Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling-Part II: High-Order Extensions

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRA) have reduced mutual coupling compared to uniform linear arrays (ULAs). These arrays also have a difference coarray with O (N-2) virtual elements, where N is the number of physical sensors, and can therefore resolve O (N-2) uncorrelated source directions. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. In a companion paper, a sparse array configuration called the (second-order) super nested array was introduced, which has many of the advantages of these sparse arrays, while removing most of the disadvantages. Namely, the sensor locations are readily computed for any N (unlike MRAs), and the difference coarray is exactly that of a nested array, and therefore hole-free. At the same time, the mutual coupling is reduced significantly (unlike nested arrays). In this paper, a generalization of super nested arrays is introduced, called the Qth-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for Q > 2. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.