A MIMO Version of the Reed-Yu Detector and Its Connection to the Wilks Lambda and Hotelling [Formula Omitted] Statistics

In this paper we study the problem of detecting a known signal transmitted over a MIMO channel of unknown complex gains and additive noise of unknown covariance. The problem arises in many contexts, including transmit-receiver synchronization. We derive the exact probability distribution for a gener...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2020-01, Vol.68, p.2925
Main Authors: Butler, Ronald W, Pakrooh, Pooria, Scharf, Louis L
Format: Article
Language:English
Subjects:
Covariance
Eigenvalues
False alarms
Incoherent scattering
Likelihood ratio
Statistical analysis
Statistics
Synchronism
Wave propagation
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Summary:In this paper we study the problem of detecting a known signal transmitted over a MIMO channel of unknown complex gains and additive noise of unknown covariance. The problem arises in many contexts, including transmit-receiver synchronization. We derive the exact probability distribution for a generalized likelihood ratio (GLR) statistic, and establish the connection between this statistic and the Wilks Lambda and Hotelling [Formula Omitted] statistics. We give alternatives to the GLR statistic, which include the Bartlett-Nanda-Pillai trace, the Lawley-Hotelling trace, and the Roy maximum eigenvalue statistics, each of which is favored under special conditions on the actual MIMO channel. For example, if the channel is an incoherent scattering channel, then the competition for greatest power is among the Bartlett-Nanda-Pillai, Lawley-Hotelling, and GLR statistics. If it is a coherent channel that supports a propagating wave, then Roy's test is more powerful. We discuss the null distribution theory of the GLR at length to show how it may be used to accurately predict false alarm probabilities.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.2988996