Measurement Matrix Design Based on Compressed Sensing for DOA Estimation

It has been well known that Massive multiple-input-multiple-output (MIMO) radar can provide a large aperture and improve the direction of arrival (DOA) estimation performance. However, a significant increased data size will seriously reduce the computational efficiency of DOA estimation. In this paper, we propose an optimization algorithm to design the dimensionality reduction measurement matrix based on compressed sensing (CS), which can extremely reduce the computational complexity. Unlike adopted random projections, we choose the measurement matrix for DOA estimation by minimizing the overall mutual coherence between measurement matrix and spatial sparse dictionary. The optimization problem of designing the dimensionality reduction measurement matrix is non-convex. To solve this problem, an alternating iterative algorithm based on singular value protection is proposed. Moreover, we analyzed the computational complexity of DOA estimators with this dimensionality reduction scheme. Numerous results demonstrate that the proposed scheme has better DOA performance than random projection method and arbitrary selection method.