Non-Gaussian robust matched subspace detectors and signal design analysis for a class of separable subspaces

The paper introduces a new class of subspaces, denoted separable subspaces, that enables the derivation of computationally efficient expressions for robust matched filter detectors for the family of generalized Gaussian (GG) density functions. These generalized likelihood ratio detectors are robust to interference whose subspace may or may not be known or learned. The detectors are generalizations of the χ² and t or F statistics used when the noise is assumed to have a Gaussian density, also a member of the GG family. The paper also describes how arbitrary subspaces can be approximated by the newly introduced separable ones should it be advantageous to do so; separable subspaces therefore make it possible to discretize the space. The computationally efficient expressions for the detectors enable the performance analysis for signal design when the basis for the separable subspaces consist solely of binary valued elements. This class, which includes the Haar basis functions, has been shown to be applicable to functional MRI detection problems.