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A Survey of Kurtosis Optimization Schemes for MISO Source Separation and Equalization

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Advances in Heuristic Signal Processing and Applications

Abstract

Blind source separation and equalization aim at recovering a set of unknown source signals from their linearly distorted mixtures observed at a sensor array output, with little or no prior knowledge about the sources or the distorting channel. This fundamental signal processing problem arises in a broad range of applications such as multiuser digital communications, biomedical data analysis, and seismic exploration. Put forward over three decades ago, the normalized fourth-order cumulant, also known as kurtosis, has arguably become one of the most popular blind source separation and equalization criteria. Using multiple-input single-output (MISO) filter structures for single source extraction combined with suitable deflation procedures, the kurtosis contrast yields separation algorithms free of spurious extrema in ideal system conditions. The lack of closed-form solutions, however, calls for numerical optimization schemes. The present chapter reviews some of the iterative algorithms most widely used for MISO source separation and equalization based on kurtosis. These include gradient and Newton search methods, algorithms with optimal step-size selection, as well as techniques based on reference signals. Their main features are briefly summarized and their performance is illustrated by some numerical experiments in digital communications and biomedical signal processing.

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Notes

  1. 1.

    Recording kindly provided by the Hemodynamics Department, Clinical University Hospital, University of Valencia, Spain, and ITACA-Bioingenieria, Polytechnic University of Valencia, Spain.

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Authors and Affiliations

  1. CNRS UMR 5157 SAMOVAR, Institut Mines-Télécom/Télécom SudParis, 9 Rue Charles Fourier, 91011, Evry Cedex, France

    Marc Castella

  2. ISITV, LSIS UMR-CNRS 7296, University of the South Toulon-Var, av. G. Pompidou, BP 56, 83162, La Valette du Var Cedex, France

    Eric Moreau

  3. I3S Laboratory, University of Nice Sophia Antipolis, CNRS, Les Algorithmes, Euclide-B, 2000 route des Lucioles, BP 121, 06903, Sophia Antipolis Cedex, France

    Vicente Zarzoso

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Correspondence to Marc Castella .

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  1. Electrical Engineering Department, Jadavpur University, Kolkata, 700032, West Bengal, India

    Amitava Chatterjee

  2. Dept. of Aerospace Engineering, Sharif University of Technology, Azadi Street, Tehran, Iran

    Hadi Nobahari

  3. Laboratory LiSSi, University of Paris 12, av. du Général de Gaulle 61, Créteil, 94010, France

    Patrick Siarry

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Castella, M., Moreau, E., Zarzoso, V. (2013). A Survey of Kurtosis Optimization Schemes for MISO Source Separation and Equalization. In: Chatterjee, A., Nobahari, H., Siarry, P. (eds) Advances in Heuristic Signal Processing and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37880-5_9

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