a Matlab package for phased array beam shape inspection

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“losing sensitivity” (due) to the multiple grating lobes, is unfair. It is unfair in the same
way as it would be unfair to complain that one is losing half of the available receive power
to the re-radiation. The re-radiation is unavoidable by the nature of electromagnetism,
not because of some incompetent engineering.
What the situation would be if we could allow irregular arrays and non-uniform excitation
fields, I don’t know. For example, people are talking about “superdirective”
arrays : for instance, it is possible to have a linear array of isotropic elements where
the gain approaches N 2 , but that requires specifically tailored non-uniform spacing and
specifically tailored excitation fields.
For conventional array designs, we need not be overly worried about the grating lobes,
but that does not mean that we should not be somewhat worried about the grating lobes.
The situation with arrays is actually not too dissimilar from the situation with dishes.
The basic gain pattern, and especially the directivity (maximum gain) of a dish is mainly
determined by the geometric aperture, so that only modest improvements in gain can be
achieved by tailoring the details. For a sizable conventional planar array, the directivity
is also largely determined by the geometric area, and can only be improved by so much by
tinkering the details. For arrays, in order to achieve the naturally available directivity,
we have the extra degree of freedom that we can use fewer elements if the elements
themselves are directive.
There is a prize to that flexibility, or course. The prize is not so much in terms of
directivity, (and hence, not in terms of maximum detection sensitivity), but rather in
terms of directional aliasing. That is, when the gain in the antenna side lobes (grating
lobes or not) is not insignificant, there can be a serious loss of information about the
actual target direction. The side lobes can poke all over the sky, and there appears to
be no way to determine via which lobe(s) the observed power came in—unless we know
a priori that there is no scattering coming from the non-intesting lobe directions.
If the large side lobes cannot be suppressed (using directional elements or irregular
element placement), we must in the very least arrange things so that potential targets
in the side lobes are not illuminated by the transmitter. When the reception antenna
is different from the transmission antenna, this should be possible, at least in principle.
But how much does this constrain the available pointing schemes in practice, especially
when using multi-beam-forming reception, must be inspected carefully.
Another potential penalty for large-gain side lobes is that even if there would be no
illumination in the side lobe directions, unwanted external RF signals may easily sneak
in. On the other hand, the gain is large in only narrow cones, so perhaps this is not such
a serious problem in practice.
4. A phased array
This section introduces the phased-array steering- and gain-related concepts, notations
and computations as implemented in the m-files in the e3ant package.
4.1. The array factor
With reference to Fig. 9, assume that the far-field electric field caused by the antenna
element at the origin, in the direction of unit vector û, is E 0 . Then the far field of
the element at position d m is E m = E 0 e iΨm , where Ψ m is the phase difference of the
two waves when they arrive at the target. This difference corresponds to the distance