Complex-valued signal processing essential models, tools and statistics

Esa Ollila, Visa Koivunen, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publication2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings
Pages296-305
Number of pages10
DOIs
StatePublished - May 13 2011
Event2011 Information Theory and Applications Workshop, ITA 2011 - San Diego, CA, United States
Duration: Feb 6 2011Feb 11 2011

Publication series

Name2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings

Other

Other2011 Information Theory and Applications Workshop, ITA 2011
CountryUnited States
CitySan Diego, CA
Period2/6/112/11/11

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Information Systems

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    Ollila, E., Koivunen, V., & Poor, H. V. (2011). Complex-valued signal processing essential models, tools and statistics. In 2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings (pp. 296-305). [5743596] (2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings). https://doi.org/10.1109/ITA.2011.5743596