ION Southern California Section Meeting

1

ION Southern California Section Meeting

Software GPS Receivers:Some Recent Developments & Trends

June 25, 2008

Chun YangSigtem Technology, Inc.

San Mateo, CA(650) 312-1132

[email protected]

2

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

3

Software GPS Receivers: Definitions• Typical Architecture of GPS Receivers in Use Today

Correlators

Code/CarrierGenerators

Baseband IC/Microprocessor

RAM ROM

I/O

Processor

ApplicationSoftware

I/O

Application Platform

Data Processor- Demodulation- Positioning- Interface

Signal Processor- Acquisition- Tracking

ANTLNA

Down-Converters

(BPF, AMP,Mixers)

ADC

RF IC

PowerSupply

~MHz ~kHz ~Hz~GHz

4

Software GPS Receivers: Definitions• Software GPS Receivers: from IF samples to position fix,

all implemented in software on a general purpose computer

RAM ROM

I/O

Processor

Software for- Acquisition- Tracking- Demodulation- Positioning

General Purpose Processor

ANTLNA

Down-Converters

(BPF, AMP,Mixers)

ADC

RF IC

PowerSupply RAM ROM

I/O

Processor

ApplicationSoftware

I/O

Application Platform

DMA

Software for- Code/Carrier Generation- Correlation

SeveralHundreds~ Tens MHz

~GHz ~Hz

As close to RFas possible

Total signal bandwidth

Several RF channels, e.g., L1, L2, L5

5

Tools for Algorithms Evaluation Hardware Receiver Simulator Post-Processing of Recorded IF Samples Real-Time Research/Commercial Receivers

Software-Configured Hardware Correlator - Configurable Code Generators & NCOs - Sequential Repeated at Very High Speed (>> fs)

Software-Implemented Correlators: - Time-Domain Sum of Products (XOR, I&D, LUT) - FFT-Implemented Correlation (Acquisition, Tracking)

Software GPS Receivers: Definitions

HistoricalDevelopmentof SoftwareReceivers

SoftwareDefinedRadio(SDR)

6

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,“Performance Evaluation of a Multi-frequency GPS/Galileo/SBAS Software Receiver,” ION-GNSS’07, Ft. Worth, TX, September 2007

7

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



8

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?

9

Outline







• Standardization

10

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

BPSK

±Tc

Code-dependent Code structure-dependent Affected by effective bandwidth

±Tc

±TsBOC(s,c)

11

AtomicClock

PRN CodeGeneration

CarrierModulation

UploadedNavigationData Bits

PowerAmplification

TransmitAntenna

ReceiveAntenna

ReceiverFront-end

Signal& Data

Processors

SignalDigitalSamples

User

Transmit Shaping Filter ht(t)

Receive Shaping Filter hr(t)

A

B

LocalClock

Recent Developments & Trends• GPS Signal’s Channel Impulse Response

GPS Satellite

Digital Receiver

12

AtomicClock

PRN CodeGeneration

CarrierModulation


PowerAmplification

TransmitAntenna

Ionosphere

Troposphere

Environment

ReceiveAntenna

ReceiverFront-end

Signal& Data

Processors


User



DirectSignal

Multipath Signals{i, i, i = 1, …, M}

PropagationChannelImpulseResponsehp(t)

A

B

LocalClock


GPS Satellite

Digital Receiver

Propagation Channel

13

AtomicClock

PRN CodeGeneration

CarrierModulation


PowerAmplification

TransmitAntenna

Ionosphere

Troposphere

Environment

ReceiveAntenna

ReceiverFront-end

Signal& Data

Processors


User



DirectSignal

Multipath Signals{i, i, i = 1, …, M}

PropagationChannelImpulseResponsehp(t)

Satellite Signal Channel Impulse Response h(t) = hr(t)*hp(t)*ht(t)Channel Transfer Function H(f) = F{h(t)} and h(t) = F-1{H(f)}(* Convolution, F Fourier Transform, F-1 Inverse Fourier Transform)

