Widened nested array: configuration design, optimal array and DOA estimation algorithm

A generalised nested array (GNA) configuration with large minimum inter-element spacing is attractive to alleviate mutual coupling. In this study, by decomposing and rearranging the sub-arrays of GNA, the authors propose a new nested array configuration named as widened nested array (WNA). The WNA enables to provide the reduced mutual coupling, enhanced degrees of freedom (DOFs), extended array aperture and improved direction of arrival (DOA) estimation performance compared to GNA. The closed-form expressions for sensor positions of WNA are given and the optimal array configuration for largest DOFs is derived. Meanwhile, the authors propose a partial angular compressed sensing(CS) based DOA estimation algorithm for WNA. Specifically, discrete Fourier transform method is first derived for consecutive DOFs of WNA to obtain initial DOA estimates. Subsequently, the initial estimates are utilised to compress the angular range of overcomplete dictionary of the CS algorithm, which is exploited to obtain the fine DOA estimates. Extensive simulation results testify that the proposed algorithm has the same estimation accuracy as CS algorithm with lower complexity.