On ESPRIT with Multiple Coprime-Invariances

In conventional ESPRIT, a single translational invariance in a sensor array is used to obtain high-resolution direction-of-arrival (DOA) estimation. However, when the invariance is greater than the classical sensor spacing λ/2, spatial frequency ambiguity may occur. In this paper, we propose to use multiple setwise coprime invariances to resolve this ambiguity. While special cases of this were known in the literature, our algorithm is more general in that we consider any number of invariances, and that it can perfectly recover any number of DOAs (limited only in terms of number of sensors) if infinite snapshots are available. We also demonstrate through simulation that our algorithm works well in a practical setting where only finite snapshots are available.