A

B

LocalClock

C. Yang and M. Miller, “Novel GNSS Receiver Design Based On Satellite Signal Channel Transfer Function/Impulse Response,”Proc. of ION-GNSS’05, Long Beach, CA, Sept. 2005


GPS Satellite

Digital Receiver

Propagation Channel

14

IdealDirac Delta Function(Flat Infinite Spectrum)


• GPS Signal’s Channel Impulse Response

15

ConventionalCorrelationFunction


Ideal Correlation with SpectrumLimited to fs/2

Correlation with Spectrum

Limited to feff

±Tc = 1/fc



16

ConventionalCorrelationFunction

ImpulseResponse(GeneralizedCorrelation)


Ideal Correlation with SpectrumLimited to fs/2

Normalized Correlationwith Spectrum Limited to fs/2

Normalized Correlationwith Spectrum Limited to feff

Correlation with Spectrum

Limited to feff

±Ts = 1/fs

±Teff = 1/feff

±Tc = 1/fc



17

• 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


18

Outline







• Standardization

19

GPS RFFront-End

ADC

FFT

FFTComplexConjugate

SpectrumShift forDopplerRemoval

CodeReplica

Sequences

IFFT

Delay-Doppler Map

f

Correlation Power

Detection

Forward Transformation - Signal

Forward Transformation - Replica

InverseTransformation

Recent Developments & Trends• Frequency-Domain Baseband Signal Processor

20

GPS RFFront-End

ADCFull/Zoom

FFT

FFTComplexConjugate

GPS SignalParameters

NarrowbandInterferenceSuppression


CodeReplica

Sequences

Full orPartial orPruning

IFFT

Delay-Doppler Map

f

Complex Correlation

Detectionms-AlignmentData Bit SyncInterpolation

DFT forResidualDoppler

CarrierDoppler

ParameterExtraction

ExtendedBuffer

Pseudo QuadratureSampling





21

GPS RFFront-End

ADCFull/Zoom

FFT

FFTComplexConjugate

GPS SignalParameters

Code Doppler

NarrowbandInterferenceSuppression


CodeReplica

Sequences

Full orPartial orPruning

IFFT

Resampling

Delay-Doppler Map

f

Complex Correlation

Detectionms-AlignmentData Bit SyncInterpolation

DFT forResidualDoppler

Code Phases

CarrierDoppler

ParameterExtraction

ExtendedBuffer

Pseudo QuadratureSampling





/

22


FFT

CompositeSignal s(t)

SignalSpectrum S(f)

FFT

Replica r(t)

ReplicaSpectrum R(f)

*

CorrelationSpectrum

AutocorrelationSpectrum

MultipathEstimation

IFFT

MultipathMitigated

Correlation

MultipathTransferFunction

SignalSpectrum

CorrelationSpectrum

TransferFunction

MultipathParameters

MultipathMitigation

Non-Parametric

Parametric

23

Incoming SignalSamples Buffer

Code ReplicaSamples Buffer

FourierTransform

FourierTransformConjugate

SpectrumFiltering U

SpectrumFiltering V

SpectrumFiltering W

InverseFourier

Transform

Delay-DopplerMap of

ComplexGeneralizedCorrelations

Peak Detection& Parameters

Extraction

Generalized Frequency-Domain Correlator (GFDC)

s(t) S(f)

r(t) R*(f)

(f)*R

(f)S

C(f)

c(t)

(f)C

Frequency-Domain Baseband Signal Processor

Recent Developments & Trends• Generalized Frequency-Domain Correlator (GFDC)

24

• Spectrum Excision of Narrowband Interference• Spectral Filtering to Reduce Additive Noise • Spectrum Segmentation of Multiple Codes • Spectrum Translation for Residual Doppler

Removal with Feedback • Spectrum Windowing/Filtering

Two Types of Filtering: Applied to Individual Frequency Bins Involving the Entire Spectrum

Examples of Filtering:


Conventional CorrelationImpulse ResponsePhase-Only CorrelationSymmetric Phase OnlySquare-Root NormalizedAmplitude-CompensatedMake One of Your Own …

