Carrier Phase Two-Way Satellite Frequency Transfer (TWCP)
Miho Fujieda
National Institute of Information and Communications Technology (NICT)
APMP TCTF workshop 9/19/2014
- Motivation
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
Motivation
For intercontinental transfer, frequency link via satellite is still necessary, especially for island country, Japan.
10-18
10-17
10-16
10-15
10-14
10-13
100 101 102 103 104 105
周波
数安
定度
平均化時間 [s]Averaging time [s]
Alla
n d
evia
tion
Our target
Our target: improvement of transfer stability of TWSTFT in the 10-16 level
Expected precision
Use of carrier phase is one of ways to improve the measurement precision.
Method Precision [ns] Rate/Frequency [MHz]
GPS code 5 1.023
GPS carrier phase 0.05 1575.42
TWSTFT code 0.5 2.5
TWSTFT carrier phase
0.005 ? 11000 ~ 14500
Brief measurement precision
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
History
ETS-VIII experiment at NICT2
First experiment by USNO and Timetech1
1 B. Fonville et al., Proc of PTTI meeting 149 (2004). 2 F. Nakagawa et al., Metrologia 50 200-207 (2013). 3 M. Fujieda et al., IEEE TUFFC 59 12 2625 (2012). 4 M. Fujieda et al., Metrologia 51 253-262 (2014).
NMIJ OP
Short-baseline3
Long-baseline4
TWCP: A technique established recently
ωs ωu ωd
ωu, ωd : uplink, downlink frequencies
ωs : local frequency at satellite
Earth station A Earth station B
Communication satellite
What is problem for TWCP?
Phase jitter: induced by onboard oscillator in down-conversion
USNO’s proposal: Mathematical solution by using four signals (A->A, A->B, B->A, B->B)
- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
What tools are necessary for TWCP?
Name Lab
NICT modem (discontinued) NICT
SATRE modem USNO, OP
Arbitrary Waveform Generator (AWG) NICT
*Signal generation (Tx)
Name Lab
SATRE modem USNO, OP
A/D sampler (vssp32) NICT
*Phase/Frequency detection (Rx)
Frequency converters should be locked to an external reference. Other instruments are identical to conventional TWSTFT (code phase).
Experimental apparatus for TWCP in NICT Setup of earth station
Power amp.
Low-noise amp.
Up converter
Down converter
Arbitrary waveform generator
A/D sampler
10MHz & 1pps
BPF
1.2-m/1.8-m/2.4-m antenna 99% OBW =
200 kHz
200-kHz signal for TWCP
Sampling : every 20 ms 50 points of 20-ms data
Least-square fit
1-sec data
Narrower bandwidth signal (200 kHz) for save satellite-link fee Slower chip rate signal (127.75 kcps) to help signal tracking
Name Specification
Sampling frequency
40 kHz ~ 64 MHz
Number of A/D bit
1, 2, 4, 8
Number of channels
4
External reference signals
5 or 10 MHz and 1 pps
A/D Sampler for phase detection
Name Specification
Sampling frequency 204.6 MHz
D/A bit 8
Number of channels 2
Waveform memory 512 kB x 2 /CH
Overlay memory 64 kB / CH
External reference signals 10 MHz and 1 pps
Arbitrary waveform generator
Arbitrary waveform generator(Right)
A/D sampler (Left)
A/D sampler and AWG
- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
Signal from station A at satellite:
Computation of time difference (1)
Sin(ωu’t+ωuτa(t))
= Sin(ωu (1 – va(t)/c)t + ωuτa(t))
Down-converted signal at satellite: Sin((ωu’-ωs)t+ωuτa(t) –ωsτs(t))
Received signal at station B:
v(t)/c ~1e-9 at GEO
Sin((ωu’-ωs)(1-vb(t)/c)t+ωuτa(t) –ωsτs(t)-ωdτb(t))
= Sin(ωdt + Φab(t))
Signal from station A: Sin(ωut+ωuτa(t))
(ωu’-ωs)(1-vb(t)/c)t = (ωu (1 – va(t)/c) -ωs) (1-vb(t)/c)t
= ωdt –ωuva(t)/c・t - ωdvb(t)/c・t + ωu・va(t)/c・vb(t)/c negligible
