Detection of 1-of-M orthogonal signals: asymptotic equivalence of likelihood ratio and multiband models

Abstract

A closed-form solution for the optimal detection of 1-of-M orthogonal signals is presented for low signal energy. The solution is obtained for the Poisson case and applies as well in the Gaussian equal-variance case. Detectability, d′, is given by S/(MB)1/2, where S is the signal energy (in photons) and B is the background. This result is obtained by demonstrating that the decision rule of the likelihood ratio (optimal) detector is identical to that of the multiband detector, which sums photon counts for all M signal loci.