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

25

4900 4950 5000 5050 5100 5150 5200 5250-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

code lag (samples at 10 MHz)

code

chi

ps

code sequenece vs. normalized phase-only code

original codephase-only

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


auto

-cor

rela

tion

normalized peak for BPSK code vs. phase-only code


Adaptive Waveforms:Correlation in AcquisitionPhase-Only in Tracking

C/A-Code to AchievePerformance of P-CodeIn Accuracy and Multipath

Same Operation for BothBPSK- and BOC-Codes

BPSK BOC

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


auto

-cor

rela

tion

normalized peak for BOC code vs. phase-only code


8.094 8.096 8.098 8.1 8.102 8.104 8.106 8.108 8.11

x 104

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


code

chi

ps

code sequenece vs. normalized phase-only code

original codephase-only Tc

D

Double Delta, Strobe, Gated, or Pulsed Aperture Correlator

Code

t

Early-LateCorrelator

ReferenceSignals

Tc

D

Double Delta, Strobe, Gated, or Pulsed Aperture Correlator

Code

t

Early-LateCorrelator

ReferenceSignals

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

26

9.754 9.7545 9.755 9.7555 9.756 9.7565 9.757 9.7575 9.758

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


norm

aliz

ed m

agni

tude

generalized frequency-domain correlator (GFDC), C/N0=30dB-Hz

spomf correlationpomf/scir

Symmetric Phase-OnlyMatched Filter (SPOMF)

Conventional Correlation

Impulse Response (SCIR)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

12

14

16

delay, chip

dela

y es

timat

ion

rms

erro

r, m

monte carlo simulation: =0.2, C/N0=30dB-Hz ,100 runs

s + n + m: correlation, early - late s + n: correlation, early - late s + n + m: impulse response, excision, curve fits + n: impulse response, excision, curve fit s + n + m: symmetric phase only, curve fit s + n: symmetric phase only, curve fit

3 Pairs of Curves: With and Without Multipath

Signal + Noise + MultipathSignal + Noise



▪ Conventional Correlation

▪ Impulse Response

▪ Symmetric Phase-Only

Infinite Bandwidth

Fixed Relative Strength = 0.2 Same Noise at Each Delay

Recent Developments & Trends• Generalized Frequency-Domain Correlator (GFDC)

27

ComplexDFT/FFT

SpectrumScreeningfor SpikeExcision

SpectrumSegmentation

NarrowbandL1 C/A-Code

NarrowbandL2C (CM & CL)

WidebandP(Y)-Code

Split-bandM-Code

WidebandL5 (I5 & Q5)

L1, L2 or L5

L1, L2

L5

Full Spectrumper Band

SpectrumFiltering

NarrowbandL1C-Code

SpectrumFiltering

Triple-Band Antenna,RF Front-End & ADC

Dual-Band Antenna,RF Front-End & ADC

Single Band Antenna,RF Front-End & ADC

Incoming Signal FFT Only Done OnceBut Used for All Codes for All Satellites! Spectrum Segmentation = Ideal Bandpass Filtering

L1/L2 or L1/L5

L1, L2 and L5

50 Msps 24 MHz

50,000ComplexDFT/FFTper 1 ms


28

Parameter 1

Parameter 2

Parameter N

Parameter 1 Parameter 2 Parameter N

Parameter 1

Parameter n

Parameter n+1

Parameter 2n

Parameter N-n+1

Parameter N

ParallelProcessing

Sequential Processing

SequentialParallel

Processing

Parameter 1

Parameter 2

Parameter N

▪▪▪

▪▪ ▪

▪▪

▪

▪▪ ▪

▪▪ ▪

Block 1 Block 2 Block 3

▪▪

▪▪

▪▪

▪▪ ▪ Block M Block N▪▪ ▪

▪▪ ▪

BlockRepetitiveProcessing

Time

Recent Developments & Trends• Block-Repeated Iterative Processing

• Multipath Mitigation

• Near-Far Interference Cancellation

• Iterative Approximation to Nonlinearity

• Successive Removal of High Dynamics

29

Outline







Strong-Weak (Near-Far) Problem

S-Curve-Shaping

• Standardization

30


• Strong-Weak Signal (Near-Far) Problem: Cause & Effect - Masking of Weak Signals by Strong Signals