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c
ρas(t)
Time at station A: τa(t)
Radial velocity: va(t)
ωs ωu ωd
A B
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
Phase from station A to station B
ωu, ωd : uplink, downlink frequencies
ωs : local frequency at satellite
τa,τs,τb : time difference of local clock
ρas,ρbs : geometric distance between earth station and satellite
c : speed of light
Computation of time difference (2)
I ij: Ionosphere delay with frequency fi at station j [s]
Time difference:
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
Phase from station A to station B
Computation of time difference (3)
*Ionosphere delays: given by TEC map *Troposphere delay independent of frequency: canceled out on the way
Iij(t) = c・fi
2
40.3・TECj(t)
TECj(t): Total electron content at position j [1016 electrons/m2]
4 Unknown values: (τa – τb), τs, ρas, ρbs
4 equations
φab(t)=ωuτa(t)-ωsτs(t)-ωdτb(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIua(t)+ωdIdb(t)
1. Phase from station A to station B
φba(t)=ωuτb(t)-ωsτs(t)-ωdτa(t)-(ωuρas(t)+ωdρbs(t))/c +ωuIub(t)+ωdIda(t)
2. Phase from station B to station A
φaa(t)=ωuτa(t)-ωsτs(t)-ωdτa(t)-(ωuρas(t)+ωdρas(t))/c +ωuIua(t)+ωdIda(t)
3. Phase from station A to station A
φbb(t)=ωuτb(t)-ωsτs(t)-ωdτb(t)-(ωuρbs(t)+ωdρbs(t))/c +ωuIub(t)+ωdIdb(t)
4. Phase from station B to station B
Computation of time difference (4)
Time difference:
Target
φab(t)-φba(t)=(ωu+ωd)(τa(t)-τb(t))-(ωu-ωd)(ρas(t)-ρbs(t))/c +ωu(Iua(t) – Iub(t)) - ωd(Ida(t)-Idb(t))
1-2
φaa(t)-φbb(t)=(ωu-ωd)(τa(t)-τb(t))-(ωu+ωd)(ρas(t)-ρbs(t))/c +ωu(Iua(t) – Iub(t)) + ωd(Ida(t)-Idb(t))
3-4
Computation using 4 phase information
Calculation of time difference (5)
ω+
ω+ ω-
ω- x(t)
x(t) y(t)
y(t)
Time difference between station A and station B with ionosphere delay terms
τa(t)-τb(t) ω+x(t)-ω-y(t)
= ω+
2 –ω-2
x(t) = φab(t) - φba(t)
ω+ = ωu + ωd
y(t) = φaa(t) - φbb(t)
ω- = ωu - ωd
Calculation of time difference (6)
φab(t) ,φba(t), φaa(t), φbb(t) : Observed data
+ ω+
2 –ω-2
2ωuωd
[(IdA(t)-IuA(t))-(IdB(t)-IuB(t))]
- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
TWCP experiments in various-length baselines
*0 km Domestic, GE23@172°, free from stability of reference clocks *100-km Domestic (Tokyo-Kashima), GE23@172°, H-maser comparison *1000-km Domestic (Tokyo-Okinawa), GE23@172°, H-maser comparison *10000-km International (NICT-PTB), AM2@80°, UTC(k) or H-maser comparison
AM2@80° GE23@172° (now Eutelsat 172A)
NICT PTB
NICT-PTB TWCP experiment (2013/3 ~ 2013/6)
*Period: 2013/3/7~2013/6/30 *Satellite: AM2 @ 80E *Satellite transponder on-time: 10:05 h ~ 22:59 h in UTC *Elevation angles: 3.7° @PTB 16.0°@NICT
PTB 1.8-m antenna
@PTB
Special thanks to D. Piester, J. Becker, A. Bauch
AWG
AD sampler
Frequency converters
SSPA
LNA
TWCP stability in various-length baselines
10-16
10-15
10-14
10-13
100
101
102
103
104
105
106
0 km100 km
1000 km10000 km10000 km
Mo
difie
d A
llan
de
via
tio
n
Averaging time [s]
Short-term stability: Independent of baseline length
(2013/3/15)
(2013/3/7~4/1)
Due to H-maser
Due to Air-
conditioner
Comparison with GPS CP in 10000-km baseline
-552
-550
-548
-546
-544
-542
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
TWcodeGPSCP (300-s avg)TWCP (300-s avg)
Tim
e d
iffe
rence
[n
s]
MJD
-800
-600
-400
-200
0
200
400
600
800
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
GPSCP
TWCP
Fre
qu
ency d
iffe
ren
ce (
x 1
01
5)
MJD
300-s averageFiber transfer system failed.
