Calibration of Spaceborne CTLR Compact Polarimetric Low-Frequency SAR Using Mixed Radar Calibrators

TL;DR: A novel algorithm for calibrating the circular-transmit-and-linear-receive mode spaceborne compact polarimetric SAR using mixed calibrators is proposed, which is able to correct precisely both FR and radar system errors.

Abstract: Spaceborne synthetic aperture radar (SAR) systems operating at lower frequencies, such as P-band, are significantly affected by Faraday rotation (FR) effects. A novel algorithm for calibrating the circular-transmit-and-linear-receive (CTLR) mode spaceborne compact polarimetric SAR using mixed calibrators is proposed, which is able to correct precisely both FR and radar system errors (i.e., channel imbalance and crosstalk). Six sets of mixed calibrators, consisting of both passive calibrators and polarimetric active radar calibrators (PARCs), are investigated. Theoretical analysis and simulations demonstrate that the optimal calibration scheme combines four polarimetric selective mixed calibrators, including two gridded trihedrals and two PARCs, together with total-electron-content measurements by the Global Navigation Satellite System system.

Summary

1. Yakkhaba, Yakkha and Yakthungba

• Kiranti languages are native to eastern Nepal and the western fringe of Sikkim.
• This subgrouping has been dubbed 'Eastern Kiranti' and comprises all Kiranti languages east of the Salpa watershed (van Driem, 1990b).
• Whereas a bindu or an orthographic half-nasal are transliterated as the corresponding nasal consonant, a candrabindu is transliterated as a tilde above the vowel.
• The dual suffix <-ci> or third person plural suffix < -mi >, both in sf3 of the Lohorung simplex.
• The language data themselves, however, unequivocally establish that the language is Yakkha and not Yak:khaba (Lohorung, Yamphe, Yamphu).

350 GEORGE VAN DRIEM

• Recorded by Gvozdanovic have been rearranged in an orderly fashion in the diagram above showing the affixes of the transitive paradigm, whereby the symbol I: represents the verb stem.
• When the recorded Yakkha forms have been shorn of this aspectivizer, an analysis of the remaining agreement morphemes yields the following possible analysis.
• The preterite suffix does not occur in 1-+ 2 forms which, if my hypothesis concerning the presence of aspectivizers in the elicited forms is correct, exhibit preterite/non-preterite homophony.
• The suffix occurs as a copy morph <-m> in suffixal slot 7 following the non-singular number morpheme of a third person patient < ci >.

352 GEORGE VAN DRIEM

• With a second person actant except where second person is indicated by the 1---+ 2 portemanteau morpheme.
• Following < -ga > in the suffixal string is a position occupied by the patient number morphemes <-ha> and < -na >.
• The suffix <-ha> marks non-singular patient number except in non-preterite ldi---+3ns forms.
• The resultant patterns of syncretism appear rather improbable: the ls---+2d, lde---+2s/2d and lpe---+2d forms are homophonous.

3. Synchrony and diachrony

• GvozdanoviC's explanations of Yakkha morphemes, each accompanied by an obfuscatory diagram, are-in a few cases--correct, if not lucid, e.g. her description of the 1---+ 2 morpheme < -nan >, and aspectivized < -metnan > ( Gvozdanovi6' s ' non past').
• Nonetheless Gvozdanovic should be lauded for making available the first substantive new data on a little known language in 80 years.
• Yakkha verbal agreement morphemes posterior to the position of the hypothetical second Proto-Kiranti auxiliary verb, AUX2 , also for the most part correspond in a straightforward way to the proto-morphemes of the Kiranti conjugation.
• The Yakkha second person plural ending <- i> appears to be cognate with the Proto-Kiranti inclusive marker *<-i>, which was reanalysed in Limbu as a first or second person plural patient/suffix morpheme, in Dumi as inclusive suffix, in Lohorung as a first person plural patient/subject marker, whereas the Bahing and Thulung reflexes express a first person plural inclusive actant.
• In view of this morpheme's tendency to develop along the lines of the meaning ' exclusive of person or persons addressed ', if indeed this is not its original Proto-Kiranti meaning, a reanalysis of the morpheme to yield a modern second person marker seems highly improbable.