- Non-orthogonality (Cross-Correlation) between Codes

y

s

s

ww

Noise Cloud

None of Strong SignalProjection (w/o

Cross Correlation)Weak SignalOut of Noise

Ideal Case (Orthogonal)

y

s

s

ww

Cross-Correlationof Strong Signal(i.e., Projection)

Weak Signal

Destructive

y

s

s

ww

Cross-Correlationof Strong Signal(i.e., Projection)

Weak Signal

Constructive

NonOrthogonal

s: StrongSignal (s)w: WeakSignal (w)y: ReceivedSignal

31

Recent Developments & Trends• Strong-Weak Signal (Near-Far) Problem: Signal Models

vWαSαy ws TNyyy )()2()1( y

mNm C sssS 21

Tsmsss 21α

kNk C wwwW 21

Twkwww 21α

Tiiii Nsss )()2()1( s

)}2(exp{)()()( 0sisdsisisii kTfjkdkcks

Tjjjj Nwww )()2()1( w

)}2(exp{)()()( 0wjsdwjwjwjj kTfjkdkckw

WeakSignals

StrongSignals

Unit Amplitude MatrixAmplitude Vector

Number of Correlation Samples

32

•Adaptive Orthogonalization with Constraints [Glennon &

Dempster, 2007]

• Signal Subspace Projection [Morton et al., 2007]

• Unnormalized Oblique Projection [Behrens & Scharf, 1994;

Thomas et al., 2004]

Constrained Optimization for Adaptive Replica

Recent Developments & Trends• Strong-Weak Signal (Near-Far) Problem: Removal

svWαvWααSSααSyy wwsss )ˆˆ(ˆˆ

swswswsywsTTT

w mRRRRR ααSwywyw ˆˆˆ

21

• Cancellation:

- Signal Domain [Madhani et al., 2001]

- Correlation Domain [Norman & Cahn, 2004]

Eq

uiv

alen

t

33

Incoming Signal:s(t) = c1(t-1)e

j1t+1

+ c2(t-2)ej2t

+ n(t), >>

Replica for aWeak Signal:r2(t) = c2(t-)ejt

Vary , During Search

1(-1, -1) 11(-1)ej(-1)T/2+1

Peak-Picking& Obtain:

, 1, 1, 1^ ^ ^ ^

Replica for aStrong Signal:r1(t) = c1(t-)ejt


Strong SignalAcquisition& Tracking

ReconstructedStrong Signal:

s1(t) = c1(t-)ejt+1̂^^^^

_+

2(-2, -2) 22(-2)ej(-2)T/2+2


, 2, 2, 2^ ^ ^ ^ Weak Signal

Acquisition& Tracking

Step 1: Acquire Strong Signals

Step 2: Reconstruct Strong Signal

Step 3: Remove Strong Signal

Step 4: AcquireWeak Signal


j1t+1

+ c2(t-2)ej2t

+ n(t), >>


j1t+1

+ c2(t-2)ej2t

+ n(t), >>





1(-1, -1) 11(-1)ej(-1)T/2+11(-1, -1) 11(-1)ej(-1)T/2+1


, 1, 1, 1^ ^ ^ ^


, 1, 1, 1^ ^ ^ ^


, 1, 1, 1^ ^ ^ ^







s1(t) = c1(t-)ejt+1̂^^^^


s1(t) = c1(t-)ejt+1̂^^^^

_+

2(-2, -2) 22(-2)ej(-2)T/2+22(-2, -2) 22(-2)ej(-2)T/2+2


, 2, 2, 2^ ^ ^ ^


, 2, 2, 2^ ^ ^ ^


, 2, 2, 2^ ^ ^ ^ Weak Signal



Step 2: Reconstruct Strong Signal

Step 3: Remove Strong Signal

Step 4: AcquireWeak Signal

Recent Developments & Trends• Successive Interference Cancellation (SIC) - Signal Domain Iteration [Madhani et al., 2001]

