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Performance Prediction and Verification for Bistatic SAR
Synchronization Link
Marwan Younis, Robert Metzig, Gerhard Krieger
German Aerospace Center (DLR), Microwaves and Radar Institute
Rainer Klein
EADS Astrium GmbH, Microwave Engineering & Technologies
Abstract
The paper describes the configuration of a synchronization link sharing hardware components with the SAR instrument.
Such a system is intended for the TanDEMX mission. The resulting restrictions on the phase synchronization scheme,
timing, and accuracy are investigated. The statistical properties of the phase compensation signal are used to derive a
figureofmerit for synchronization performance. The focus is on the influence of the synchronization link RF hardware
on the quality of the derived compensation signal. A system model taking the various influence factors into account is
described. The system model is parameterized using statistical analysis from measurement data.
1Introduction
Bistatic SAR systems have a high potential for scientific,
commercial and security applications. One of the bene
fits is the possibility to generate highly accurate digital
elevation models using bistatic interferometry. Examples
for proposed bi and multistatic satellite missions with in
terferometric capabilities are TanDEMX and Cartwheel.
Both are based on radar instruments placed on different
spacecrafts, which gives rise to several technical chal
lenges for the system realization.
A factor which may severely degrade the performance of
a bistatic SAR is the phase instability of the two oscil
lators involved. Investigations have shown [1], that, un
less highly stable oscillators are used, the oscillators phase
noisehastobecompensatedbyestablishingasynchroniza
tion link to directly exchange signals providing informa
tion on the oscillator phase noise. The method is based on
recordingthe receiveddemodulatedphases, whichare then
used to derive a compensation signal to correct the SAR
data. The paper describes the synchronization as intended
for implementation in TanDEMX [2].
2Synchronization Scheme
For TanDEMX synchronization each satellite repeatedly
transmits a pulsed synchronization signal, however, there
is a time delay between the transmit instances of the
TerraSARX and TanDEMX satellite, thus the synchro
nization is also alternate. A parameterized timing diagram
is shown in Figure 1. At time t satellite 1 transmits the
synchronization signal of duration Tp, which is received
τ12seconds later by satellite 2. Similarly, after an internal
system delay of τsys, satellite 2 transmits its synchroniza
tion signal at t+τsys, which is received by satellite 1 with
a delay corresponding to the signal travel time τ21. This
procedure is repeated at the synchronization rate fsyn. The
synchronization lasts over the data take time Tdata.
t
t
Sat 1
Sat 2
t
Tp
?12
?21
?sys
t+?sys
1/fsyn
?
Sat 1Tx
?
Sat 2Rx
?
Sat 2Tx
?
Sat 1Rx
Figure 1: Timing diagram for the exchange of synchro
nization pulses.
3Synchronization System Model
The contribution of the oscillator phase noise to the SAR
signal phase error can be compensated by establishing a
method of phase referencing. In the following a mathe
matical model is established, which is later used as a basis
for deriving quantitative estimates for the performance of
the synchronization link.
3.1 Oscillator Signal Phase
Satellite i transmits a synchronization signal, which is re
ceived by satellite j, where i,j ∈ {1,2}. The frequencyof
oscillator i at start of data take t0is fi= f0+ ∆fi, with
the nominal frequency f0, and a constant frequency off
set ∆fi. The phase ϕi(t) at time t is the integration over
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frequency:
ϕi(t) = 2π
t
?
t0
fi(t)dt + ϕinii+ nϕi(t)
(1)
with the initial —time independent— phase ϕinii, and the
oscillators phase noise1nϕi(t) [3].
At the receive instance t + τij the phase ϕj(t + τij) of
oscillator j is:
ϕj(t+τij) = 2π
t+τij
?
t0
fj(t)dt+ϕinij+nϕj(t+τij) (2)
The demodulated phase ϕji(t) available at satellite j for a
signal transmitted by satellite i is the difference between
(2) and (1) after including the system and path contribu
tions. The data take start time t0can be set to zero with
out restricting generality. The phase differencesϕji(t) and
ϕij(t) are used to obtain the compensation phase.
