4,500 research outputs found
New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources
Blind signal extraction, a hot issue in the field of communication signal processing, aims to retrieve the sources through the optimization of contrast functions. Many contrasts based on higher-order statistics such as kurtosis, usually behave sensitive to outliers. Thus, to achieve robust results, nonlinear functions are utilized as contrasts to approximate the negentropy criterion, which is also a classical metric for non-Gaussianity. However, existing methods generally have a high computational cost, hence leading us to address the problem of efficient optimization of contrast function. More precisely, we design a novel “reference-based” contrast function based on negentropy approximations, and then propose a new family of algorithms (Alg.1 and Alg.2) to maximize it. Simulations confirm the convergence of our method to a separating solution, which is also analyzed in theory. We also validate the theoretic complexity analysis that Alg.2 has a much lower computational cost than Alg.1 and existing optimization methods based on negentropy criterion. Finally, experiments for the separation of single sideband signals illustrate that our method has good prospects in real-world applications
Cram\'er-Rao Bounds for Complex-Valued Independent Component Extraction: Determined and Piecewise Determined Mixing Models
This paper presents Cram\'er-Rao Lower Bound (CRLB) for the complex-valued
Blind Source Extraction (BSE) problem based on the assumption that the target
signal is independent of the other signals. Two instantaneous mixing models are
considered. First, we consider the standard determined mixing model used in
Independent Component Analysis (ICA) where the mixing matrix is square and
non-singular and the number of the latent sources is the same as that of the
observed signals. The CRLB for Independent Component Extraction (ICE) where the
mixing matrix is re-parameterized in order to extract only one independent
target source is computed. The target source is assumed to be non-Gaussian or
non-circular Gaussian while the other signals (background) are circular
Gaussian or non-Gaussian. The results confirm some previous observations known
for the real domain and bring new results for the complex domain. Also, the
CRLB for ICE is shown to coincide with that for ICA when the non-Gaussianity of
background is taken into account. %unless the assumed sources' distributions
are misspecified. Second, we extend the CRLB analysis to piecewise determined
mixing models. Here, the observed signals are assumed to obey the determined
mixing model within short blocks where the mixing matrices can be varying from
block to block. However, either the mixing vector or the separating vector
corresponding to the target source is assumed to be constant across the blocks.
The CRLBs for the parameters of these models bring new performance bounds for
the BSE problem.Comment: 25 pages, 8 figure
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