34


j1t+1

+ c2(t-2)ej2t

+ n(t), >>



1(-1, -1) 11(-1)ej(-1)T/2+1


, 1, 1, 1^ ^ ^ ^




12(-1, -1) 12(-1)ej(-1)T/2+1^ ^ ^ ^ ^ ^

= 12(-1)ej(-1)T/2+1

+ 22(-2)ej(-2)T/2+2


s1(t) = c1(t-)ejt+1̂^^^^

_

+2(-2, -2) 22(-2)e

j(-2)T/2+2


, 2, 2, 2^ ^ ^ ^ Weak Signal



Step 2: Estimate Cross-Correlation

Step 3: Correlate with WeakSignal Replica

Step 4: RemoveStrong SignalCorrelation


j1t+1

+ c2(t-2)ej2t

+ n(t), >>


j1t+1

+ c2(t-2)ej2t

+ n(t), >>





1(-1, -1) 11(-1)ej(-1)T/2+11(-1, -1) 11(-1)ej(-1)T/2+1


, 1, 1, 1^ ^ ^ ^


, 1, 1, 1^ ^ ^ ^


, 1, 1, 1^ ^ ^ ^






12(-1, -1) 12(-1)ej(-1)T/2+1^ ^ ^ ^ ^ ^12(-1, -1) 12(-1)ej(-1)T/2+1^ ^ ^ ^ ^ ^

= 12(-1)ej(-1)T/2+1

+ 22(-2)ej(-2)T/2+2

= 12(-1)ej(-1)T/2+1

+ 22(-2)ej(-2)T/2+2


s1(t) = c1(t-)ejt+1̂^^^^


s1(t) = c1(t-)ejt+1̂^^^^

_

+2(-2, -2) 22(-2)e

j(-2)T/2+22(-2, -2) 22(-2)ej(-2)T/2+2


, 2, 2, 2^ ^ ^ ^


, 2, 2, 2^ ^ ^ ^


, 2, 2, 2^ ^ ^ ^ Weak Signal



Step 2: Estimate Cross-Correlation

Step 3: Correlate with WeakSignal Replica

Step 4: RemoveStrong SignalCorrelation

Recent Developments & Trends• Successive Interference Cancellation (SIC) - Correlation Domain Iteration [Norman & Cahn, 2004]

35

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

36

ySSSSyPy TTS

1)(ˆ vSαvWαSαSSSS ~)()( 1 sws

TT

yPyyyy S ˆ svWα w

)( yPywyw STT

wR )())(( 1 ySSSSwyw TTTT

yPwywyw STTT

wR ywywPI TTS

~])[(

0)()()(~ SSwSPSwSPIwSw TS

TS

TT

NN ST

STT

STT wPwwPwwwwPIwww )(~

Recent Developments & Trends• Signal Subspace Projection [Morton et al.]

- Strong Signal Subspace: <S> = span{s1, s2, …, sM} Projection onto <S>:PS = S(STS)-1ST

wPwPIwPwwS )(~

SSProjection onto Orthogonal SubspaceEquivalent code replica

- Recover Strong Signals via Subspace Projection:

- Remove Strong Signals:

- Detect Weak Signals:

1N mm N1

N N

37

0~ SwT

NT ww~

Recent Developments & Trends• Constrained Optimization for Adaptive Replica

- Constraints for Adaptive Code Replica :

TT N 0Sww ˆ~ TT dDw ~

)(~~~ Svwαyw T

wT

w NR

- Correlation with Synthesized Code:

wRwww

~~minarg~~

* T2}{}))({( v

TT EE IvvSvSvR

dDRDDRw 111* ))((~ T

To Minimize

TT dDw ~Subject to

Similar to Subspace Projectionwith R = diagonal “Optimal” – noise minimized

w~

- Constrained Optimization:

- Solution:

