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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:

                                              1N      mm      N1



                                             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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