On the design of the measurement matrix for Compressed Sensing based DOA estimation

In this paper we investigate the design of the measurement matrix for applying Compressed Sensing (CS) to the problem of Direction Of Arrival (DOA) estimation with antenna arrays. So far, it has been suggested to choose the coefficients randomly since this choice satisfies the restricted isometry property (RIP) with a high probability. We demonstrate that this choice may be sub-optimal since it can result in an effective array with significant sidelobes and blind spots. The sidelobes are especially problematic when we use correlation-based greedy algorithms for the sparse recovery stage as they can lead to detecting spurious peaks. To address the problem, we introduce a design methodology for constructing a measurement matrix that mitigates these unwanted effects to achieve a better DOA estimation performance. Numerical results demonstrate the usefulness of our design.