38

wPw

ww~~

)~( 2

Tw

T

SINR

vTT

ssE RSASSαvSαvP }))({(T

ssααA

wPwww

~~minarg~~

* T NT ww~

)(~~~~ s

Tw

Tw

TR SαvwWαwyw )(~~s

Tw

T Sαvwww

Recent Developments & Trends• SINR Maximization for Adaptive Replica

- Correlation with Synthesized Code to Find :w~

CC between weak signals ignored Signal Noise + Interference

Subject to


- Solution:

wPw

wPw

1

1*~

T

N

sTs

TTss

NI

αα

SαSα

22

1 1

vsTs

TTss

v N αα

SαSαIP

- Optimality: Signal to Interference plus Noise Ratio

39

Recent Developments & Trends• MSE Minimization for Adaptive Replica [Lacatus et al., 2007]

- Signal already synchronized, to improve its reception quality

nSPby KssS 1 TKbb 1b }{ TE nnW ]}{[ 1 Kppdiag P WSPSyyR TTE }{

- Optimality: Mean square error (MSE) minimization

ppbE

TT

T wRwsw

yw ~~~21})

~{(MSE 2

Subject to


MSEminarg~~

*

ww 1~~ wwT

- Solution: sRw 1*~ p

w

www ~

)~(MSE~~ **1

tt )]~(

2~[ * swRw ppt

- Complexity: R, p

40

Recent Developments & Trends• Signal Subspace Projection [Morton et al.]

Suc

cess

Rat

e (%

)

Suc

cess

Rat

e (%

)

Suc

cess

Rat

e (%

)

Without Removal

Without Removal

Achieve 90% Success Rate

41







Strong-Weak (Near-Far) Problem

S-Curve-Shaping

• Standardization

Outline

42

Recent Developments & Trends• Multipath Error with “E-L” Code Error Discriminator

P

p-T Tq

S

p

-T Tq

S

In-Phase: Constructive Out-of-Phase: Destructive

Late: Positive Range Error (Longer) Early: Negative Range Error (Shorter)

E L

Ed

Er

Ld

Lr

P

E L

Ed

Ld

Er Lr

E = Early, P = Prompt, L = Late

S = Correlator SpacingT = Chip Duration

p = Multipath Delay wrt Direct Pathq = Bias in Delay Error Discriminator

Ed, Pd, Ld = Direct Signal CorrelationEr, Pr, Lr = Multipath Signal Correlation

43

Recent Developments & Trends• Multipath Mitigation Methods at Correlator

Narrow Correlator

Double Delta Correlator: - Strobe Correlator - Pulse Aperture Correlator - Gated Correlator

Multipath Elimination Technique (Slopes)

E1/E2 Tracking

Multipath Estimating Correlator (Parametric)

High Resolution Vision Correlator

Impulse Response

Number of correlatorsCorrelator spacingCorrelator locationCorrelator weighting

Improved MultipathPerformance at the Cost ofIncreased Thermal Noise

44

Recent Developments & Trends• Synthesize Code Error Discriminator (S-Curve Shaping)

T. Pany, M. Isigler, & B. Eissfeller, “S-Curve Shaping: A New Method for Optimum Discriminator BasedCode Multipath Mitigation,” ION-GNSS’2005, Long Beach, CA

OptimalCode Error

Discriminator

VVL

VL

P

L

VE

E

VVE

CodeGenerator

R(t-d)

d

R(t)

R(t+d)

R(t-3d)

R(t-2d)

R(t-4d)

R(t+2d)

R(t+3d)

R(t+4d)

Incoming Signal

Local Code D(t) = t

L

Lii idtRtD )()(

t

D(t)

S-Curve

Operating Interval(±1 chips)

As wideas possible

in acquisition

As narrowas possiblein tracking

45



N

Njjdesiredji tDtD

i

2* )]()([minarg

N

Njjdesired

L

Liji tDidtR

i

2)]()([minarg

=

d

tj

-Ld 0 Ld

R

N

-N

=

id

L

Lijij idtRtD )()(

Convolution of i and R(id)

dRRRα TT 1)(

)}({

)}({

j

jdesiredt

idi tRFFT

tDFFTconjIFFT j

Alternative Solution

46



8 MHz8 MHzInfinite Infinite

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 0.2Offset: 0 0.02 0.002 0.05

