IEEE Geoscience and Remote Sensing Magazine - September 2021 - 19

the following effects [39]: a pulse extension loss, a radiometric
bias, and an amplitude taper on the spectrum of
the return signal (the latter results in a worsening of the
range resolution). These unwanted effects increase when
considering ground topography. Frequency-dependent
beamforming can be used to mitigate these effects, as
detailed next.
Spaceborne SAR systems transmit linearly frequencymodulated
pulses known as chirps. As a consequence of
the pulse extent, the frequency scattered by an arbitrary
ground point at a specific time instance depends on its
position within a pulse; this is indicated by the colored
point scatterers in Figure 12(a). Since the illuminated
scene consists of many such point scatterers (extended
targets), the instantaneous return signal is no longer a
chirp; instead, it contains all transmitted frequencies.
Nevertheless, each frequency within the return signal's
spectrum corresponds to a specific angle of arrival. A
narrow frequency filter applied on the spectrum of the
return signal is also a spatial (and angular) filter suppressing
the contribution of scatterers outside the selected
frequency band (in a way, equivalent to selecting
only the point scatterers of a single color in Figure 12(a),
thus effectively reducing the pulse extent and, by this, the
pulse duration. This correspondence between the spectrum
and the angle manifests itself because of the special
time-frequency relation of the transmitted pulse (chirp)
in Figure 12(b).
A bank of (digital) bandpass filters (BPFs) partitioning
the return signal's frequency spectrum, of bandwdith
Bw, into subbands (frequency domain) will subdivide the
signal into short pulses (time domain). Now, a dedicated
set of SCORE weights can be applied to each subband for
optimum beam steering; see Figure 12. The technique of
generating frequency-(i.e., wavelength)-dependent beams
is known as dispersive SCORE, which is addressed, for example,
in [49]. The effective pulse duration and bandwidth for
each subband are reduced by a factor equal to the number
of subbands; for Nsb
w /, respectively.
subbands, this becomes xp /Nsb and
BNsb
The inherent wavelength dependency of the reflector
secondary patterns motivates the use of dispersive
SCORE, even if the pulse extension loss itself is not severe.
Partitioning the bandwidth into subbands enables
compensating for this effect. Dispersive SCORE is applied
to mitigate frequency-dependent antenna patterns to improve
ambiguity suppression or when the angular transmitted
pulse extent becomes larger than the secondary
antenna beamwidth.
It should be noted that the approach detailed here
would fail if, for example, an orthogonal frequencydivision
multiplexing signal were transmitted since
the one-to-one correspondence between the frequency,
time, and angle of arrival is lost. Frequencydependent
beamforming could still be applied, but it
would fail in subdividing the pulse into shorter time
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
Subband b
Subband Duration
intervals and, by this, not provide the required performance
improvement.
HARDWARE REALIZATION: OPTION 1
The hardware implementation of the BPFs can be achieved
using a finite impulse response (FIR) filter bank, as pictured
in Figure 13. The input data sn
filtered by N bs
BPFs, each implemented as an N pta
filter; the output data stream sn
b
plied by the time-varying complex weight ().wtn
b
input and output data streams sn
at a rate of fs
and cn
are generated
samples/s. The FIR filter bank in Figure 13
is applied to each digital channel; i.e., each multiplier in
Figure 7 is replaced by a filter bank. As shown later, this
configuration can, however, be simplified.
In matrix notation, the fixed N pta
filter for each subband are used to generate an NN
of each channel are
FIR
of each BPF is then multiBoth
the
coefficients of the FIR
rb # rb
Feed Array
Single
Active
Element
Point Scatterer
Ground
(a)
Time
(b)
FIGURE 12. Dispersive SCORE divides the signal spectrum into subbands
and applies a different weight to each frequency band, thus
generating a distinct set of frequency-dependent beams. (a) A chirp
signal traversing the ground and dispersive SCORE beams. (b) A
time-frequency diagram of a transmitted chirp signal.
19
Reflector
Subband b Beam
Instantaneous Frequency
IEEE Geoscience and Remote Sensing Magazine - September 2021

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