Rational Arrays for DOA Estimation: New Insights and Performance Evaluation

Abstract

Rational arrays were recently proposed for direction of arrival (DOA) estimation. In particular, rational coprime arrays were demonstrated to be useful when the aperture and the number of sensors are constrained. In this paper, we provide a necessary and sufficient condition for steering vector invertibility of a general rational array. We demonstrate that shrunk rational ULAs can have smaller MSE than integer ULAs when multiple sources impinge from the directions away from the normal to the array. We also propose a new way for generating rational arrays which readily ensures the "rational coprimality condition" for identifiability. Arrays generated according to this new way provide better DOA estimation performance compared to pre-viously used rational coprime arrays. Next, the paper provides a detailed performance evaluation for rational coprime arrays in terms of numerical and analytical mean square errors with root-MUSIC. For this, a modification of root-MUSIC for search-free estimation of DOAs with rational arrays is introduced. It is found that rational coprime arrays have smaller MSE than three possible integer arrays with the same aperture and number of sensors, including ULAs and integer coprime arrays.

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