Wo/ fiber link stabilization
1-s average, 300-s sampling
Phase ambiguity in TWCP: Filled by integral multiple of one period to agree with GPS CP
Result of TWCP: Consistent with GPS CP within the uncertainty of GPS CP
5 days
2 ns
2e-13
5 days
Comparison with GPS CP in 10000-km baseline
-552
-550
-548
-546
-544
-542
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
TWcodeGPSCP (300-s avg)TWCP (300-s avg)
Tim
e d
iffe
rence
[n
s]
MJD
-800
-600
-400
-200
0
200
400
600
800
56355 56360 56365 56370 56375 56380 56385
UTC(NICT)-UTC(PTB) via AM2
GPSCP
TWCP
Fre
qu
ency d
iffe
ren
ce (
x 1
01
5)
MJD
300-s averageFiber transfer system failed.
Wo/ fiber link stabilization
1-s average, 300-s sampling
Phase ambiguity in TWCP: Filled by integral multiple of one period to agree with GPS CP
Result of TWCP: Consistent with GPS CP within the uncertainty of GPS CP GPSCP-TWCP:(1.3±0.8)x10-15
standard error
5 days
2 ns
2e-13
5 days
10-16
10-15
10-14
102
103
104
105
106
GPSCPTWCPGPSCP-TWCP
Mo
difie
d A
llan
de
via
tio
n
Averaging time [s]
w/ gap
GPSCP-TWCP: 5e-16 @ 1 day
- Introduction & history
- Tools
- Equations
- Demonstration
- Error sources
- Summary and Future plans
Outline
1E-17
1E-16
1E-15
1E-14
1E-13
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6
Error sources (1) *Short term
Item Phase jitter [ps]
Frequency converters ~ 0.2
Instability by common-clock meas. Frequency converters updated.
via Eutelsat 172A
old
new
Averaging time [s]
Alla
n d
evia
tio
n
*Mid ~ Long term
Item Amplitude in time[ps]
Amplitude in Frequency
Compensation methods
Ionosphere ~ 300 ps 10-15~10-14
-Compensation using global ionosphere map -Average over 1 day
Troposphere A few ps < 10-16 -Not necessary at present
Sagnac effect < 20 ps (AM2, NICT-PTB)
< 10-15
-Calculation using orbit information
2nd order of Doppler shift
< 0.1 ps < 10-17 -Not necessary at present
Phase variation in instruments
A few ~ 200 ps < 10-13 -Temperature stabilization -Correction by measurement
Error sources (2)
Phase variation due to frequency converters
-1
-0.5
0
0.5
1
1.5
7 8 9 10 11 12
GPSCP, 120-sec avgTWCP, 1-sec avg
Tim
e d
iffe
rence
[n
s]
Day in 2012/12
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20
21
22
23
24
25
26
27
28
7 7.05 7.1 7.15 7.2 7.25 7.3 7.35 7.4
Tim
e d
iffe
rence
[n
s]
Indo
or te
mp
era
ture
[de
g C
]
Day in 2012/12
TWCP
Room temp.
