Fast communication: Advantages of nonuniform arrays using root-MUSIC

Authors:
Carine El Kassis;José Picheral;Chafic Mokbel
Affiliations:
Department of Signal Processing and Electronic Systems (SSE), SUPíLEC, Plateau du moulon, 3, street Joliot-Curie, 91192 Gif-sur-Yvette Cedex, France;Department of Signal Processing and Electronic Systems (SSE), SUPíLEC, Plateau du moulon, 3, street Joliot-Curie, 91192 Gif-sur-Yvette Cedex, France;University of Balamand, Deir El-Balamand, El-Koura, Lebanon
Venue:
Signal Processing
Year:
2010

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Abstract

In this paper, we consider the Direction-Of-Arrival (DOA) estimation problem in the Nonuniform Linear Arrays (NLA) case, particularly the arrays with missing sensors. We show that the root-MUSIC algorithm can be directly applied to this case and that it can fully exploit the advantages of using an NLA instead of a Uniform Linear Array (ULA). Using theoretical analysis and simulations, we demonstrate that employing an NLA with the same number of sensors as the ULA, yields better performance. Moreover, reducing the number of sensors while keeping the same array aperture as the ULA slightly modifies the Mean Square Error (MSE). Therefore, thanks to the NLA, it is possible to maintain a good resolution while decreasing the number of sensors. We also show that root-MUSIC presents good performance and is one of the simplest high resolution methods for this type of arrays. Closed-form expressions of the estimator variance and the Cramer-Rao Bound (CRB) are derived in order to support our simulation results. In addition, the analytical expression of the CRB of the NLA to the CRB of the ULA ratio is calculated in order to show the advantages of the NLA.