Aerospace and Electronic Systems Magazine December 2017 - 41

Riddolls
There are, therefore, some unavoidable inefficiencies in the horizontal array
approach. First, there is an underutilization of transmitter resources, because all
power amplifier units must be sized to the
element(s) with the largest power level,
and the location of the highest-power elements can shift around depending on the
beam-steering direction. Second, there is
reflected power at the feed points, particularly at the rear elements, where the match
to Z0 is poor. Third, although not present in
this particular example, any elements that
require large forward power, but also have
large reflection coefficient, may violate
the maximum reverse power requirements
of that channel's power amplifier, and then
the power of the entire array will need to
be backed off to keep the elementwise
power excitation pattern intact.
Provided one properly works through
the previous considerations in designing
the horizontal array, it is an entirely viable
approach as a transmit array, with some
Figure 3.
reasonable concessions in efficiency. ReElement data for a planar transmit array (see text for details).
al-time assessment of the mutual impedand receive arrays in the vicinity of a 45° steer angle, both arrays
ances is useful for optimal performance, but one can also run an
provide some elevation resolution by virtue of the conical shape
"open loop" operation with premeasured mutual impedances for
of the beams, which permits the resolution of multimode propagasuboptimal, but still satisfactory, performance. The situation is
tion both to and from the target, although this type of operation is
somewhat simpler on receive, because the interelement coupling
beyond the scope of this discussion [23].
can be reduced by making the array more lossy. Loss on receive
At high latitudes, experiment results (discussed in the Experican be tolerated to some extent because the radar is typically either
ments section) suggest that there are cases in which even a large
limited by clutter or by external radio noise.
planar receive array, combined with a quasi-isotropic transmitter,
does not provide sufficient array gain to suppress the auroral clutJOINT TRANSMIT-RECEIVE OPERATION
ter to levels needed for the detection of small airborne targets at
high latitudes. In these cases, the minimum cost solution for the reThe previous subsection contemplated a planar array providing
quired array gain may, in fact, involve combining a planar receive
joint azimuth-elevation resolution. Coordinated transmit and rearray with a planar transmit array. The exact sizing would need to
ceive operation can also be exploited. The first case we will conconsider the array gains achieved for a particular type of clutter.
sider is where a quasi-end-fire linear transmit array is combined
The array gain for any beamformer is [24]
with a quasi-broadside receive array [21] or some similar variation. The combined manifold of an M-element transmit array and
G = ( w H ρ w ) −1 ,
an N-element receive array approximates a virtual planar array of
(2)
size MN elements, using only M + N physical elements. To achieve
adaptive beamforming in both elevation and azimuth, the transmit
where w is the beamforming weight vector normalized to unity
array emits orthogonal wave forms from each of its M elements (or
gain, H is the Hermitian conjugate, and ρ is the clutter covariance
subarrays, depending on steer angle requirements), and then each
matrix normalized to unity variance. For conventional beamformof the N elements in the receive array has to record the M target
ing, this array gain is given by
echoes. The beamforming then involves forming linear combinaG = ( v H v ) 2 / ( v H ρ v ),
tions of the MN signal echoes.
(3)
The requirement for M orthogonal wave forms drastically reduces the unambiguous range-Doppler space available to the raand for minimum variance distortionless response (MVDR) adapdar [22]; thus, the scheme is most suited to low-Doppler surface
tive beamforming [24], it is
targets. For fast targets, the system can operate nonadaptively on
transmit and adaptively on receive, resulting in a virtual semiadapG = v H ρ −1v.
(4)
tive filled planar array. Furthermore, by operating both the transmit
DECEMBER 2017

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine December 2017