From GPS Satellite to Observable How JPLs Occultation Receiver Works

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From GPS Satellite to Observable How JPLs
Occultation Receiver Works

• Larry E. Young
• NCAR COSMIC Colloquium
• 6/21/2004

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Introduction

• GPS link budget
• Topics in digital sampling
• GPS signal structure
• Receiver operation
• System noise errors
• Codeless/code-enhanced processing

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Link Budget (simplified, very approximate)

• Transmit 20 W onto hemisphere of earth
• Power density 20 W/(2PI(6.378E6m)2)
• 7.8E-14 W/m2
• Antenna effective area given by
• G 4PI/(?2) Ae
• For G 1(omnidirectional), ? 0.19 m, Ae 0.003
  m2
• Received signal power is
• Ps power density antenna effective area
• 7.8E-14 W/m2 0.003 m2
• 2.4E-16 W
• assume even power over hemisphere, receive gain
  1, ignore receiver processing loss

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Noise power

• Receiver noise comes primarily from preamplifier
  noise and noise radiated into antenna
• Noise characterized by equivalent black body
  temperature, typical 250 K
• Noise power kTb
• K is the Boltzman constant, 1.38E-23 W/Kelvin/Hz
• B is the sampled bandwidth 20E6 Hz
• Noise 1.38E-23 W/K/Hz 250K 20E6 Hz
• 6.9E-14 W

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SNR

• One sample SNR 2.4E-16 W / 6.9E-14 W
• 3.5E-3 (pretty low!)
• P V2/R, so SNRv sqrt(SNR)
• One sample SNRv 5.9E-2
• Still low, but wait, there are 20.456E6
  samples/sec actually 40.912E6, including real
  and imaginary

Signal , 1 sample
Quadrature
Noise , 1 sample
In phase
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SNR (cont)

• Since signal adds coherently, and noise adds as a
  random walk,
• S samples s
• N sqrt(samples ) n
• 1-sec SNRv 1-sample SNRv sqrt(samples /sec)
• 1-sec SNRv 5.9E-2 sqrt(20.456E6)
• 268

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One-bit sampling

• Signal
• 1-bit quantized signal
• Myth One-bit sampling does not provide
  information on signal amplitude.

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One-bit sampling (contd)

• Signal with noise
• 1-bit quantized signal
• average of many samples
• Fact With help of noise, ensemble average of
  one-bit samples gives signal amplitude.

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More one-bit sampling

• Myth There is a quantization error of 1/sample
  rate. If the signal moves less than 1 sample,
  there is no difference in the samples.
• Signal and delayed signal
• showing sample epochs
• Sampled data

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More one-bit sampling

• Fact There can be negligible quantization error
  if the sample rate is chosen to be incommensurate
  with the signal. Noise also helps!
• Signal and delayed signal
• showing sample epochs
• Sampled data (After 0.02 s
• Quantization error is only about
• 1E-6 cycles)

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GPS Signals

• CA D(t)CA(t)cos (F1t)
• D(T) is either 1 or 1, and carries data on
  satellite location, etc, at 50 bits/sec
• CA(t) is a ranging code that has a 50-
  probability of changing between 1 and 1 at
  1.023E6 Hz, T 977 E-9 seconds (977 ns).
• F1 carrier is 1575.42 MHz, T 0.635 ns

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Signals (contd)

• Y1 D(t)P(t)A(t)cos (F1t)
• P(t) is a known ranging code at 10.23E6 Hz, T
  97.7 ns
• A(t) is an encryption code at about 5E5 Hz
  (sequence and exact frequency classified)
• Y2 D(t)P(t)A(t)cos (F2t)
• Same as Y1 except F2 carrier is 1227.60 MHz, T
  0.815 ns

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Signals Pseudorange vs Carrier Phase

• Pseudorange is like a meter stick with labeled
  marks each meter, can measure range with 0.1
  meter accuracy.
• Carrier phase is like a measuring stick with cm
  and mm marks labeled, but no labels on meters,
  ie, precise but with146/14/0414 meter-level
  ambiguity

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Signals (contd)

