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)