  We analyze a multiple-input multiple-output (MIMO) radar model and provide
recovery results for a compressed sensing (CS) approach. In MIMO radar
different pulses are emitted by several transmitters and the echoes are
recorded at several receiver nodes. Under reasonable assumptions the
transformation from emitted pulses to the received echoes can approximately be
regarded as linear. For the considered model, and many radar tasks in general,
sparsity of targets within the considered angle-range-Doppler domain is a
natural assumption. Therefore, it is possible to apply methods from CS in order
to reconstruct the parameters of the targets. Assuming Gaussian random pulses
the resulting measurement matrix becomes a highly structured random matrix. Our
first main result provides an estimate for the well-known restricted isometry
property (RIP) ensuring stable and robust recovery. We require more
measurements than standard results from CS, like for example those for Gaussian
random measurements. Nevertheless, we show that due to the special structure of
the considered measurement matrix our RIP result is in fact optimal (up to
possibly logarithmic factors). Our further two main results on nonuniform
recovery (i.e., for a fixed sparse target scene) reveal how the fine structure
of the support set affects the (nonuniform) recovery performance. We show that
for certain "balanced" support sets reconstruction with essentially the optimal
number of measurements is possible. We prove recovery results for both perfect
recovery of the support set in case of exactly sparse vectors and an
$\ell_2$-norm approximation result for reconstruction under sparsity defect.Our
analysis complements earlier work by Strohmer & Friedlander and deepens the
understanding of the considered MIMO radar model.
