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

Abstract

Linear [one-dimensional (1-D)] sparse arrays such as nested arrays and minimum redundancy arrays have hole-free difference coarrays with $O(N^2)$ virtual sensor elements, where $N$ 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 $O(N^2)$ property implies that $O(N^2)$ uncorrelated sources can be identified. For the 2-D case, planar sparse arrays with hole-free coarrays having $O(N^2)$ 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 $O(N^2)$ sources have to be handled with more care in 2-D. This paper introduces new planar sparse arrays with hole-free coarrays having $O(N^2)$ elements just like the OBA, with the additional property that the number of sensor pairs with small spacings such as $\lambda /2$ 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.