10-15
10-14
10-13
100
101
102
103
104
105
106
TWCPGPSCP
MD
EV
Averaging time [s]
3x10-13@1 s
1 day
0.5 ns
0.15 ns / 1.5 ℃
H-maser comparison
Ionosphere delay correction using TEC map
TEC: Total Electron Contents Some TEC maps -Global ionosphere maps (GIM) ftp://ftp.unibe.ch/aiub/CODE
*Provided by the Center for Orbit Determination in Europe (CODE) *Time resolution: every 2 hours *Position resolution: 2.5°in latitude, 5.0°in longitude
-Japanese local TEC map http://wdc.nict.go.jp/IONO/gps-tec/tecv/
*Provided by NICT *Every 15 min. *2.0°in latitude, 2.0°in longitude
-European TEC map ftp://gnss.oma.be/gnss/products/IONEX/
*Provided by the Royal Observatory of Belgium (ROB) *Every 15 min. *0.5°in latitude, 0.5°in longitude
Iij(t) = c・fi
2
40.3・TECj(t)
Ionosphere delay effect in NICT-PTB link Ionosphere delay in NICT-PTB link computed using GIM
Elevation angle: 3.7°@PTB ⇒ Significant impact in TWCP
Ionosphere delay effect in NICT-PTB link Ionosphere delay in NICT-PTB link computed using GIM
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
10 11 12 13 14 15 16
GPS CP - TWCP: UTC(NICT)-UTC(PTB)
GPSCP-TWCPGPSCP-(TWCP w/ionosphere correction)Ionosphere correction
Do
uble
diffe
ren
ce [
ns]
Day in 2013/4
1-hour average
10-16
10-15
103
104
105
106
GPSCP-TWCP
wo/ correctionw/ correction
Mo
difie
d A
llan d
evia
tio
n
Averaging time [s]
The ionosphere effect was visible and the compensation using GIM was effective in NICT-PTB link.
3e-16
4/10~4/19
GPSCP-TWCP
1 day 0.05 ns
Optical clock comparison in NICT-PTB link
10-16
10-15
10-14
10-13
100
101
102
103
104
2013/6/26
Sr(PTB)-H8Sr(NICT)-H4H4-H8H4-H8 (all data)Sr(PTB)-Sr(NICT)
Alla
n d
evia
tio
n
Averaging time [s]
Final result: Sr(PTB) = Sr(NICT) ± 1.6e-15
TWCP instability was worse than that of common-clock measurement. Due to instrument’s phase variation, imperfect compensation of ionosphere delays?
Further study is necessary.
Summary
-TWCP is recently confirmed technique. -It has a measurement precision in the 10-13 level. -The precision is independent of the baseline length. -The result is consistent with GPSCP. Future plans for further study about the instability *24-hours measurement in 10000-km order link *Comparison of frequency standards
Thank you for your kind attention.
Global ionosphere maps (GIM) ftp://ftp.unibe.ch/aiub/CODE
*Provided by the Center for Orbit Determination in Europe (CODE) *Vertical total electron content (VTEC) *Time resolution: every 2 hours *Position resolution: 2.5°in latitude, 5.0°in longitude *Accuracy: 2~8 TECU [1016 electrons/m2] Ionosphere effect in TWSTFT: 40.3*(TECa-TECb)/c*(1/fu
2-1/fd2)
= 40.3*8 [TECU]/c*(1/fu2-1/fd
2)
~ 30 ps → 30 ps / 2/3600 ~ 4e-15
Ionosphere delay correction using global ionosphere map
VTEC 0,1 VTEC 1,1
VTEC 0,0 VTEC 1,0
VTEC(ti, j)
Time interpolation using VTEC(ti, j) and VTEC(ti+1, j)
Conversion from VTEC to slant TEC, along with signal path slant_TEC ~ VTEC/sinφ φ: elevation angle
φ
Iij(t) = c・fi
2
40.3・TECj(t)