A Theoretical Survey of the Spreading Modulation of the New GPS Signals L1C, L2C, and L5

1
A Theoretical Survey of the Spreading Modulation
of the New GPS Signals (L1C, L2C, and L5)

Giftet
Inc.

• Ilir F. Progri, Giftet Inc., Pomona, CA
• Matthew C. Bromberg, Elected Engineering, MA
• William R. Michalson, WPI, Worcester, MA
• Jinling Wang, University of New South Wales,
  Sydney, Australia
• Presented at
• ION-NTM 2007, January 22-24, 2007
• San Diego, CA

2
Motivation

Giftet
Inc.

• Spreading modulation of the new signals L1C, L2C,
  and L5
• New signals offer several improvements
• Higher power
• Better code selection
• Improved spreading modulation schemes
• GNSS user benefit
• Unmatched performance against multipath and
  interference
• Is it possible to come up with better spreading
  modulation schemes?
• The answer is yes! This is the motivation of the
  paper

3
Overview

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Inc.

• Brief introduction on the new signals (L1C, L2C,
  and L5)
• How does modulation affect the smallest RMS code
  tracking error?
• Phase Shift Keying (PSK) or Binary Phase Shift
  Keying (BPSK) spreading modulation
• C/A code modulation
• Binary Offset Coding (BOC) modulation
• BOC(1,1) suggested for L1C, L2C, and L5

4
Overview Cont.

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Inc.

• Variable Binary Offset Coding Modulation VBOC
• VBOC(2,1,a) as a possible candidate for
  TMBOC(6,1,4/33)
• a coefficient of variability
• We present an intuitive approach for computing a
• The formal approach will be presented in our
  journal paper version?
• Summary and Conclusions

5
Brief Introduction

Giftet
Inc.

• Global Positioning System (GPS) consists of three
  segments
• Satellite segment all the GPS satellites which
  transmit at L1 and L2
• Control segment monitoring stations
• User segment all the GPS receivers.
• The Original GPS was unable to provide users with
  required capabilities of todays needs in
• Position, velocity, and timing accuracy
• Worldwide and especially indoors, underground,
  and underwater.
• Improvements in all aspects of GPS are necessary
• For added GNSS user benefits worldwide

6
Brief Introduction

Giftet
Inc.

• The list of required improvements on GPS is very
  long
• It is a process that will span in decades
• Phase IModernization
• Phase IIGPS III
• Highlight some of the improvements that have
  occurred in the past decade (or Phase
  IModernization)
• First improvements occur in mid 1990s
• May 2000 SA turned off (or set to zero) new era
  of GPS modernization
• In 2005 the transmission of the L2C
  begunIIR-14(M) satellite
• L5 will be transmitted in the IIF satellites

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Brief Introduction Cont.

Giftet
Inc.

• Highlight some of the improvements that will
  occur in the next decade (or Phase IIGPS III)
• Next generation of the satellites and the new L1C
  signal
• Modernizer control segment (OCX)
• Interoperability with Galileo Open Service Signal
• Virtually seamless interoperability with signals
  from Japans Quazi-Zenith Satellite System (QZSS)
• Lets consider next some of the unique
  opportunities of the L1C signal

8
L1C Signal Opportunities

Giftet
Inc.

• L1 center frequency--
• These opportunities are well understood and there
  is anything we can add or subtract here
• Advancements in signal design knowledge (expand
  this part further)
• There is room for further improvements in this
  area
• Advancements in statistical receiver signal
  processing
• There is room for further improvements in this
  area.
• Developments in circuit technologies
• There is room for further improvements in this
  area.
• Supporting communications services
• There is room for further improvements in this
  area.

9
L1C Signal Design Knowledge

Giftet
Inc.

• Signal structure
• Signals spreading codes and overlay codes
• Spreading modulation (Topic of our paper)
• TMBOC, MBOC or VBOC or TMVBOC?
• Message structure and encoding and decoding of
  message information
• IS-GPS-800 provides the complete description of
  these aspects of the new L1C signal.

