Abstract
Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed-form expression for the Cramér-Rao bound (CRB) of the complex ICA problem has not yet been established. In this paper, we fill this gap for the noiseless case and circular sources. The CRB depends on the distributions of the sources only through two characteristic values which can be easily calculated. In addition, we study the CRB for the family of circular complex generalized Gaussian distributions (GGD) in more detail and compare it to simulation results using several ICA estimators.
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References
Wirtinger, W.: Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen. Mathematische Annalen 97(1), 357–375 (1927)
Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: identifiability, uniqueness, and separability. IEEE Transactions on Information Theory 52(3), 1017–1029 (2006)
Tichavsky, P., Koldovsky, Z., Oja, E.: Performance analysis of the FastICA algorithm and Cramér-Rao bounds for linear independent component analysis. IEEE Trans. on Sig. Proc. 54(4) (April 2006)
Ollila, E., Kim, H.-J., Koivunen, V.: Compact Cramér-Rao bound expression for independent component analysis. IEEE Trans. on Sig. Proc. 56(4) (April 2008)
De Lathauwer, L., De Moor, B.: On the blind separation of non-circular sources. In: EUSIPCO 2002, Toulouse, France (September 2002)
Douglas, S.C.: Fixed-point algorithms for the blind separation of arbitrary complex-valued non-gaussian signal mixtures. EURASIP J. Appl. Signal Process. 2007(1) (January 2007)
Li, H., Adali, T.: Algorithms for complex MLICA and their stability analysis using Wirtinger calculus. IEEE Trans. on Sig. Proc. 58(12), 6156–6167 (2010)
Li, X.-L., Adali, T.: Complex independent component analysis by entropy bound minimization. IEEE Transactions on Circuits and Systems I: Regular Papers 57(7), 1417–1430 (2010)
Novey, M., Adali, T.: Adaptable nonlinearity for complex maximization of nongaussianity and a fixed-point algorithm. In: Proc. IEEE Workshop on Machine Learning for Signal Processing (September 2006)
Remmert, R.: Theory of complex functions. Graduate texts in mathematics. Springer, Heidelberg (1991)
Brandwood, D.H.: A complex gradient operator and its application in adaptive array theory. IEE Proc. 130, 11–16 (1983)
Ollila, E., Koivunen, V., Eriksson, J.: On the Cramér-Rao bound for the constrained and unconstrained complex parameters. In: Proc. IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM (2008)
Jagannatham, A.K., Rao, B.D.: Cramér-Rao lower bound for constrained complex parameters. IEEE Sig. Proc. Letters 11(11) (November 2004)
Novey, M., Adali, T., Roy, A.: A complex generalized gaussian distribution – characterization, generation, and estimation. IEEE Trans. on Sig. Proc. 58(3), 1427–1433 (2010)
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Loesch, B., Yang, B. (2012). Cramér-Rao Bound for Circular Complex Independent Component Analysis. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_6
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DOI: https://doi.org/10.1007/978-3-642-28551-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28550-9
Online ISBN: 978-3-642-28551-6
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