We study a multiple-input multiple-output (MIMO) model for radar and provide recovery guarantees for a compressive sensing approach. Several transmit antennas send random pulses over some time-period and the echo is recorded by several receive antennas. The radar scene is resolved on an azimuth-range-Doppler grid. Sparsity is a natural assumption in this context and we study recovery of the radar scene via l-minimization. On the one hand we provide an estimate for the well-known restricted isometry property (RIP) ensuring stable and robust recovery. Compared to standard estimates available for Gaussian random measurements we require more measurements in order to resolve a scene of certain sparsity. Nevertheless, we show that our RIP estimate is optimal up to possibly logarithmic factors. By turning to a nonuniform analysis for a fixed radar scene, we reveal that the fine-structure of the support set (not only its size) influences the recovery performance. By introducing a parameter measuring the well-behavedness of the support we derive a bound for the number of measurements sufficient for recovery that resembles the minimal one for Gaussian random measurements if this parameter is close to optimal, i.e., if the support set is not pathological. Our analysis complements earlier work due to Friedlander and Strohmer where the support set was assumed to be random.
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