Geometry of Random Sparse Arrays

We consider random sparse arrays whose sensors are randomly placed on a grid of fixed size. Although deterministic sparse array geometries such as nested, coprime and their many variants have been extensively studied, less is known about difference/sum sets of random arrays. In this work, we analytically characterize the size of the contiguous segment of the so-called difference coarray of random sparse arrays. The difference coarray determines fundamental performance limits of sparse arrays and is therefore an essential object of study. Moreover, a large contiguous coarray is usually desired to guarantee unambiguous identification of many signal sources. We show that i.i.d. sampling schemes can be inadequate for guaranteeing a large contiguous coarray with high probability. Instead, one needs to design alternative random sampling schemes. We propose such a scheme and verify numerically that it yields random arrays with a difference coarray whose contiguous segment scales super-linearly with the expected number of sensors.