3.2Compensation Phase
The compensation phase ϕc(t) is difference:
ϕc(t) =1
2
?ϕ21(t) − ϕ12(t)?
(3)
where ϕ21(t) and ϕ12(t) are the demodulated phases of
the synchronization signals recorded by satellite 2 and 1,
respectively.
The advantage of using the phase difference —the com
pensation phase is actually the differenceof the difference,
since the phases ϕ12(t) and ϕ21(t) already represent a
phase difference— is that the antenna, link path, and all
common Tx/Rx system phase variations will cancel out as
long as their contribution do not change within the time a
pair of synchronization signals are exchanged. The com
pensation phase can then be used to correct the time vary
ing oscillator phase noise errors and the frequency offset
of the SAR signal.
3.3Approach and Definition of Terms
The basic idea behind phase synchronization is to deter
mine the phase noise and frequency offset differences in
(2) and (1). Thus, the phase noise, described through its
spectral density is the useful, i.e. “wanted”, quantity. The
phase spectrum Sϕ(f), at oscillator frequency fosc, is de
scribed analytically by a linear superposition of five dif
ferent frequency components according to [3]. At nominal
upconverted RF frequency f0the valid phase noise spec
tral density is given by γ2Sϕ(f), where γ is the ratio of RF
to oscillator frequency γ = f0/fosc.
A general signal flow block diagram is shown in Figure 2
for a priori phase correction, i.e. before SAR focusing.
Several factors will influence the phase of the synchro
nization link as shown in the lower signal path in the fig
ure. Here the transfer function HLP(f) describes the ef
fect of alternate pulse synchronization. The receiver noise
ϕSNR(t) determined by the signaltonoise ratio SNR is
of special interest; its influence on the signal phase is de
scribed by the receiver phase noise spectral density func
tion SϕSNR(f). The hardware system error is represented
ϕsys(t). Further, for pulsed synchronization the phase is
sampled, which requires a later interpolation of the com
pensationphase. We maychoosetofilter thecompensation
phase with an —arbitrary—transfer function Hsyn(f). Fi
nally the compensated SAR phase (SAR phase after sub
tracting the compensationphase) is filtered through the az
imuth compression. This filter is described through the
transfer function Haz(f) and is dependent on the azimuth
processing [1].
+
Hsyn(f)
HLP(f)

fsyn
interpolation sync filtersampling
alternate
sync.
comp. phase
SAR phase
?SNR(t)
?
?(t)
?link
2
Haz(f)
azimuth
compression
+
?sys(t)
Figure 2: Synchronization and SAR signal flow diagram.
The performanceof the synchronizationlink is determined
by the quality of the phase noise reconstruction.
figureofmerit is the phase variance σ2
ing the oscillator phase noise and performing the azimuth
compression (see Figure 2). The link phase error, i.e. the
residual contribution to the synchronized SAR, is repre
sented by the standard deviation (STD) σlink.
Note that according to the above model, the SAR transfer
function Haz(f) is applied on the signal’s phase instead of
the signal itself. It can be shown that this is valid —from
thesynchronizationpointofview, wherethe SAR focusing
is understoodas anaveragingprocess—forsmallvaluesof
the residual phase error σlink.
The
linkafter subtract
4Synchronization Performance
In the following the link phase error is given for the syn
chronization scheme in section 2 including the error con
tributions resulting from the synchronization link itself as
describedin the model of section 3.3. The results are given
for an Xband radar with f0 = 9.65GHz using an oscil
lator similar in performance to the TanDEMX oscillator.
Ionospheric effects are negligible for this frequency range
and satellite separations in the order of a few 100 meters.
The compensation phase according to (3) is com
puted at discrete time instances tk
=k/fsyn for
1It is irrelevant whether fiis the oscillator frequency or the upconverted RF frequency as long as the representation of the oscillator phase noise is
consistent. Consequently the term oscillator phase noise identifies the phase noise originating from the oscillator without specifying the frequency.
