Augmented Coprime Array Design via Hole Analysis for Direction of Arrival Estimation

Abstract

Coprime array (CA) is a highly regarded sparse geometry for direction-of-arrival (DOA) estimation because it offers heightened degrees of freedom (DOF) and alleviated mutual coupling (MC) effect. Nevertheless, the appearance of holes in the difference coarray (DCA) of CA extremely shortens the continuous DOF (cDOF) available for the spatial smoothing technique. To cope with this deficiency, we develop an augmented CA (ACA) in this article by deploying a uniform subarray and one sensor at the left end and right end of the CA, respectively. The placement of these additional sensors is determined by the analytical expressions and a 2-D representation that account for all the holes in the DCA of CA. The precise mathematical expressions for the attainable DOF and the first three weight functions of ACA are further derived, which show that ACA achieves the equivalent quantity of cDOF as the hole-free (super) nested arrays, while retaining a comparable level of MC effect to CA. Moreover, in comparison to the majority of advanced sparse array geometries, the devised ACA proves more effective at striking a balance between the quantity of cDOF and MC effect. Numerical examples are provided to confirm the outstanding characteristics of our designed ACA and its remarkable efficacy in DOA estimation.