IEEE Geoscience and Remote Sensing Magazine - December 2022 - 22

aforementioned feed element misalignment. Nevertheless,
comparing Figure 10(b) and Figure 12(b) clearly shows
that the optimum beamformer generates superior secondary
radiation patterns in terms of the sidelobe level and
gain (a 41.5- versus 38.9-dBi gain).
COMPARISON OF DIFFERENT BEAMFORMERS
The performance of the beamforming is mainly determined
by the shape of the secondary radiation pattern. Figure 13
compares the previously introduced optimum beamformer
to a sidelobe-constrained beamformer [16], both steered to
an angle of 7.5º, for a maximum of seven active feed rows.
The scale is extended to cover 0 to -18 dB to emphasize the
different weights and illumination. The optimum beamformer
yields the narrowest radiation pattern beamwidth,
while the sidelobe-constrained beamformer lowers the sidelobe
level at the expense of a wider beamwidth and a slightly
lower gain. In practice, this is beneficial for SAR instruments
since the disturbance is not only made of thermal noise
but also influenced by ambiguities; a sidelobe-constrained
beamformer leads to a slightly worse SNR but much higher
ambiguity suppression.
Although the amplitudes of the feed array weights
appear to be similar for the two cases, the beamformers
utilize the active element excitation differently: the low-amplitude
feed elements at -18 dB have a minor effect on the
reflector illumination for the optimum beamformer, which
shows a nearly ideal -11-dB rim taper, for a maximum
SNR; in the case of the sidelobe-constrained beamformer,
the low-amplitude feed elements are used to mitigate the
sidelobes caused by the higher-amplitude feed elements,
which manifests itself in the different reflector illumination.
One further factor to consider when comparing beamforming
algorithms is the effect of the feed array's phase
and amplitude errors on the resulting radiation pattern.
These errors and other imperfections as well as calibration
(covered, for example, in [6], [36], [37], [38], [39], [40], [41],
[42], [43], and [44]) are highly relevant but considered beyond
the scope of this tutorial article.
The inherent usefulness of beamforming is shown in
comparison to the unity, i.e., simple on-off, beamformer
with two active feed rows in Figure 14. The antenna pattern's
peak of the latter may be slightly shifted with respect
to the design value and yields an approximately 1-dB lower
gain value with a higher sidelobe level.
Relative Level (dB)
Primary Illumination
Feed Excitation
Secondary Elevation Pattern
40
30
20
10
Gain: 41.9 dBi
-15 -10 -5 05 10 15
Angle (°)
FIGURE 14. The reflector excitation and radiation patterns for the
case of a unity beamformer equally exciting two feed rows.
22
MULTIBEAM GENERATION
The cases covered up to now were intended to foster the
understanding of beam steering, the influence of the number
of active elements, and the different beamforming
methods. However, the example radiation patterns given
could all have been realized using an analog feed array
(based on transmit/receive modules). The superiority of
a digital feed array is that it allows generating multiple simultaneous
and independent antenna beams. From a DBF
perspective, the excitation coefficients of multiple beams
are generated by a simple complex-valued superposition
of the individual antenna beams' excitation coefficients.
In the case of a receiving antenna system (remember that
the reciprocity theorem mentioned earlier allows applying
the same argumentation to a transmit or receive antenna),
each beam generates its own data stream; in terms of the
hardware schematic, the DBF unit configuration of either
Figure 4(b) or Figure 4(c) may be utilized.
Figure 15(a) shows the feed excitation resulting in three
(simultaneous) antenna beams, which are steered to the center
of the imaged subswaths of the reference SAR. Each beam
activates four feed rows, and the large angular separation
between the secondary antenna beams yields nonoverlapping
(disjunctive) active feed rows. It is emphasized that each
secondary antenna beam can be understood as generated by
its own independent antenna. Thus, although the secondary
antenna patterns are plotted on a common abscissa, they do
not represent a joint radiation pattern of the three antenna
beams. From the beamforming perspective, each secondary
radiation pattern is associated to its own data stream
and distinct excitation coefficient [the index k is used in
(2) to indicate the beam number of the output data stream
b ].k
This explains the high gain of each beam, on the order
of 43.5 dBi. The ability to generate multiple simultaneous
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IEEE Geoscience and Remote Sensing Magazine - December 2022

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