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k = 0,1,...?Tdata·fsyn? with ?Tdata·fsyn? the total
number of synchronization pulses during data take. Using
(1) and (2) the compensation phase is:
ϕc(tk) =
1
2
?ϕSNR1(tk+ τ + τsys) − ϕSNR2(tk+ τ)?
+ π(∆f2− ∆f1)·(τ + τsys+ 2tk) − πfDτsys
+ ∆ϕsys1(tk,τsys+ τ) − ∆ϕsys2(tk,τsys)
+ nϕ2(tk+ τ) + nϕ2(tk+ τsys)
− nϕ1(tk+ τ + τsys) − nϕ1(tk)
(4)
the first line in the above expression is the phase varia
tion due to receiver noise ϕSNR. The second line con
tains the frequencyoffset and the Doppler terms. Here, the
frequency offset term 2π(∆f2− ∆f1)tkresults in a lin
ear phase ramp, which can be extracted to correct the fre
quency offset error of the SAR signal; consequently this
term is neglected for the further analysis. The third line
representsthe phase introducedby the transmit and receive
hardware system of the two satellites. The last two lines in
(4) represent the wanted phase noise compensation terms.
Doppler Phase
The Doppler phenomenon, with the Doppler frequency
fD= f0vsat/c0due to the relative velocity vsatbetween
the two satellites, manifests itself for alternate synchro
nization pulses, because of the unequal signal travel times
τ12?= τ21due to the changingsatellite separationbetween
the transmit instances tk and tk+ τsys. However, the
Doppler phase contribution is constant for constant vsat.
Only a relative satellite acceleration, i.e. a time dependent
vsat(t) will cause a phase error. For severe intersatellite
acceleration a Doppler phase compensation is necessary
which requires the satellite separation to be known.
Receiver Noise
The receiver noise, consisting of thermal noise and the
noise collected by the antenna, will introduce both ampli
tude and phase fluctuation to the synchronization signal.
Here, the phase variations described by their spectral den
sity function are of interest. For band limited white Gaus
sian noise the spectral density function SϕSNR(f) is related
to the SNR through [4]:
SϕSNR(f) =
1
2Bw·SNR
(5)
with the receiver (noise) bandwidth Bw.
The signaltonoise ratio is improved through the azimuth
compression where the compensated SAR signal is aver
aged over a period Ta, which is equivalent to a lowpass
filter Haz(f). The receiver noise variance then is:
1
2σ2
SNR=
1
4fsyn·SNR
fsyn/2
?
−fsyn/2
Hsyn(f)Haz(f)2df (6)
where uncorrelated noise and equal SNR values are as
sumed for both receivers.
Hardware System Error
The phase of the hardware system, dominated by active
and passive radar RF components, will change within the
duration of data take. Concerning the performance of the
synchronization link, all the contributions from compo
nents common to the Tx and Rx path will cancel out, due
to two way operation [5]. The remaining phase drift con
tributions are given in (4) by
∆ϕsys1(tk,τsys+ τ) − ∆ϕsys2(tk,τsys) =
+1
2
(7)
?ϕRx1(tk) − ϕTx1(tk)?−1
2
?ϕRx2(tk) − ϕTx2(tk)?
with the subscriptsRx,Txindicatingthe phase of the trans
mit or receive path, respectively. In the above expression,
the changein hardwarephase within the periodsτ andτsys
is ignored.
0100200300400500600
−1.5
−1
−0.5
0
0.5
1
time [s]
phase change [deg]
(a) phase variation ∆ϕsys1(tk)
0 100200300400500600
30
32
34
36
38
40
time [s]
temperature [°C]
(b) temperature variation
Figure 3: A measured phase variation of a single synchro
nization path and corresponding temperature variation of
the phase critical RF components for a 600s data take.
