  We study the problem of actively imaging a range-limited far-field scene
using an antenna array. We describe how the range limit imposes structure in
the measurements across multiple wavelengths. This structure allows us to
introduce a novel trade-off: the number of spatial array measurements (i.e.,
beams that have to be formed) can be reduced significantly lower than the
number array elements if the scene is illuminated with a broadband source. To
take advantage of this trade-off, we use a small number of "generic" linear
combinations of the array outputs, instead of the phase offsets used in
conventional beamforming. We provide theoretical justification for the proposed
trade-off without making any strong structural assumptions on the target scene
(such as sparsity) except that it is range limited. In proving our theoretical
results, we take inspiration from the sketching literature. We also provide
simulation results to establish the merit of the proposed signal acquisition
strategy. Our proposed method results in a reduction in the number of required
spatial measurements in an array imaging system and hence can directly impact
their speed and cost of operation.