47

Outline







• Standardization

48

Core Framework (CF)

Commercial Off-the-Shelf (COTS)

Applications

OperatingEnvironment (OE)

Red Hardware Bus

CFServices &

Applications

CORBA ORB &Services

(Middleware)

Network Stacks & Serial Interface Services

Board Support Package (Bus Layer)

Black Hardware Bus

CFServices &

Applications

CORBA ORB &Services

(Middleware)

Network Stacks & Serial Interface Services

Board Support Package (Bus Layer)

Operating System

Core Framework IDL

Non-CORBAModem

Components

Non-CORBASecurity

Components

Non-CORBA I/O

Components

RF

ModemComponents

Link, NetworkComponents

SecurityComponents

ModemAdapter

SecurityAdapter

SecurityAdapter

I/OAdapter

I/OComponents

MAC API LLC/Network API LLC/Network API

Link, NetworkComponents

Security API

Operating System

Physical API

I/O API

(“Logical Software Bus” via CORBA)

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

49

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

50

Summary







- Semi-Coherent Integration

• Standardization

51

Thank you for your attention.

Questions?

52

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)

53

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

• Tracking - Correlators: 3(N+N)M = 6NM, M = Number of codes

- FFT: Nlog2N + 3NM + 5NM = (log2N + 8)NM ~ (19, 20)NM

• 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

N/log2N ~ 186, 341 Times Lessfor N = 2048, 4096

3.5 Times More

54

Search in Time & Frequency: Search point Area of coverageLong Integration Interval: Unknown data bits Changes in frequency

f

½ Tc ½ s

1/2Ti= 500 Hz

Search Point

IF Samples DespreadingIntegration

SearchDirector

Carrier Replica

Code Replica

Post-CorrelationIntegration with

{zn, n = 0, 1, …, N-1}

zn = sn + wn

Correlator

@ 1 kHz

Area covered

Signal movement during integration

Recent Developments & Trends• Semi-Coherent Integration

55

1 - Ideal Coherent: }Re{)( *1

0n

N

nnCI szz

2 - Practical Coherent with FFT: |}}{max{|)(_ zFFTzFFTCI

3 - Non-Coherent: *1

0

)( n

N

nnNCI zzz

4 - Semi-Coherent for First Lag: *1

1

1

)(

n

N

nnSCI zzz

5 - Semi-Coherent up to First N/2 Lags:

2/

1

2

1

*2/_ )(

N

k

N

knknnNSCI zzz

6 - Semi-Coherent for First Lag with FFT: |}})({max{|)( *2:01:1_ NNFFTSCI zzdiagFFTz

z = [z0, z1, …, zN-1]Tnssnnn wTnnTfjAbz ]})(2[exp{ 0

220

Recent Developments & Trends• Semi-Coherent Integration

sn Known Perfectly

Squaring Removes Data Bits & Residual DopplerBut Also Squares Noise & Loses Info bt & f

Data Bits & Changesin Doppler

Between Coherent &Non-coherent

56

Ts

nth Block (over 1 Data Bit), 20 ms

i = 1 2 3 …… 8 9 10 11 …… 20½ ½

1½ 1½

9½ 9½

t

t – /2 t – /2

N = 1000 for Ts = 1 ms

K blocks with M samples(e.g., M = 20, K = 50)

N = KM

Centered Autocorrelation Between Two Samples with Delay

)2

()2

(),( * txtxtz )2(22 0 tfjeA 1,,3,1 M Kt ,,2,1

Data bit sign is squared out

Chirping rate

Bilinear in t and , thus allowing FFT

Center of block Offset from the center

FFT over , peak at f0+2t, linear in t

FFT over t, peak at 2, linear in

C. Yang, M. Miller, T. Nguyen, and E. Blasch, “Wigner-Hough/Radon Transformfor GPS Post-Correlation Integration,” ION-GNSS’07, Ft. Worth, TX, Sept. 2007