In Figure 3 an exemplary measured phase variation over
time is shown for one synchronization path (one system)
for a fsyn= 10Hz and a 100MHz chirp [6].
there is a correlation between temperature and phase vari
ation, which suggests using the recorded temperature data
to remove the systematic phase variation. However, even
without correction the maximum phase change (for the
given measurement) within the duration of a data take is
∆ϕsys1(tk) = +1
Clearly
2ϕRx1(tk) − ϕTx1(tk) = 0.39◦.
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Filter Effect on Sampled Phase Noise
From (4) it is recognized that each oscillator’s phase noise
is sampled at different time instances. This is equivalent to
a lowpass comb filter having the transfer function:
HLP(f) = exp(−jπfτsys)· cos(πfτsys)
(8)
Thus here the compensation phase will contain a lowpass
filtered oscillator noise, where the amount of attenuation
depends on the system delay τsys. This results in a filter
mismatch error σfiltgiven by [7]:
σ2
filt= 2γ2
fsyn/2
?
0
Sϕ(f)Haz(f)2·HLP(f)Hsyn(f)−12df
(9)
Interpolation Error
The interpolation error is because frequency components
outside the range −1
the sampling and hence can not be reconstructed. The in
terpolation variance is [1]
2fsyn < f < +1
2fsynare lost due to
σ2
int= 2γ2
∞
?
fsyn/2
Sϕ(f)Haz(f)2df,
(10)
Aliasing Error
This error results from the cyclic repetition of the spec
trum at integer multiples of the sampling frequency
fsyn;thus, frequency components outside the range
−1
spectrum causing the aliasing error with the variance [1, 7]
2fsyn< f < +1
2fsyn will be folded into the original
σ2
alias= 2γ2
∞
?
i=1
fsyn/2
?
−fsyn/2
Sϕ(f + i·fsyn)·
HLP(f + i·fsyn)Hsyn(f)Haz(f)2df
(11)
4.1Total Error
The total phase variance is the sum given by:
σ2
link=1
2σ2
SNR+ σ2
sys+ σ2
filt+ σ2
int+ σ2
alias
(12)
Figure 4 shows the interpolation, aliasing and receiver
noise contributions to the total phase error versus the syn
chronization rate calculated for the TanDEMX satellite.
Here τsysis adapted to the synchronization rate so as to
maximize the lowpass filter effect τsys= 1/2fsyn(in this
case the transmit instances of satellite 1 are interleaved
midway between those of satellite 2) in which case the
aliasing error is minimized.
Figure 4: Contributions to the link error versus the syn
chronization rate fsyn for SNR = 35dB, Ta = 0.5s,
τsys= 1/2fsyn, and HLP(f)Hsyn(f) = 1.
Acknowledgment
We would like to thank Martin Stangl, Uwe Schönfeldt,
and Harald Braubach from EADS Astrium GmbH for
their valuable support when performing the characteriza
tion measurements for TanDEMX.
References
[1] G. Krieger and M. Younis, “Impact of oscillator noise
in bistatic and multistatic SAR,” IEEE Geoscience
and Remote Sensing Letters, accepted for publication,
2006.
[2] H. Braubach and M. Volker, “Method for drift com
pensation with radar measurement with the aid of ref
erence radar signals,” U.S. Patent US 2005/0083225
A1, Apr. 21, 2005.
[3] J. Rutman, “Characterization of phase and frequency
instabilities in precision frequency sources: Fifteen
years of progress,” Proceedings of the IEEE, vol. 66,
no. 9, pp. 1048–1074,Sept. 1978.
[4] F. G. Stremler, Introduction to Communication Sys
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[5] M. Younis, G. Krieger, R. Metzig, and M. Werner,
“TanDEMX bistatic synchronization system per
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and Radar Institute, Tech. Note TDXTNDLR1102,
Sept. 2005.
[6] R. Metzig, M. Younis, M. Zink, and M. Werner,
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onground tests,” German Aerospace Center, Mi
crowaves and Radar Institute, Tech. Note TXSEC
TN4206, Oct. 2005.
[7] M. Younis, R. Metzig, and G. Krieger, “Performance
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