IEEE Geoscience and Remote Sensing Magazine - June 2020 - 96

these points will move away from the ground phase. The
changed coherence values will finally cause forest-height
estimation error.
INSAR SYSTEM AND PLATFORM PARAMETERS
In this section, we continue to analyze the impact of system and platform parameters that may affect forest parameter inversion accuracy in the interferometric radar echoes.
With additive and statistically independent error sources
assumed, the total coherence factor cu tot can be simply modeled as a cumulative product [103], [113]:
cu tot = c SNR $ c Quant $ c Amb $ c Coreg $ c Geo $ c Az $ cu Vol $ cu Temp. (53)
The first six terms are the decorrelation contributions
due to system processing and acquisition geometry effects. They are scalar quantities and contribute only to
the overall interferometric correlation coefficient. The
last two terms are introduced by the scatterers and reflect
their structural and temporal stability. They are complex
contributions as they also affect the measured interferometric phase. The following sections discuss each factor
individually.
VOLUME DECORRELATION (c˜ VOL)
The penetration of long waves into natural volume scatterers (such as forest, sand, and ice) causes volume decorrelation, the fundamental decorrelation factor on which
forest parameter inversion design is based. cu Vol contains
the physical information about the vertical structure of the
volume scatterer. The RVoG scattering model describes the
relationship between the vertical distribution of the forest
scatterer and the volume decorrelation factor, as explained
in previous section.
THERMAL NOISE DECORRELATION
The coherence loss c SNR caused by system thermal noise
can be expressed as a function of the thermal signal-tonoise ratio (SNR) as [103], [113]
c SNR =

1
.
1 + SNR -1

(54)

The thermal noise decorrelation mainly affects the regions
characterized by low backscattering. For example, thermal
noise decorrelation becomes serious for smooth surface
scatterer due to its low backscattering intensity.
QUANTIZATION ERROR
Quantization error comes from the quantization of the raw
data signals. In a strict sense, quantization error should be
seen as nonlinear. Current research shows that it can also
be approximated as additive white noise. Quantization
decorrelation can be expressed as a function of the signalto-quantization-noise ratio (SQNR) as [114], [115]
c Quant =
96

1
.
1 + SQNR -1

(55)

RANGE AND AZIMUTH AMBIGUITIES
Range and azimuth ambiguities are mainly dependent on system parameters, such as pulse repetition frequency, imaging
swath, incidence angle, and so on. The contribution from ambiguities can be treated as additive noise. For the given rangeambiguity-to-signal ratio (RASR) and azimuth-ambiguity-tosignal ratio (AASR), the coherence loss is given by [103], [114]
1
1
c Amb = 1 + RASR · 1 + AASR .

(56)

COREGISTRATION ERROR
Processing and coregistration errors can be modeled as
phase aberrations in the transfer functions of the SAR processor. Assuming that the relative azimuth and range shift
between the two interferometric images in a fraction of a
resolution cell are daz and drg, respectively, the coherence
loss caused by the coregistration error is given by [116], [117]
c Coreg = sin c ^rd rg h . sin c ^rd azh .

(57)

BASELINE DECORRELATION
Nonoverlapping ground range spectra, known as wavenumber shift, cause coherence loss. Baseline decorrelation is
caused by the difference of the incidence angles between
the two observations and is given by
Bn
c Geo = max ' 1 - B
, 0 1,
=,crit

(58)

where B n is the interferometric baseline perpendicular to
the line of sight. B =,crit is the critical baseline of the interferometer and is given by [103], [118]
B =,crit =

B rg mR tan ^i 0 - a h
,
c

(59)

where B rg is the bandwidth of the radar pulse, a is the local
slope angle, and c is the velocity of light.
DOPPLER DECORRELATION
Nonoverlapping Doppler spectra, known as Doppler shift,
cause coherence loss. Doppler shift occurs mainly due to
the uncertainty of the antenna orientation in the azimuth
direction. The Doppler decorrelation is given by [7], [119]
Tfd
c Az = 1 - B ,
proc

(60)

where Tfd = fDop,1 - fDop,2 is the frequency difference between the Doppler centroids and B proc is the processed Doppler bandwidth. The coherence loss due to the wavenumber
and Doppler shift can be compensated for by performing
range and azimuth spectral filtering to obtain a common frequency band. After compensation, the baseline decorrelation
and Doppler decorrelation become c Geo = c Az = 1.0.
TEMPORAL DECORRELATION
In conventional repeat-pass InSAR scenarios, temporal decorrelation is the most critical factor for successful implementation
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020
IEEE Geoscience and Remote Sensing Magazine - June 2020

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