TY - GEN
T1 - Complex-valued signal processing essential models, tools and statistics
AU - Ollila, Esa
AU - Koivunen, Visa
AU - Poor, H. Vincent
PY - 2011
Y1 - 2011
N2 - Complex-valued signals arise in many diverse fields such as communications, radar, biomedical sciences, physical sciences, and related fields. This paper briefly reviews some important tools, statistics, models and estimators that are useful for handling complex-valued random signals. Over the past four decades, circularity (i.e. invariance of the distribution under multiplication by a unit complex number) or second-order circularity (i.e. uncorrelatedness of the random vector with its complex conjugate) has been a common implicit assumption. Hence in this paper a special emphasis is put on this circularity property, as optimal signal processing methods for circular and non-circular signals are often different and choosing the right type of processing can provide significant performance gains. Topics reviewed in this paper include different types of circularity measures and detectors of circularity, complex elliptical symmetry of random variables, Cramer-Rao lower bounds on the estimation of complex-valued parameters, optimization of a real-valued cost function with respect to complex-valued parameters using ℂℝ-calculus, and complex-valued independent component analysis.
AB - Complex-valued signals arise in many diverse fields such as communications, radar, biomedical sciences, physical sciences, and related fields. This paper briefly reviews some important tools, statistics, models and estimators that are useful for handling complex-valued random signals. Over the past four decades, circularity (i.e. invariance of the distribution under multiplication by a unit complex number) or second-order circularity (i.e. uncorrelatedness of the random vector with its complex conjugate) has been a common implicit assumption. Hence in this paper a special emphasis is put on this circularity property, as optimal signal processing methods for circular and non-circular signals are often different and choosing the right type of processing can provide significant performance gains. Topics reviewed in this paper include different types of circularity measures and detectors of circularity, complex elliptical symmetry of random variables, Cramer-Rao lower bounds on the estimation of complex-valued parameters, optimization of a real-valued cost function with respect to complex-valued parameters using ℂℝ-calculus, and complex-valued independent component analysis.
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U2 - 10.1109/ITA.2011.5743596
DO - 10.1109/ITA.2011.5743596
M3 - Conference contribution
AN - SCOPUS:79955774285
SN - 9781457703614
T3 - 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings
SP - 296
EP - 305
BT - 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings
T2 - 2011 Information Theory and Applications Workshop, ITA 2011
Y2 - 6 February 2011 through 11 February 2011
ER -