The Augmented Complex Kernel LMS

• Published in: IEEE transactions on signal processing Vol. 60; no. 9; pp. 4962 - 4967
• Main Authors: Bouboulis, P., Theodoridis, S., Mavroforakis, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filter; Applied sciences; Calculus; complex RKHS; complex signal processing; Detection, estimation, filtering, equalization, prediction; Estimation; Exact sciences and technology; Hilbert space; Information, signal and communications theory; Kernel; kernel LMS; Least squares approximation; noncircular data; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; Telecommunications and information theory; widely linear estimation; Wirtinger's calculus; Performance evaluation; complex RKHS; Adaptive signal processing; Complex signal; Adaptive filter; widely linear estimation; Kernel method; kernel LMS; Linear filter; Signal processing; Hilbert space; Linear estimation; Wirtinger's calculus; noncircular data; Least mean squares methods; complex signal processing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2012.2200479

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex reproducing kernel Hilbert spaces, developed a suitable Wirtinger-like calculus for general Hilbert spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely linear estimation filters suitable for applications involving noncircular data. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.