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Blind Identification and Separation of Complex-valued Signals

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This is the 1st edition with a publication date of 10/7/2013.
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We consider the blind estimation of a multiple input/multiple output (MIMO) system that mixes a number of underlying signals of interest called sources. We also consider the case of direct estimation of the inverse system for the purpose of source separation. We will describe the estimation theory associated with the identifiability conditions and dedicated algebraic algorithms. The algorithms depend critically on (statistical and/or time-frequency) properties of complex sources that will be described precisely.

Table of Contents

1. Introduction:  A brief history, the importance of the problem, non-circular signals, applications

2. Model and useful statistics: Mixing model, assumptions about mixing matrix and sources, statistics matrices and non-circular statistics matrices, Maximum Likelihood framework, Identifiability conditions, CRLB.

3. Normalization: Whitening, the case with additive noise, the case of over-determined systems, advantages/drawbacks

4. Direct estimation; Algebraic tools, exact diagonalization of two matrices, identifiability issues, some illustrations by computer simulations

5. Unitary recursive estimation: Unitary joint diagonalization of a set of Hermitian matrices, unitary joint diagonalization of a set of complex symmetric matrices, illustrations by computer simulations

6. General recursjve estimation: General Joint diagonalization of a set of Hermitian matrices, General joint diagonalization of a set of complex symmetric matrices, some illustrations by computer simulations

7. Adaptive complex estimation:  ML and maximization of negentropy

8. Conclusion

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