Transformation of a circular array to a linear array with a Vandermonde structure

Abstract

We address the transformation of a uniform circular array to a virtual uniform linear array. This phase mode transformation is widely used because many computationally efficient techniques that are not applicable to circular arrays can be implemented after the transformation. However, the transformed array is only approximately linear and its steering vector lacks a crucial property of a uniform linear array: a Vandermonde structure. The performances of the algorithms designed for uniform linear arrays can be substantially improved by removing the error in the transformation, thereby enforcing the Vandermonde structure in the steering vectors. We present an analytical technique to remove errors in the transformation and validate its efficacy by demonstrating an improvement in the root MUSIC algorithm.