Identifiability Results for Nonuniform Linear and Rectangular Sensor Arrays

Sensor arrays with simple geometries play an important role in solving direction of arrival estimation and source separation problems. To reduce the number of sensors used, nonuniform linear and rectangular array geometries have been proposed. Unlike the case of uniform linear and rectangular arrays, identifiability conditions for direction of arrival estimation and source separation using nonuniform linear and rectangular arrays are not well-studied. Based on rank properties of Fourier matrices and tools from algebraic geometry, we present generic identifiability conditions for direction of arrival estimation and source separation problems when nonuniform linear and rectangular array geometries are used. Furthermore, based on properties of bilinear factorizations subject to polynomial/monomial equality constraints, we also briefly discuss how to obtain deterministic identifiability conditions.