A. J. Van Dierendonck, AJ Systems

August 16, 2000 IMA 1

Mathematical Challenges in GPS: New Opportunities Using New Civil Signals for Multipath Mitigation and Carrier Phase Ambiguity Resolution

A. J. Van Dierendonck, AJ Systems


TopicsNew Civil Signal RequirementsCharacteristics SummaryPN Code Structure and PropertiesSignal ModulationData StructureData Content


Signal Parameters to ConsiderFrequency & BandwidthReceived PowerCode StructureCode Chipping RateData RateData Structure


Frequency and Bandwidth Considerations

Wide bandwidth required for good multipath mitigation

Original allocation = 24 MHzFrequency separation from L1 and L2 required for large baseline carrier phase ambiguity resolution

Called “Tri-Lane Ambiguity Resolution”


New Signal Frequency Selection Requirements for Aviation

Allocated and protected as ARNSAs seen by the user, the signal must be independent of L1 and L2 signals

Completely redundant signalUser need not rely on other signals for acquisition and tracking


Other Requirements for Good Aviation Signal

Increased power relative to L1 (-154 dBW)To overcome higher interference levels• Due to radar, DME/TACAN and JTIDS

20 MHz broadcast bandwidth (minimum)To provide required accuracy in presence of noise and multipathRegistration will be for 24 MHz


More RequirementsImproved code cross-correlation properties

To overcome inadequacies of L1 C/A codeTo provide better signal integrityTo allow for more satellites in view

Improved bandwidth efficiencyBetter accuracy and alarm limit marginReduce the effects of “Evil Waveforms”

Improved parity/CRC and data encodingTo provide better signal and data integrity


GPS C/A Code Deficiencies1.023 MHz chipping rate does not provide bandwidth efficiency

Very susceptible to waveform distortionCross-correlation properties are marginal

Acquisition problems• False alarms and wrong signal acquisition

Susceptible to CW and narrow-band interference


Characteristics of Longer, Higher Chipping-Rate Gold Codes

Longer codes reduce cross-correlation to more acceptable levels

Although, acquisition time is longerHigher chipping-rates provide better accuracyEasy to implement


Gold Code PropertiesTwo shift registers of maximum length ever to be usedProgrammable feedback tapsCode length = 2n - 1, n = no. of stages2n + 1 codes, not all goodCross-correlation level inversely proportional to code length


Candidate Code PropertiesSame multipath/noise accuracy as P codeNarrowband and CW interference rejection is 10 dB better than the GPS C/A code

Not quite as good as P code, but OKWideband noise rejection is same as P codeDirect acquisition capability

Not practicably available using P code


Multipath VS Chipping Rate and Bandwidth

-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 0.2 0.4 0.6 0.8 1

MULTIPATH DELAY - C/A CHIPS

MUL

TIPA

TH E

RRO

R EN

VELO

PES

- C/A

CH

IPS

20 MHz BW, 10.23 MHz CODE20 MHz BW, 10.23 MHz CODE20 MHz BW, C/A20 MHz BW, C/A24 MHz BW, 10.23 MHz CODE24 MHz BW, 10.23 MHz CODE

ALPHA = 0.01

0.1 C/A Chip Spacing


Cross-Correlation PropertiesCode length reduces size of cross-correlation peaks (see Spilker, ION red book, volume I)

3 dB for each factor of 2 (different Doppler, worst case)6 dB for each factor of 4 (same Doppler)12 dB for a factor of 8 (same Doppler)

Code LengthParameter1023 2047 4095 8191 16383

Peak cross-correlation (any Doppler shift) -21.6 dB -24.6 dB -27.6 dB -30.6 dB -33.6 dBPeak cross-correlation (zero Doppler) -23.8 dB -29.8 dB -29.8 dB -35.8 dB -35.8 dB

Average probability of near worst case at zero Doppler 0.25 0.5 0.25 0.5 0.25


Characteristics SummaryL5 = 1176.45 MHzAllocated BW = 24 MHz (Requested)Minimum Received Power = -154 dBWPN Code Chipping Rate = 10.23 MHzQPSK Signal

In-Phase (I) = Data ChannelQuadraphase (Q) = Data-Free ChannelEqual Power in I and Q (-157 dBW)Independent PN Codes on I and Q


Characteristics Summary (Cont.)I and Q Modulation (1 kbps)

FEC encoded 50 bps data on I (100 sps)• Further encoded with 10-bit Neuman-

Hoffman CodeQ encoded with 20-bit Neuman-Hoffman CodeMore details to follow


L5 Codes and Code Properties


L5 CodesCodes with 2 - 13 stage shift registers

Length of one (XA code) = 8190 chipsLength of second (XB code) = 8191 chipsExclusive-Or’d together to generate longer code

