Hourglass Arrays and Other Novel 2-D Sparse Arrays With Reduced Mutual Coupling

Linear [one-dimensional (1-D)] sparse arrays such as nested arrays and minimum redundancy arrays have hole-free difference coarrays with <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> virtual sensor elements, where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of physical sensors. The hole-free property makes it easier to perform beamforming and DOA estimation in the coarray domain which behaves like an uniform linear array. The <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math> </inline-formula> property implies that <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> uncorrelated sources can be identified. For the 2-D case, planar sparse arrays with hole-free coarrays having <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> elements have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2-D nested arrays. Their merits are similar to those of the 1-D sparse arrays mentioned above, although identifiability claims regarding <inline-formula> <tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> sources have to be handled with more care in 2-D. This paper introduces new planar sparse arrays with hole-free coarrays having <inline-formula><tex-math notation="LaTeX"> $O(N^2)$</tex-math></inline-formula> elements just like the OBA, with the additional property that the number of sensor pairs with small spacings such as <inline-formula><tex-math notation="LaTeX">$\lambda /2$</tex-math></inline-formula> decreases, reducing the effect of mutual coupling. The new arrays include half-open box arrays, half-open box arrays with two layers, and hourglass arrays. Among these, simulations show that hourglass arrays have the best estimation performance in presence of mutual coupling.