IEEE Geoscience and Remote Sensing Magazine - December 2022 - 18

of directional coordinates, is referred to as the element pattern,
following common antenna terminology. The total electric
field strength excited by the complete feed array, known as
the primary radiation pattern, is determined by the element
pattern, the array geometry (position of radiators), and the
excitation. The latter depends on the amplitude and phase
of the current at the input terminals of each feed antenna
element. For identical radiators and assuming no coupling
effects, the primary antenna pattern is the product of the
element pattern and the array factor, where the latter is
entirely determined by the feed geometry and the excitation.
The feed array illuminates the reflector (Figure 8), imposing
a current distribution on its surface, which, in turn,
results in a propagating electromagnetic wave [22]. The normalized
field distribution in the far field as a function of
directional coordinates is known as the secondary radiation
pattern. An observer far away from the reflector measuring
the field strength will experience the reflector surface as the
source of electromagnetic radiation. Ignoring the contribution
of the feed array's back radiation to the total field at
the observer's position, this indicates that the feed array
excitation could be removed without altering the secondary
antenna pattern as long as the currents imposed on the
Relative Level (dB)
-15-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Primary Illumination
Feed Excitation
reflector surface remain the same. This explains why the
power density on the reflector, referred to as the illumination
intensity, is crucial for understanding the beamforming
process.
The type of visualization used here to describe and analyze
the reflector antenna system of Table 1 is shown in Figure
9 and includes the following:
◗ Feed excitation: This is the 24 × 3 feed array excitation
(upper right) in elevation (row) and azimuth (column)
as the normalized amplitude weights in decibels. Elements
that are not activated appear in white.
◗ Reflector illumination: This is shown at the upper left and
represents the power density on the reflector surface
normalized to the total power. The ordinate and abscissa
refer to the elevation and azimuth (along-track) directions,
respectively. Dashed contour lines indicate the -3
and -11 dB power density levels.
◗ Secondary radiation pattern: This is the resulting secondary
gain pattern versus the elevation angle and is shown
(the bold line) at the bottom together with the individual
secondary gain patterns resulting from activating single
feed rows (thin cyan lines). The maximum antenna
pattern gain value is also included.
Since the emphasis here is put on the elevation beamforming,
the focus will be on the rows of the feed array,
which determine the secondary radiation pattern in elevation.
The feed element columns are included for completeness
and to yield a realistic representation (remember that
reflector radiation patterns are nonseparable). The three
azimuth elements of each feed row are utilized to set the
azimuth beam taper, which determines the azimuth radiation
pattern cut for any specific elevation angle. Azimuth
beamforming is detailed in part 3 of the tutorial article; it
is thus suggested that at this point, the center element of
each row (the center column of the feed array) is of the most
interest here.
40
30
20
10
-15
-10
Secondary Elevation Pattern
Gain: 42.6 dBi
-5 05 10
Angle (°)
15
FIGURE 9. The reflector excitation (top right), illumination (top
left), and secondary radiation patterns (bottom). The center feed
array row is activated. dBi: decibels per isotropic.
18
SINGLE FEED ROW ACTIVATION
As detailed in part 1, the secondary beam direction (i.e.,
the direction of the main lobe of the secondary radiation
pattern) of a reflector system is determined by the
active feed element. Beam steering is thus achieved by
activating different feed rows, as shown in Figure 10(a)
and (b). Knowing that the reflector rim taper for optimum
illumination efficiency is at -10 to -12 dB [22],
it is seen that activating a single row causes an overillumination
in the elevation (ordinate) direction. This
is not a design flaw but rather a necessity to ensure
smooth SCORE beam-to-beam transitions (see [1] and
[32]). As shown in the following, activating several rows
provides better illumination efficiency, thus yielding a
higher gain (maximum value) of the secondary radiation
patterns.
The secondary gain patterns show a degradation when
activating edge rows, as evident in Figure 10(b), which is
due to the defocusing effect of the reflector geometry for
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2022
Gain Pattern (dBi)
IEEE Geoscience and Remote Sensing Magazine - December 2022

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