Chipping rate of 10.23 MHzReset with 1 ms epochs (10,230 chips)

Two codes per satellite (4096 available)One for Data channel, one for Data-Free channel


L5 I & Q Code Generators1 2 3 4 5 6 7 8 9 10 11 12 13

1 2 3 4 5 6 7 8 9 10 11 12 13

Exclusive OR

Initial XBI State

Exclusive OR

All 1's

1 ms Epoch

Code Clock

XA(t)

XBI(t+ n iT c)

XI i(t)

XA Coder

XBI Coder

XBI State for SV i

ResetXQ i(t)

XBQ(t+ n iT c)

1 2 3 4 5 6 7 8 9 10 11 12 13

Initial XBQ State

Exclusive OR

XBQ Coder

XBQ State for SV i

Decode 1111111111101

Reset to all 1s on next clock


L5 Code Generator Timing

B0 XB Code

XA Code1 1

119 9

1

B0

1 ms = 10230

8190

8191

1 = 1111111111111 8 = 1111111111101

b) B0 = Initial State at 1 ms (greater than State 6151)

8 2

9 = 1111111111110 2 = State 2040

XB CodeB0

XA Code1 1

1

8 1

B0

1 ms = 10230

8190

1 = 1111111111111 8 = 1111111111101

a) B0 = Initial State at 1 ms (less than State 6152)

9 = 1111111111110

9

2 = State 2040

2


Cross-Correlation Properties vs. C/A-Code: Zero Doppler Difference

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-74 -72 -70 -68 -66 -64 -62 -60 -58 -56 -54 -52 -50 -48 -46 -44 -42 -40 -38 -36 -34 -32 -30 -28 -26 -24 -22

Cross-Correlation Power - dB

Prob

abili

ty o

f Occ

uren

ce

L5/I5 PRN 1/PRN 2 XCorrC/A PRN 6/PRN20 XCorrL5/I5 PRN 1 AutoCorrC/A PRN 6 AutoCorr

0.7644

0.6862


L5 Code Performance Summary74 Codes have been selected

37 I, Q pairsMax non-peak autocorrelation -30 dBMaximum cross-correlation with other selected codes -27 dBMaximum cross-correlation between I, Q pairs < -74.2 dBAnother pair selected as non-standard code


L5 Signal Modulation


L5 I & Q Code and Symbol Modulation

(Coded) coherent carrier in-quadrature with data

Allows for robust code & carrier tracking with narrow pre-detection bandwidthIndependent codes to remove QPSK tracking bias

GPS L5 DataMessages Add CRC

10 - symbolNeuman-Hoffman

Code

Code Generator10.23 MHzCode Clock

1 ms epochs

XI(t)

1 kbaud

XQ(t)

Encode withFEC 100 sps

20 - symbolNeuman-Hoffman

Code

1 kbaud

276 bits 300 bits

50 Hz Data Clock

QPSK ModulatorComposite

Signal

Carrier

100 Hz Symbol Clock


Neuman-Hoffman CodesEncoded symbols and carrier

Modulate at PN Code epoch rateSpreads PN Code 1 kHz spectral lines to 50 Hz spectral lines (including FEC)

• Reduces effect of narrowband interference by 13 dB

– Primary purpose of NH Codes– Also allows detection of narrowband interference

• Reduces SV cross-correlation most of the time• Provides more robust symbol/bit synchronization


10-ms Neuman-Hoffman Code on I

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7 8 9 10

Code Delay - Milliseconds

Neum

an-H

offm

an C

ode

Valu

e


20-ms Neuman-Hoffman Code on Q

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Code Delay - Milliseconds

Neum

an-H

offm

an C

ode

Valu

e


L5 Data Content & Format


L5 Data Content & Format5 – Six-Second 300-bit Messages

Format with 24-bit CRC (same as WAAS)Encoded with Rate 1/2 FEC• To make up for 3-dB QPSK reduction

Symbols modulated with 10-bit Neuman-Hoffman Code

Messages scheduled for optimum receiver performanceLined up with L1 sub-frame epochs


L5 Message Types (of 64 possible)

Message Type 1 - Ephemeris/Clock IMessage Type 2 - Ephemeris/Clock IIMessage Type 3 - Ionosphere/UTCMessage Type 4 - AlmanacMessage Type 5 - Text MessageAnticipated that Ephemeris/Clock Messages would be repeated every 18-24 seconds


