Constrained epsilon-equalizer test for multiple hypothesis testing

A constrained epsilon-equalizer test is proposed to detect and classify non-orthogonal vectors in Gaussian noise. The classification error probabilities of this test are equalized up to a negligible difference, subject to a constraint on the false alarm probability. It has a small loss of optimality with respect to the purely theoretical and incalculable constrained equalizer test provided that the norms of vectors to classify are sufficiently large. A numerical example confirms the theoretical findings.