• Pseudorange
• When I sent this signal, I was located at X,Y,Z
  and my clock read Ts
• Received signal is tagged with Tr per receiver
  clock.
• Pseudorange is defined as
• PR Tr-Ts and is R/c (Tsat-Trcvr)
• Tsat and Trcvr are the satellite and receiver
  clock offsets

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Receiver front end, antenna to ASIC
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Aliasing Downconversion
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Nyquist sampling

• This does not violate the Nyquist sampling
  theorem.
• Nyquist says the sample rate must be twice the
  signal bandwidth, not twice the RF frequency

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Antenna to ASIC
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Through the ASIC, and beyond
Sums are over 0.020 sec data bit
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Receiver correlator amplitude vs delay (lag)
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Pseudorange observable

• P1 total observable
• Residual P1 (signal - model)
• (E-L)/2 1 chip/P
• Assumes P is at peak of triangle
• P1 obs res P1 model delay
• (signal - model) model
• signal delay
• Note that total observable is not affected by
  model error

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Pseudorange error (excluding multipath, )

• P1 (E-L)/2 1 chip/P
• Use ??????? (f(xi) SUM (d f(xi )/d xi sigma
  xi 2
• P1 error sqrt2/2 1 chip/P N
• Recognize P/N are the signal/noise amplitudes, so
• P1 error 0.7 chip/SNRv
• Remember the 1-s SNRv 268,
• P1 error (1-sec) 0.729.3 m/268
• 0.08 m

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Phasor diagram
Q
Signal amplitude
Quadrature correlator value
Residual phase
I
In phase correlator value
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Carrier Phase observable

• Phase total observable
• Res ph (signal - model) arctan (Q/I)
• Phase obs res ph model phase
• (signal - model) model
• signal phase
• Note that model error cancels in total
  observable. Data rate not a function of tracking
  loop BW. No steady-state tracking error.

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Phase error
Q
noise
Quadrature correlator value
signal
phase error N/S in radians radians/SNRv
cycles/(2PISNRv) ?/(2PISNRv)
I
In phase correlator value
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One second carrier observable error (excluding
multipath, )

• Error in radians noise/signal
• Error in m ?/(2PISNRv)
• Use 1-sec SNRv 268,
• L1 ? 3E8 m/sec/1.57542E9cy/sec
• 0.190 m/cy
• 1-sec phase error 190 mm/(2PI268)
• 0.1 mm

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Three important times

• Receiver clock offset
• Maps one to one into pseudorange
• Solved for in processing
• Blackjack steers clock to GPS time
• Data time tag error
• Data collection interval

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Three important times(contd)

• Receiver clock offset
• Data time tag error
• Model error tt error range rate,
• For example 10 us 7,000 m/s gt 7 cm error
• Blackjack assigns time tags very precisely
• Data collection interval

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Three important times(contd)

• Receiver clock offset
• Data time tag error
• Data collection interval
• If differs between satellites, receiver clock
  error is not exactly common
• Blackjack maximizes overlap, to /- 0.01 sec
• In the case of high-rate occultation data, can
  differ by 1/2 interval
• This is the source of the CHAMP 1-sec clock
  glitch

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Model feedback loops
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Carrier smoothed pseudorange
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Codeless
P1 data
To P1 accumulator
Code operation
P1 model
P2 data
To P2 accumulator
P2 model
Encrypted P1 data
To P1-P2 accumulator
Codeless operation
No P1 model
Encrypted P2 data (Looks like noisy P1
model Delayed by ionosphere)
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Penalty of Codeless (contd)

• In previous slide, replaced multiply by model
  with multiply by P2 data
• Since 1-sample SNRv 0.06, SNR is reduced by
  this factor, so 1-sec SNRv goes from 268 to 16
• HELP!

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One enhanced codeless technique

• Remember encrypted code
• Y1 D(t)P(t)A(t)cos (F1t)
• The Trick
• Since A(t) is 5E5 chips/sec, A(t) Y2xP2
  model can be integrated over 1 A-chip, 40
  samples, reducing SNR loss from 0.06 to
  0.06sqrt(40) 0.38, an SNRv gain of 6.3 (16 dB)

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Conclusion

• It tracks GPS CA, Y1, and Y2 signals
• It reports phase, range, SNR for each signal
• It schedules high-rate output for limb-sounding
  signals
• Any questions on how the occultation receiver
  works?