The purpose of remote sensing is to acquire information about an object through the propagation of electromagnetic waves, specifically radio waves for radar systems. However, these systems are constrained by the costly Nyquist sampling rate required to guarantee efficient recovery of the signal. The recent advancements of compressive sensing offer a means of efficiently recovering such signals with fewer measurements. This thesis investigates the feasibility of employing techniques from compressive sensing in on-grid MIMO radar in order to identify targets and estimate their locations and velocities. We develop a mathematical framework to model this problem then devise numerical simulations to assess how various parameters, such as the choice of recovery algorithm, antenna positioning, signal to noise ratio, etc., impact performance. The experimental formulation of this project leads to further theoretical questions concerning the benefits of incorporating an underlying signal structure within the compressive sensing framework. We pursue these concerns for the case of sparse and disjoint vectors. Our computational and analytical treatments illustrate that knowledge of the simultaneity of these structures within a signal provides no benefit in reducing the minimal number of measurements needed to robustly recover such vectors from noninflating measurements, regardless of the reconstruction algorithm.
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