The detection and parameter estimation of moving targets is one of the most
important tasks in radar. Arrays of randomly distributed antennas have been popular for
this purpose for about half a century. Yet, surprisingly little rigorous mathematical
theory exists for random arrays that addresses fundamental question such as how many
targets can be recovered, at what resolution, at which noise level, and with which
algorithm. In a different line of research in radar, mathematicians and engineers have
invested significant effort into the design of radar transmission waveforms which satisfy
various desirable properties. In this paper we bring these two seemingly unrelated areas
together. Using tools from compressive sensing we derive a theoretical framework for the
recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one
manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some
of their peculiar properties in our analysis. Our paper provides two main contributions:
(i) We derive the first rigorous mathematical theory for the detection of moving targets
using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties
that are very desirable and important from a practical viewpoint. Thus our approach does
not just lead to useful theoretical insights, but is also of practical importance. Various
extensions of our results are derived and numerical simulations confirming our theory are
presented.