Hourglass arrays: Planar sparse arrays with hole-free coarrays and reduced mutual coupling

Abstract

Linear (1D) sparse arrays such as nested arrays have hole-free difference coarrays with O(N 2) virtual sensor elements, where N is the number of physical sensors. This property implies that O(N 2) monochromatic and uncorrelated sources can be identified. For the 2D 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 2D nested arrays. Their merits are similar to those of the 1D sparse arrays mentioned above, although identifiability claims regarding O(N 2) sources have to be handled with more care in 2D. In this presentation, we propose hourglass arrays, which have closed-form 2D sensor locations and hole-free coarrays with O(N 2) elements just like the OBA. Furthermore, the mutual coupling effect, which is the undesired interaction between sensors, is reduced since the number of sensor pairs with small spacings such as λ/2 decreases. Among the planar arrays mentioned above, simulations show that hourglass arrays have the best estimation performance in the presence of mutual coupling.