Message Type 1

8 BITS

MESSAGE TYPE ID

6BITS

PREAMBLE

PRN

6BITS

MESSAGETOW COUNT*

17 BITS

"ALERT" FLAG - 1 BIT

WN

10 BITS

9 3315 39 49

L5 HEALTH - 5 BITS

55

URA5 INDEX - 4 BITS

IDOT

14 BITS

59

n

16 BITS

73

Crc

16 BITS

Cus

16 BITS

89

105 121

Crs - 4 LSBs

DIRECTION OF DATA FLOW FROM SV MSB FIRST100 BITS 2 SECONDS


Cuc

16 BITS

137

Cis

16 BITS

153

Cic

16 BITS

169

1

TGD15

8 BITS

185

toc5

8 MSBs

193

IODC

10 BITS

209


af05

22 BITS

219

af15

16 BITS

241

af25

8 BITS

257

CRC

24 BITS

277

toc5

8 LSBs

273

32 54

ANTI-SPOOF FLAG - 1 BIT

* MESSAGE TOW COUNT = 17 MSBs OF ACTUAL TOW COUNT AT START OF NEXT 6-SECOND MESSAGE

Crs

12 MSBs

TIQ5 - 4 BITS

TGD25

8 BITS

265


Message Type 2

8 BITS

MESSAGE TYPE ID

6BITS

PREAMBLE

MESSAGETOW COUNT*

17 BITS


32 BITS

9 15 33

M 0

32 BITS

65

e

28 LSBs

i032 BITS

97

129



0

32 BITS

161

1

8 MSBs

193

225


toe

16 BITS

24 BITS

241

IODE

10 BITS

265

CRC

24 BITS

24 LSBs

276

32

275

FIT INTERVAL FLAG - 1 BIT

A

e - 4 MSBs

RESERVED - 1 BIT

277



Message Type 3

8 BITS

MESSAGE TYPE ID

6BITS

PREAMBLE

PRN

6BITS

MESSAGETOW COUNT*

17 BITS


9 15 33 43

6BITS

CODE(S) ON L2 - 2 BITS

49

L1/L2 SV HEALTH

1

8 BITS

57 65

1

8 BITS

3

8 BITS

A0

32 BITS

89

105

2 - 4 LSBs



A1

24 BITS

145

tLS

8 BITS

169

1

tot

8 BITS

177

WN t

8 BITS

185

DN

8 BITS

201


209

CRC

24 BITS

RESERVED

44 BITS

277

WNLSF

8 BITS

413932

DATA ID - 2 BITS

0

8 BITS

2

8 BITS

3

8 BITS

0

8 BITS

8173 97

2 - 4 MSBs

113 193

tLSF

8 BITS


A05

8 BITS

217 225

A15

8 BITS

233


Message Type 4

8 BITS

MESSAGE TYPE ID

6BITS

PREAMBLE

PRN

6BITS

MESSAGETOW COUNT*

17 BITS


9 3315 41

PRN a

6BITS

47

8 BITS

57 65

M0

24 BITS

e

16 BITS

105

- 4 LSBs



i

16 BITS

145

24 BITS

161

1

0

16 MSBs

185

16 BITS

209


CRC

24 BITS

RESERVED

26 BITS

277229225

AS/SV CONFIG - 4 BITS

3932

DATA ID - 2 BITS

WN a

10 BITS

7 BITS

toa

8 BITS

20 MSBs

8173

L1/L2 SV HEALTHL5 HEALTH

A

A

129

0

8 LSBs

a f05

11 BITS

af15

11 BITS

251240


72

RESERVED - 1 BIT


Message Type 5

8 BITS

MESSAGE TYPE ID

6BITS

PREAMBLE

PRN

6BITS

MESSAGETOW COUNT*

17 BITS


9 15 33 41

TEXT MESSAGE (29 8-BIT CHAR)

60 MSBs


BITS 61-160



1


CRC

24 BITS

277273

TEXT PAGE - 4 BITS

3932

DATA ID - 2 BITS


72 LSBs



Message ContentMostly, content is same as on L1

Clock parameters describe L1-C/A/L5 combined offset rather than L1-P/L2-P combined offsetL1/L5 Group Delay variable for single frequency users

Add L5 HealthDifferent Text MessageAdd PRN numberPeculiar L5 information can be provided by civil community


Special AcknowledgementsGary McGraw, Rockwell CollinsPeter Fyfe, BoeingKarl Kovach, ARINCKeith Van DierendonckTom Morrissey, Zeta AssociatesTom Stansell & Charlie CahnRich Keegan (Leica)Jim Spilker

Documents

A. J. Van Dierendonck, AJ Systems