ULA Fitting for Sparse Array Design

TL;DR

This paper introduces ULA fitting, a novel array design principle that constructs sparse arrays from sub-ULAs to enhance degrees of freedom and reduce mutual coupling, validated through numerical experiments.

Contribution

It proposes a new array design method called ULA fitting that simplifies sparse array construction from sub-ULAs with low mutual coupling.

Findings

Designs SAs with low mutual coupling and large DOF

Provides closed-form expressions for specific SAs

Numerical results show improved performance under heavy mutual coupling

Abstract

Sparse array (SA) geometries, such as coprime and nested arrays, can be regarded as a concatenation of two uniform linear arrays (ULAs). Such arrays lead to a significant increase of the number of degrees of freedom (DOF) when the second-order information is utilized, i.e., they provide long virtual difference coarray (DCA). Thus, the idea of this paper is based on the observation that SAs can be fitted through concatenation of sub-ULAs. A corresponding SA design principle, called ULA fitting, is then proposed. It aims to design SAs from sub-ULAs. Towards this goal, a polynomial model for arrays is used, and based on it, a DCA structure is analyzed if SA is composed of multiple sub-ULAs. SA design with low mutual coupling is considered. ULA fitting enables to transfer the SA design requirements, such as hole free, low mutual coupling and other requirements, into pseudo polynomial equation, and hence, find particular solutions. We mainly focus on designing SAs with low mutual coupling and large uniform DOF. Two examples of SAs with closed-form expressions are then developed based on ULA fitting. Numerical experiments verify the superiority of the proposed SAs in the presence of heavy mutual coupling.