High order super nested arrays

Mutual coupling between sensors has a negative impact on the estimation of directions of arrival (DOAs). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs) have less mutual coupling than uniform linear arrays (ULAs). These sparse arrays also have a difference coarray of size O(N
²
), where N is the number of sensors, and can therefore resolve O(N
²
) uncorrelated source directions. The various sparse arrays proposed in the literature have their pros and cons. The nested array is practical and easy to use but has a dense ULA part which suffers from mutual coupling effects like the traditional ULA. The recently introduced super nested arrays reduce this mutual coupling problem, while maintaining the desirable hole-free O(N
²
) difference coarray of the nested array. 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. A numerical example is included to demonstrate the superior performance of these arrays.
¹