10
PSK-R Spreading Modulation

Giftet
Inc.

• Binary Phase Shift Keying (BPSK) or Phase Shift
  Keying with rectangular spreading symbols (PSK-R)
• Currently used in the L1 C/A code
• Phase transition at a C/A code rate _at_ 1.023 MHz
  or the chipping period of 1/1.023 ms
• Autocorrelation function on the right

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PSK-R Spreading Modulation Cont.

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Inc.
The power spectral density (PSD) of the
autocorrelation function can be used to make
accurate calculation of the effective bandwidth
of the signal.
2 MHz
10 MHz
20 MHz
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The Smallest RMS Code Tracking Error PSK-R
Spreading Modulation

Giftet
Inc.

• Assuming that the loop bandwidth is BL 1 Hz
• Carrier to Noise ratio is 30 dB
• No multipath
• The smallest RMS code-tracking error that can be
  achieved in white noise for the C/A code (or
  PSK-R or BPSK) signal
• 12.25 cm for signal bandwidth of Br 2 MHz
• 5.48 cm for signal bandwidth of Br 10 MHz
• 3.54 cm for signal bandwidth of Br 20 MHz
• An increase of the effective bandwidth by a
  factor of 10 gives only a decrease of the RMS
  code-tracking error by a factor of 3.46

13
Binary Offset Carrier or BOC(1,1) Spreading
Modulation

Giftet
Inc.

• BOC modulation was designed specifically to
  outperform the PSK-R modulation while using the
  same or even less bandwidth while at the same
  time using simpler transmitter and receiver
  designs.
• We will consider only the expression of the
  BOC(1,1) autocorrelation function and then its
  power spectral density to enable similar
  calculations of the RMS code-tracking error.

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BOC(1,1) Spreading Modulation Cont.

Giftet
Inc.
The power spectral density (PSD) of the
autocorrelation function can be used to make
accurate calculation of the effective bandwidth
of the signal.
2 MHz
10 MHz
20 MHz
15
The Smallest RMS Code Tracking Error BOC(1,1)
Spreading Modulation

Giftet
Inc.

• Assuming that the loop bandwidth is BL 1 Hz
• Carrier to Noise ratio is 30 dB
• No multipath
• The smallest RMS code-tracking error that can be
  achieved in white noise for the BOC(1,1) code
  signal
• 7.07 cm for signal bandwidth of Br 2 MHz
• 3.16 cm for signal bandwidth of Br 10 MHz
• 2.04 cm for signal bandwidth of Br 20 MHz
• An increase of the effective bandwidth by a
  factor of 10 gives only a decrease of the RMS
  code-tracking error by a factor of 3.46

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BOC(1,1) vs PSK-R

Giftet
Inc.

• At 2 MHz the RMS code tracking error for the
  BOC(1,1) is only 57.7 of the RMS code tracking
  error for the PSK-R signal.
• And the same result is true also for the RMS code
  tracking error for the BOC(1,1) at 10 and 20 MHz,
  which means that BOC(1,1) modulation enables more
  efficient spectrum utilization than the PSK-R
  modulation.
• We have added additional minor complexity on the
  transmitter and receiver design which is fine.

17
VBOC(2,1,a) Spreading Modulation

Giftet
Inc.

• An increase of the sub-carrier frequency by a
  factor of 2 or BOC(2,1) would logically result in
  an increase of the bandwidth utilization and in a
  decrease of the RMS code tracking error.
• Changing the transition reduces the out of phase
  autocorrelation peaks!

Blue a 0.2 Green a 0.1 Pink a 0.05
18
VBOC(2,1,a) Spreading Modulation Cont.

Giftet
Inc.
The power spectral density (PSD) of the
autocorrelation function can be used to make
accurate calculation of the effective bandwidth
of the signal.
2 MHz
10 MHz
20 MHz
Blue a 0.2 Green a 0.1 Pink a 0.05
19
The Smallest RMS Code Tracking Error VBOC(2,1,a)
Spreading Modulation

Giftet
Inc.

