ULA Fitting for Sparse Array Design

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.