Journal article

Eigenvalue-Based Detection of a Signal in Colored Noise: Finite and Asymptotic Analyses

Lahiru D Chamain, Prathapasinghe Dharmawansa, Saman Atapattu, Chintha Tellambura

IEEE Transactions on Information Theory | Institute of Electrical and Electronics Engineers | Published : 2020

Abstract

Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance matrix, which is constructed via m-dimensional p signal-plusnoise samples and m-dimensional n noise-only samples. A finite dimensional characterization of this statistic under the alternative hypothesis has hitherto been an open problem. We answer this problem by deriving cumulative distribution function (c.d.f.) of this l.g.e. via the powerful orthogonal polynomial approach, exploiting the deformed Jacobi unitary ensemble (JUE). Two special cases and an as..

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