4. Summary

• In conclusion, Gvozdanovi6's 'Yakkhaba' data are actually Yakkha data, which may imply that the Yakkha too call themselves or their language 'Yakkhaba '.
• The Yakkha data prompt Gvozdanovic to embark on speculations of a general linguistic nature which have no clear bearing on the data she presents.
• An alternative analysis of her data has been proposed here.
• The Yakkha verbal agreement system is very much of the canonical Kiranti type and snugly fits the model of the Proto-Kiranti verb.
• The only anomalous characteristics are the posterior patient number suffixes, < -na > and <-ha>, which may not be conjugational affixes, and the second person suffix < -ga >, which may be a recent accretion.

Figures

Fig. 4 Simulation of estimating cross-talk c amplitude (|f | = 1.5, arg{f} = /3, |1| = |2 |=0.1, arg{1}= arg{2}= arg{c}=0, = /4)

Fig. 5 Simulation of estimating cross-talk c phase (|f | = 1.5, arg{f} = /3, |1| = |2 |= 0.1, |c| =0.32, arg{1}= arg{2}= 0, = /4)

Fig. 3 Simulation of channel phase imbalance estimation (|f | = 1.5, |1| = |2 |= 0.1, |c| =0.32, arg{1}= arg{2}= arg{c}=0, = /4).

Fig. 2 Simulation of channel amplitude imbalance estimation (arg{f} = /3, |1| = |2 |= 0.1, |c| =0.32, arg{1}= arg{2}= arg{c}=0, = /4).

Fig. 8 Simulation of estimating cross-talk 2 amplitude (|f | = 1.5, arg{f} = /3, |1| = 0.1, |c| =0.32, arg{1}= arg{2}= arg{c}=0, = /4).

Fig. 6 Simulation of estimating cross-talk 1 amplitude (|f | = 1.5, arg{f} = /3, |2 |= 0.1, |c| =0.32, arg{1}= arg{2}= arg{c}=0, = /4).

Fig. 9 Simulation of estimating cross-talk 2 phase (|f | = 1.5, arg{f} = /3, |1| = |2 |= 0.1, |c| =0.32, arg{1}= arg{c}=0, = /4).

Fig. 14 SD of FR estimation error, amplitude an phase estimation errors of channel imbalance and cross-talks for Scheme 5 as a function of SNR, under the conditions of no APN error (i.e. = 0), and |f | = 1.5, arg{f} = /3, |1| = |2 | = 0.1, |c| = 0.32, arg{1} = arg{2} = arg{c}= 0, = /4. (a) FR estimation error; (b) amplitude errors of channel imbalance and cross-talks; (c) phase errors of channel imbalance and cross-talks.

Fig. 12 Comparison of estimated channel imbalance and cross-talk phase errors derived from (a) Scheme 5 and (b) Scheme 6 as a function of APN

Fig. 13 Comparison of the estimated FR errors from Schemes 5 and 6 as a function of (a) amplitude (arg{} = 0) and (b) APN phase (| | = -40dB),

Fig. 11 Comparison of estimated channel imbalance and cross-talk amplitude errors derived by (a) Scheme 5 and (b) Scheme 6 as a function of APN

Fig. 10 Simulation of the estimated FR error as a function of true FR angle, with |f | = 1.5, |1| = |2 |= 0.1, |c| =0.32, arg{1}= arg{2}= arg{c}=0, but different phase imbalance values: (a) arg{f} = /3, (b) arg{f} = 0.

TABLE II STATISTICAL ANALYSIS OF ESTIMATED FR ERRORS CORRESPONDING TO FIG.10 WITH DIFFERENT PHASE IMBALANCE VALUES

Fig. 1 The passive calibrators.

TABLE I STATISTICAL ANALYSIS OF AMPLITUDE AND PHASE ERRORS CORRESPONDING TO THE OPTIMAL CHANNEL IMBALANCE AND CROSS-TALK ESTIMATES IN FIGS.2-9

Full text

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Universities of Leeds, Sheffield and York
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This is an author produced version of a paper published in IEEE Transactions
on Geoscience and Remote Sensing.
White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/43175
Published paper
Chen, J., Quegan, S., Calibration of spaceborne CTLR compact polarimetric low-
frequency SAR using mixed radar calibrators, IEEE Transactions on Geoscience
and Remote Sensing, 49 (7), pp. 2712-2723
http://dx.doi.org/10.1109/TGRS.2011.2109065

