Aerospace and Electronic Systems Magazine December 2017 - 43

Riddolls

Figure 5.

Figure 6.

bins, at the expense of a noisier histogram. Conversely, Data Set
2 comes from a narrow range of azimuths and also occupies a
narrow Doppler range.
We now proceed to calculate the array gains from Data Sets
1 and 2, namely, the improvement in signal-to-clutter ratio, for
conventional and adaptive beamforming arrays. We inverse Fourier transform the directional spectra shown in Figures 6a and
6b to obtain the auroral clutter spatial correlation function. We
then evaluate this spatial correlation function at the positions of
the elements in a candidate array to obtain the clutter covariance
matrix ρ, following the notation previously described. Then, we
calculate the array gains, which for conventional arrays is given
by Equation (3) and for MVDR adaptive beamformers is given
by Equation (4).
Results are shown in Figures 7 and 8, assuming 0.4 λ spacing between elements in all cases. Figure 7a shows conventional
beamforming on Data Set 1. The one-dimensional (1D) linear array end fire and broadside beamforming show similar gain up
to about 10 elements. Beyond 10 elements, the target and clutter signals become resolvable in elevation, and the end-fire gain
increases more rapidly than the broadside gain, up to about 20

elements, at which point the target and clutter signals are fully
resolved in elevation. In contrast, the broadside beamformer is
never able to resolve the target and clutter, and realizes array gain
only through the narrowing of the beamformer main lobe. The
two-dimensional (2D) filled square planar array gain is roughly the product (or sum, in decibel scale) of the 1D end-fire and
broadside gains, whereas the L-shape array shows only modest
improvement over the 1D beamformers.
The conventional beamforming for Data Set 2, shown in Figure
7b, is somewhat different. Here, the target and clutter have separation in azimuth as well as elevation. The broadside beamformer
has considerably higher resolving power than the end-fire beamformer, due to its larger crossbeam aperture. Thus, the broadside
array gain rises rapidly, and one can see ripples in the gain at 5,
10, and 15 elements, as the clutter passes through the sidelobes of
azimuth fan beam. In contrast, the clutter does not pass through the
first sidelobe of the elevation beamformer until 25 elements are
reached. Finally, the 2D array gain is again roughly the product of
the gain of the 1D azimuth and elevation beamformers.
The adaptive beamformers (Figures 8a and 8b) show features
similar to the conventional beamformers, with two exceptions.

(a) Wave number spectrum of ground clutter mode (Data Set 1). (b)
Wave number spectrum of ground clutter mode (Data Set 2).

DECEMBER 2017

(a) Wave number spectrum of auroral clutter mode (Data Set 1). (b)
Wave number spectrum of auroral clutter mode (Data Set 2).

IEEE A&E SYSTEMS MAGAZINE

41



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