IEEE Geoscience and Remote Sensing Magazine - September 2021 - 14

yield the required secondary beam shape, pointing to
the changing direction of arrival of the echo while it
traverses the ground.
The schematic in Figure 7
THE RF HARDWARE
COMPLEXITY OF DBF
SYSTEMS IS REDUCED BY
MOVING THE DIGITAL
PROCESSING CLOSER TO
THE ANTENNA.
demonstrates another important
aspect of SCORE:
data reduction. SCORE combines
Nel
input data streams
into a single output. As such,
SCORE can also be understood
as a (lossless) data
reduction technique [27].
This
N :1el
Throughout this article, complex sampling will be
assumed; in this case, Nyquist sampling requires the
sampling rate fs
to be higher than the signal (chirp) bandwidth
B .w For example, in the case of the aforementioned
I/Q demodulation, each of the I and Q channels would be
sampled at a rate ,fs
plex number every /f1s.s
complex signal samples.
resulting in a data stream of one comTherefore,
Nrb
is the number of
data reduction is
the main reason that SCORE
would be implemented in
real time onboard a SAR instrument despite the additional
complexity and cost.
To arrive at the mathematical model, the resulting
SCORE beam output sample []
bl is represented as
Nel
bl
[] / []·(), ,,
1
== f -
=
n
n
rb
n
where l is the sample index; [] () is the sampled signal
induced on antenna feed element n, with tl /fls
sl st
nn l
=
= being
the discrete sample time for a signal sampled at frequency
f ;s
and () is the complex weight function applied on
wtn
the signal of channel n. Separate notations are used here
to indicate the different time dependencies: the sampled
signal changing on a sample-to-sample basis and the
weights, which change more slowly than the signal sampling.
The number of samples Nrb
is given by
NT .f· s
rb = echo
b
1
1
Azimuth Sample Index N
(4)
sl wt lNfo 01r
(3)
◗ Parameter values: For the reference SAR system, which
images a swath width of 70 km, the echo duration
Techo
is ...03ms With a sampling rate of f 85MHz ,
this gives N 25 ,500 (complex-valued) samples
per channel per range line.
s =
rb =
A graphical representation that is useful for understanding
the beam data, referred to as a range-azimuth
diagram, is given in Figure 8. It basically shows the signals
(data streams) after the beamforming process and
thus is an extension of the range-time diagram shown in
Figure 6. Each column of Nrb
(complex-valued) samples
represents the beam echo data of the full swath for one
transmitted pulse, which is also known as the range line.
Successive range lines represent the echo data of consecutive
transmitter pulses at different azimuth positions of
the platform. In Figure 8, two range lines have been filled
with data, while the echo data of the third pulse have not
been fully processed/received.
Adopting matrix notation, the sequence []
sln
samples of channel n is written as a column vector
s [[ ], [],, []],
nn nn rb
=-fss sN01
where N ,rb
1
T
of time samples of one range line of duration T ,echo
nels becomes
Ss ss el@
= f,, ,.N
6 12
Similarly, the Nrb
defined as
(6)
element SCORE output beam vector is
b [[ ], [],, []].=-fbb bN01
rb
1
T
(7)
Nrb
Then, the vector equation corresponding to (3) becomes
bS (),tw=
with the Nel
FIGURE 8. A range-azimuth data diagram showing the data streams after
combining (i.e., beamforming) the signals of the individual elements.
14
element weight vector
() (),( ), ,().
w tw tw tw tN
=6 12 el
f
@
T
of input
(5)
introduced earlier, represents the total number
which
is equal to the dimension of the vector (the number of elements).
The NN
rb # el signal matrix of all elevation chan(8)
(9)
IEEE
GEOSCIENCE AND REMOTE SENSING MAGAZINE SEPTEMBER 2021
Range Sample Index
Echo 1
Echo 2
Echo 3
Tx
IEEE Geoscience and Remote Sensing Magazine - September 2021

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