• Assuming that the loop bandwidth is BL 1 Hz
• Carrier to Noise ratio is 30 dB
• No multipath
• The smallest RMS code-tracking error that can be
  achieved in white noise for the VBOC(2,1,a) code
  signal
• 6.12 cm (a 0.2), 8.33 cm (a 0.1), 9.82 cm (a
  0.05) for signal bandwidth of Br 2 MHz
• 2.74 cm (a 0.2), 2.66 cm (a 0.1), 2.73 cm (a
  0.05) for signal bandwidth of Br 10 MHz
• An increase of the effective bandwidth by a
  factor of 5 gives only a decrease of the RMS
  code-tracking error by a factor of 2.23, 3.13 and
  3.6

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The Smallest RMS Code Tracking Error VBOC(2,1,a)
Spreading Modulation Cont.

Giftet
Inc.

• 1.94 cm (a 0.2), 1.89 cm (a 0.1), 1.91 cm (a
  0.05) cm for signal bandwidth of Br 20 MHz
• An increase of the effective bandwidth by a
  factor of 2 gives only a decrease of the RMS
  code-tracking error by a factor of 1.412, 1.407!!
  1.43
• Although this is a little empirical procedure for
  finding a the formal derivation for computing a
  and with the rational will be provided in our
  journal version of the paper.

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VBOC(2,1,a) vs BOC(1,1)

Giftet
Inc.

• The added benefit of the new modulation is on the
  user bandwidths of 10 MHz and higher.
• However, it remains to calculate the RMS code
  tracking error in the presence of multipath.
• However, VBOC(2,1,a) offers slightly more
  complexity in implementation than BOC(1,1)

22

Giftet
Inc.
23

Giftet
Inc.
VBOC(2,1,0.1) offers the same pick sharpness as
TMBOC(6,1,4/33)
A multiplexed version of VBOC(2,1,0.1) could
reduce the out of phase peaks even further!!
24

Giftet
Inc.
VBOC(2,1,0.1) has a much better spectrum
utilization than BOC(1,1) or PSK-R!!
10 MHz
25
Summary

Giftet
Inc.

• In summary we have revisited the spreading
  modulation techniques so far employed in the GNSS
  signals namely the PSK-R (or BPSK) and BOC(1,1)
• We have proposed a VBOC(2,1,a) signal which is a
  version of the BOC signal but with a variable
  transition of the binary offset signal.
• It appears that VBOC(2,1,0.1) could be a better
  candidate than the currently suggested
  TMBOC(6,1,4/33) (see 2) because it achieves
  similar main autocorrelation peak as the smaller
  out of phase autocorrelation peaks.

26
Summary Future Work

Giftet
Inc.

• If we assume a 20 MHz signal bandwidth for
  processing then the smallest RMS code tracking
  error is 1.89 cm.
• In the future, GNSS receivers with wide effective
  bandwidth will be preferred to enable more
  sophisticated signal processing on the receiver
  therefore, VBOC(2,1,0.1) would be the preferred
  modulation.
• A time multiplexed version of VBOC(2,1,a) could
  be a better candidate than VBOC(2,1,a) itself.
• It remains to perform these studies in the
  presence of multipath. We suspect that similar
  computation performance will be obtained in the
  presence of multipath.

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Giftet Inc.

• Giftet is a privately held company for
  developing, marketing, and distributing global
  navigation, software, and web solutions for
  Indoor Geolocation Systems, GPS, GLONASS,
  Galileo, QZSS, and other Global Satellite and/or
  Pseudolite Navigation (or Positioning and/or
  Timing) Systems based on customers needs.
• Giftet philosophy is based on partnership!
• Giftet welcomes partnership!
• Giftet was founded on December 26, 2006, Pomona,
  CA.
• http//www.giftet.com/