kHz {zn, n = 0, 1, …, N-1} Code Replica Search Director Carrier Replica 54 Recent Developments & Trends • Semi-Coherent Integration z = [z0, z1, …, zN-1]T N -1 1 - Ideal Coherent: lCI ( z ) = Re{ zn sn} * sn Known Perfectly n =0 Data Bits & Changes 2 - Practical Coherent with FFT: lCI _ FFT ( z ) = max{| FFT{z} |} in Doppler N -1 3 - Non-Coherent: lNCI ( z ) = zn zn * Squaring Removes Data Bits & Residual Doppler n=0 But Also Squares Noise & Loses Info bt & Df N -1 4 - Semi-Coherent for First Lag: l SCI ( z ) = z n z n-1 * Between Coherent & n=1 Non-coherent N/2 N 2 5 - Semi-Coherent up to First N/2 Lags: lSCI _ N / 2 ( z ) = * zn zn - k k =1 n = k +1 6 - Semi-Coherent for First Lag with FFT: l SCI _ FFT ( z ) = max{| FFT{diag ( z 1:N -1 ) z 0:N -2 } |} * 55 Recent Developments & Trends • Semi-Coherent Integration: Intra Block Products nth Block (over 1 Data Bit), 20 ms Ts N = 1000 for Ts = 1 ms i= 1 2 3 …… 8 9 10 11 …… 20 ½ ½ K blocks with M samples 1½ 1½ t – t/2 t – t/2 (e.g., M = 20, K = 50) 9½ t 9½ N = KM t Center of block Offset from the center Centered Autocorrelation Between Two Samples with Delay t Data bit sign is squared out Bilinear in t and t , thus allowing FFT Chirping rate a FFT over t , peak at f0+2a t, linear in t Bit Sync FFT over t, peak at 2at , linear in t Not Bit Sign C. Yang, M. Miller, T. Nguyen, and E. Blasch, “Wigner-Hough/Radon Transform for GPS Post-Correlation Integration,” ION-GNSS’07, Ft. Worth, TX, Sept. 2007 56 Recent Developments & Trends • Semi-Coherent Integration: Inter Block Products Delay t = MTs yk+2 = [x(k+2)i, i = 1, 2, …, M] k = 1, …, K: Block Index 12 …… M i = 1, …, M: Sample Index 12 …… M t = MTs: Delay between Blocks Ts = 1 ms, M = 20, K = 50 yk = [xki, i = 1, 2, …, M] Block k+1 Block k Block k+2 N = KM = 1000 (1 s) yk+1 = [x(k+1)i, i = 1, 2, …, M] Obtain Two Blocks of Complex Correlations: Construct (K-1)×M Matrix of Inter-Block Conjugate Products: 12 …… M Linear in k and i, thus allowing FFT Differential 2×1 1 FFT over k, peak at 2 at for each i Bit Sequence Z 3×2 … 2 … FFT of complex peaks over i 57 K×K-1 K-1 Recent Developments & Trends Block 1 Block 2 Block 3 MM 3M True Bit ++ + 1 2 3 4 …… 12 M 3M1 Transition 2M 2M+ 1 y1 y2 Twenty Sequences y3 of Delayed Blocks for yb Summation Aligned Delayed yM Blocks Joint Bit Sync, Sign & a Estimation: Detection with 3D Search Differential bit sequence Peak bin = l ~ a (Acceleration) Bit transition (sync) C. Yang, T. Nguyen, E. Blasch, and M. Miller, “Post-Correlation Semi-Coherent Integration for Weak 58 & High Dynamic GPS Signal Acquisition,” IEEE PLANS/ION-AM’08, Monterey, CA, May 2008 Recent Developments & Trends • Semi-Coherent Integration Pd vs. SNR for N = 100 (b = 37.45 Hz/s) Inter-Block Products C. Yang, M. Miller, T. Nguyen, and E. Blasch, “Comparative Study of Coherent, Non-Coherent, and Semi-Coherent Integration Schemes for GNSS Receivers,” Proc. of ION-AM’07, Boston, MA, April 2007. 59

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