EURASIP Journal on Advances in Signal Processing 
Volume 2008 (2008), Article ID 765615, 9 pages
doi:10.1155/2008/765615
Research Article

Complex-Valued Adaptive Signal Processing Using Nonlinear Functions

Hualiang Li and Tülay Adalı

 Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Received 16 October 2007; Accepted 14 February 2008

Recommended by Aníbal Figueiras-Vidal

Abstract

We describe a framework based on Wirtinger calculus for adaptive signal processing that enables efficient derivation of algorithms by directly working in the complex domain and taking full advantage of the power of complex-domain nonlinear processing. We establish the basic relationships for optimization in the complex domain and the real-domain equivalences for first- and second-order derivatives by extending the work of Brandwood and van den Bos. Examples in the derivation of first- and second-order update rules are given to demonstrate the versatility of the approach.