Unitary Esprit for Coprime Arrays

Abstract

Coprime arrays are normally used to identify more sources than sensors, using the coarray domain. They can also be used directly in element-space and still have benefits of better accuracy and resolution compared to ULAs. An invariance is buried in each of the two sparse ULAs which constitute a coprime array. In this paper, ESPRIT is applied separately to each ULA to yield a set of residues of DOAs, and residues from the ULAs are paired to resolve DOAs. With unitary ESPRIT, residues are automatically paired in the real and imaginary parts of the eigenvalues of a matrix obtained from outputs of the two ULAs. These eigenvalues are proved to be distinct, so the eigendecomposition is unique. Previous works used traditional ESPRIT for similar application, so the eigenvalues corresponding to each invariance were complex; elaborate steps were taken to pair residues. Advantages of the proposed method are demonstrated by simulations.