1
Calibration of Spaceborne CTLR Compact
Polarimetric Low Frequency SAR Using Mixed
Radar Calibrators
Jie Chen
(1)
, Member, IEEE, Shaun Quegan
(2)
, Member, IEEE
(1) School of Electronic and Information Engineering, Beihang University (BUAA), Beijing, 100191, China
e-mail: chenjie@buaa.edu.cn; Jie.Chen@sheffield.ac.uk
(2) School of Mathematics and Statistics, University of Sheffield, Sheffield, S37RH, UK
e-mail: s.quegan@sheffield.ac.uk
Abstract—Spaceborne synthetic aperture radar (SAR) systems operating at lower
frequencies, such as P-band, are significantly affected by Faraday rotation (FR) effects. A novel
algorithm for calibrating the circular transmit and linear receive mode spaceborne compact
polarimetric SAR using mixed calibrators is proposed, which is able to correct precisely both FR
and radar system errors (i.e. channel imbalance and cross-talk). Six sets of mixed calibrators,
consisting of both passive calibrators and polarimetric active radar calibrators (PARCs), are
investigated. Theoretical analysis and simulations demonstrate that the optimal calibration
scheme combines four polarimetric selective mixed calibrators, including two gridded trihedrals
and two PARCs, together with total electron content measurements by the GNSS system.
Index Terms— Calibration, Faraday rotation, Ionosphere, Compact polarimetry, Synthetic
aperture radar (SAR).
I. INTRODUCTION
There is growing interest in deploying lower frequency spaceborne Synthetic Aperture Radars (SARs)
for monitoring of the Earth, such as the P-band BIOMASS mission to measure forest biomass [1],
which is currently under Phase-A study by the European Space Agency. However, the ionosphere can

2
significantly affect such systems; in particular, L- and P-band spaceborne SAR measurements will
suffer from Faraday rotation (FR) [1]–[4]. Furthermore, two conflicting factors often affect the design
of such systems, namely the need for frequent global coverage and the need to maximize information
content, which often requires polarimetric information. Full polarimetry (FP) suffers from reduced
swath width compared to SAR systems transmitting on a single polarization, thus increasing the time
needed for global coverage. As a result, there has been growing interest in the compact polarimetric (CP)
SAR mode [5]-[14], because, for a given swath width, it operates with reduced data rate, system power
and pulse repetition frequency compared to a FP system, while still allowing estimates of some of the
key polarimetric quantities.
The first system of this type, proposed by Souyris et al. [5], [6], used the /4 CP mode, which
transmits H+V (45
o
linearly polarized) and receives echoes in the H and V polarizations. However, such
a system could also be severely affected by FR [11]–[14]. A way to reduce the effects of FR was
suggested by Raney [8] when he introduced the hybrid mode (also called the /2 mode [11] or CTLR
mode [12]) which transmits on circular polarization and receives on the two linear (H, V) polarizations.
This is a promising approach, since circular polarizations are preserved under FR [6], [10], [12] and
[13]; hence the polarization of the incident wave would be undistorted and only FR effects on the return
signal would need to be corrected.
Freeman [14] developed a system model for CTLR mode compact polarimetry with FR. On the basis
of this model, this paper proposes a novel algorithm for calibrating the CTLR mode using both passive
and active calibration targets. After an introduction to the system model in Section II, the mathematical
analysis in Section III leads to a set of new calibration algorithms and an optimized set of calibrators.
Computer simulations presented in Section IV verify the effectiveness of the approach; these include
simulations accounting just for radar system errors and FR, and simulations that also take calibrator

3
errors into account.
II. SYSTEM MODEL FOR CTLR COMPACT POLARIMETRY
A. Faraday Rotation
When a polarized electromagnetic wave traverses the ionosphere, its interaction with free electrons
and the Earth’s magnetic field leads to rotation of the polarization vector [4], [15]. This phenomenon is
known as Faraday rotation. The one-way FR for a SAR signal can be approximated as [15]

TECseccos
400
2
0


B
f
K
(1)
where f
0
is the carrier frequency in Hz, K is a constant of value 2.36510
4
[Am
2
/kg], B is the magnetic
flux density in Wb/m
2
, and

and

are the angles the wave-normal makes with the Earth’s magnetic
field and the downward vertical, respectively. TEC is the total electron content in TEC units (1 TECU =
10
16
electrons m
-2
). The “magnetic field factor”,


400
seccos



B
, is calculated at a height of 400 km.
B. System Model
We assume a CTLR mode SAR system that transmits right-circular polarization chirps and receives
linear (H, V) polarization echoes. In the presence of cross-talk, the transmitted electric field will include
a component from the orthogonal left-circular polarization, so has the form [14]









































c
c
c
V
H
j
jj
T
T



1
1
2
1
11
2
1
where

c
is a cross-talk parameter.
With Faraday rotation, , the electric field incident on the Earth’s surface will be [14]






































j
c
j
j
c
j
V
H
i
V
i
H
eej
ee
T
T
E
E


2
1
cossin
sincos
(2)
Freeman [14] introduced a system model for this CTLR mode, in which the measured scattering vectors
are given by

