Cramér-Rao bound for circular complex independent component analysis

Authors:
Benedikt Loesch;Bin Yang
Affiliations:
Insitute for Signal Processing and System Theory, University of Stuttgart, Germany;Insitute for Signal Processing and System Theory, University of Stuttgart, Germany
Venue:
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Year:
2012

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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.