Bit SyncNot Bit Sign

Recent Developments & Trends• Semi-Coherent Integration: Intra Block Products

57

1 2 …… M

1 2 …… M

Delay = MTs

yk = [xki, i = 1, 2, …, M]

yk+1 = [x(k+1)i, i = 1, 2, …, M]

yk+2 = [x(k+2)i, i = 1, 2, …, M]

Block k Block k+2

Block k+1

N = KM = 1000 (1 s)

M = 20,

],...,1,[ Mixy kik ],...,1,[ )1(1

Mixy ikk

k = 1, …, K: Block Index

i = 1, …, M: Sample Index

= MTs: Delay between Blocks

Ts = 1 ms, K = 50

Construct (K-1)×M Matrix of Inter-Block Conjugate Products:

]1,...,1,,...,1,[ KkMizZ ki

Obtain Two Blocks of Complex Correlations:

]))1([2(221

*)1(

220 ikMMTfj

kkkiikkiseAbbxxz

Linear in k and i, thus allowing FFT

FFT over k, peak at 2 for each i

FFT of complex peaks over i

1 2 …… M12…

K-1

2×13×2

…

K×K-1

Z

Recent Developments & Trends• Semi-Coherent Integration: Inter Block Products

DifferentialBit Sequence

58

1 2 3 4 …… M

Block 1

M+1

2M

M+2

2M+1

3M3M+1

],...,1,[ 11

1Mixy i

],...,1,[ )1(12

1Mixy i

],...,1,[ )2(13

1Mixy i

],...,1,[ )1(11Mixy bi

b

],...,1,[ )1(11Mixy Mi

M

2

2y 2

3y

2

4y

1

2y

1

4y1

3y

3

2y

by2

3

3y

by3

My2

3

4y

by4

My3

Block 2 Block 3

True BitTransition

TwentySequencesof DelayedBlocks for

Summation

y1

y2

y3

yb

yMAligned DelayedBlocks

Joint Bit Sync, Sign & Estimation: Detection with 3D Search

|)(|maxargˆ1

]1,...,1[lSl b

KKl

b

|)()(|maxarg)(ˆ1

]1,1[lHlSl b

kbk

bk

bk

])(ˆ),([)( 1 llBlB bk

bk

bk

)()(ˆ)()( 1 lHllSlS bk

bk

bk

bk

}{)( kk hlH FTTkK

Tk

Tkk zh ]00[ 11 )2( 0 kj

kk Bez

Peak bin = l ~ (Acceleration)Differential bit sequence

|)ˆ(|maxargˆ1

],...,1[

bbK

MblSb

Bit transition (sync)


C. Yang, T. Nguyen, E. Blasch, and M. Miller, “Post-Correlation Semi-Coherent Integration for Weak& High Dynamic GPS Signal Acquisition,” IEEE PLANS/ION-AM’08, Monterey, CA, May 2008

59

-30 -25 -20 -15 -10 -5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

single measurement SNR, 10log10

(A2/2), dB

Pd

Pfa

= 0.001, z = 2 = 2, N = 100, runs = 10000

coherentcoherent, fftnon-coherentsemi-coherent, k=1semi-coherent, k->N/2semi-coherent, k=1, fft

Pd vs. SNR for N = 100 ( = 37.45 Hz/s)

C. Yang, M. Miller, T. Nguyen, and E. Blasch, “Comparative Study of Coherent, Non-Coherent, and Semi-Coherent IntegrationSchemes for GNSS Receivers,” Proc. of ION-AM’07, Boston, MA, April 2007.


• Semi-Coherent Integration

0 5 10 15 20500

600

700

800

900

1000

1100bit sync with 20 delayed sums

cum

ula

ted

pe

ak

transition location

cumulated peakbit transition

Inter-Block Products

ION Southern California Section Meeting

Documents

Transcript of ION Southern California Section Meeting