Adaptive detection of subspace signals from two independent sets of samples drawn from a matrix-variate Student distribution

Abstract

In this paper we address estimation and detection problems using multiple multichannel observations drawn from a matrix-variate Student distribution, also referred to as uncorrelated t distribution. In a first part we derive the Fisher information matrix when the distribution depends on an unknown parameter vector. Next, we consider adaptive detection of a subspace signal using independent test and training data following a matrix-variate Student distribution. We derive the maximum likelihood estimates of the signal amplitude and of the noise covariance matrix and subsequently the generalized likelihood ratio test. Additionally, the score function and the Fisher information matrix derived in the first part of the paper are used to compute Rao, Wald and gradient tests. The detection performance of these methods is illustrated via numerical simulations.