Union of Subspaces Signal Detection In Subspace Interference

Abstract

This paper investigates detection theory for signals belonging to a union of subspaces (UoS) in the presence of an interference subspace and white noise of unknown variance. Generalized likelihood ratio tests are provided for both signal detection and “active” subspace detection under the UoS model. The paper also derives performance bounds on the associated detection problems and relates them to the geometry of subspaces in the union and the interfering subspace. These relations are then corroborated through numerical experiments on synthetic data.