Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling—Part I: Fundamentals

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> denoting the number of sensors, these sparse arrays offer <inline-formula><tex-math notation="LaTeX">$O({N}^{2})$</tex-math></inline-formula> freedoms for source estimation because their difference coarrays have <inline-formula><tex-math notation="LaTeX"> $O({N}^{2})$</tex-math></inline-formula>-long ULA segments. 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. This paper introduces a new array called the super nested array, which has all the good properties of the nested array, and at the same time achieves reduced mutual coupling. There is a systematic procedure to determine sensor locations. For fixed <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula>, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with small separations (<inline-formula><tex-math notation="LaTeX">$\lambda /2,2\times \lambda /2$</tex-math></inline-formula>, etc.) is significantly reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays. In the companion paper, a further extension called the <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>th-order super nested array is developed, which further reduces mutual coupling.