  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.