4

















































2
1
1
2
cossin
sincos
1
2
1
,
N
N
eej
ee
SS
SS
f
erA
M
M
j
c
j
j
c
j
VVVH
HVHH
j
RV
RH






(3)
where S
HH
, S
HV
, S
VH
and S
VV
are the components of the true scattering matrix, M
RH
and M
RV
are the
components of the measured scattering vector, f denotes channel imbalance,

i
, i = 1-2, are crosstalk
terms in the receiving channel, and N
i
, i = 1-2, are additive noise terms present in each measurement.
III. CALIBRATION ALGORITHM VIA MIXED CALIBRATORS
A. Signatures of Mixed Calibrators
By mixed calibrators we refer to a set of passive and active radar calibrators operating in combination.
Their use for calibrating spaceborne FP SAR systems is discussed in [16]-[22]. Passive radar calibrators
usually consist of the dihedral, trihedral and gridded trihedral (the classical trihedral with gridded base
wires or thin plates [22], see Fig.1(c)), while the polarimetric active radar calibrators (PARCs) include
three types [16], denoted as PARC
X
, PARC
Y
and PARC
P
, respectively, having signature matrices:







01
00
X
S







00
10
Y
S








11
11
P
S
(4)
where PARC
X
and PARC
Y
are polarimetric selective active calibrators.
For the passive calibrators illustrated in Fig.1, the scattering matrixes can be written as [22]










10
01
,
,


Tri
j
TriTri
eAS
(5)















2cos2sin
2sin2cos
,
,
Di
j
DiDi
eAS
(6)























22
2
222
,
sincossincossin
sincossinsin
sincossin
,
Gt
j
Gt
Gt
eA
S
(7)
where A
Tri
, A
Di
and A
Gt
are gain factors,

Tri
,

Di
and

Gt
are phase factors,

and

are the azimuth and
elevation angles, and

is the rotation angle of the dihedral.
Without loss of generality, we assume that the gain and phase factors in the ideal responses of (4)-(7)
are known, and can be normalized for simplicity. Then we have







10
01
Tri
S








10
01
Di
S







00
01
1Gt
S







10
00
2Gt
S
(8)
where S
Tri
, S
Di
, S
Gt1
and S
Gt2
denote the signature matrices of the trihedral, dihedral (

= 0) and gridded

Frequently asked questions

Q1. What have the authors contributed in "Calibration of spaceborne ctlr compact polarimetric low frequency sar using mixed radar calibrators" ?

In this paper, the authors proposed an algorithm for calibrating the circular transmit and linear receive mode spaceborne compact polarimetric SAR using mixed calibrators, which is able to correct precisely both FR and radar system errors. 

Q2. What is the polarization vector of a polarized electromagnetic wave?

When a polarized electromagnetic wave traverses the ionosphere, its interaction with free electronsand the Earth’s magnetic field leads to rotation of the polarization vector [4], [15]. 

Q3. How much is the SNR of a passive calibrator?

An SNR of at least 50 dB seems necessary to reduce the phase error in 1 to tolerable levels, which gives some guide to the required size of the passive calibrators, the performance of the active calibrators and the dimensions of the low backscatter background on which they must be positioned. 

Q4. What is the calibration algorithm for gridded trihedrals?

gridded trihedrals, as used in Scheme 5 have the advantages of providing large beamwidth and giving average polarimetric noise (i.e., the coherent averaging of scattering vectors from different angular positions) less than -30 dB [22]. 

Q5. What is the polarization vector for a CTLR system?

The authors assume a CTLR mode SAR system that transmits right-circular polarization chirps and receiveslinear (H, V) polarization echoes. 

Q6. What is the way to test the proposed algorithms?

Note that in these simulations the data were corrupted with the maximum values of the radar system errors,i.e. | f | = 1.5 (3.5 dB), arg{f} = /3 (60) and |1| = |2| = 0.1 (-20 dB), |c| = 0.32 (-10 dB), in order to test the proposed algorithms severely. 

Q7. What is the calibration algorithm for scheme 6?

In contrast, scheme 6’s use of a trihedral and dihedral instead of gridded trihedrals brings the merits of simple construction and little effect from rain, but the narrow beamwidth of the dihedral causes orientation difficulties, and the dihedral suffers from high polarimetric noise due to pointing error [22].