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2018•Anadolu University Journal of Science and Technology-A Applied Sciences and EngineeringOpen access

COPRIME ARRAYS WITH ENHANCED DEGREES OF FREEDOM

Ahmet M. Elbir

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Abstract

Coprime array geometries provide robust performance for direction-of-arrival estimation problem with more sources than sensor elements. In previous works it is shown that K source directions can be resolved using only 2M + N -1 sensor elements where K is less than or equal to MN. In this paper we introduce a new approach to enhance the degrees of freedom (DOF) from MN to 2MN by using the same number of sensor elements. The proposed method is based on computing the covariance matrix of the observation data multiple times. Hence more DOF can be obtained. The resulting cross terms corresponding to the coherent sources are modeled as an interference in a sparse recovery algorithm which is solved effectively by an alternating minimization procedure. The theoretical analysis of the proposed method is provided and its superior performance is evaluated through numerical simulations.

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Coprime array geometries provide robust performance for direction-of-arrival estimation problem with more sources than sensor elements. In previous works it is shown that K source directions can be resolved using only 2M + N -1 sensor elements where K is less than or equal to MN. In this paper we introduce a new approach to enhance the degrees of freedom (DOF) from MN to 2MN by using the same number of sensor elements. The proposed method is based on computing the covariance matrix of the observation data multiple times. Hence more DOF can be obtained. The resulting cross terms corresponding to the coherent sources are modeled as an interference in a sparse recovery algorithm which is solved effectively by an alternating minimization procedure. The theoretical analysis of the proposed method is provided and its superior performance is evaluated through numerical simulations.

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Available abstract

Coprime array geometries provide robust performance for direction-of-arrival estimation problem with more sources than sensor elements. In previous works it is shown that K source directions can be resolved using only 2M + N -1 sensor elements where K is less than or equal to MN. In this paper we introduce a new approach to enhance the degrees of freedom (DOF) from MN to 2MN by using the same number of sensor elements. The proposed method is based on computing the covariance matrix of the observation data multiple times. Hence more DOF can be obtained. The resulting cross terms corresponding to the coherent sources are modeled as an interference in a sparse recovery algorithm which is solved effectively by an alternating minimization procedure. The theoretical analysis of the proposed method is provided and its superior performance is evaluated through numerical simulations.

Key concepts: Coprime integers, Degrees of freedom (physics and chemistry), Minification, Algorithm, Matrix (chemical analysis), Interference (communication), Covariance matrix, Computer science

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