Duality between widely linear and dual channel adaptive filtering

Authors:
Danilo P. Mandic;Susanne Still;Scott C. Douglas
Affiliations:
Electrical and Electronic Engineering Department, Imperial College London SW7 2AZ, UK;Department of Information and Computer Sciences Honolulu, HI 96822, USA;Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75275-0338, USA
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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Abstract

We address the duality between adaptive filtering in ℂ and ℝ2 and provide a comparison between the well understood dual channel real valued least mean square (DCRLMS) algorithm in ℝ2 and the corresponding algorithms in ℂ. These include the complex LMS (CLMS) and the recently introduced augmented CLMS (ACLMS), a widely linear algorithm designed for the processing of noncircular complex valued signals. The analysis shows that the standard CLMS and DCRLMS in general provide different adaptive filtering solutions, whereas the ACLMS and DCRLMS are isomoprhic and can be made equivalent. The analysis is supported by simulations on noncircular real world signals.