Tutorial 13: Complex-Valued Adaptive Signal Processing: Algorithms and Applications

Monday, May 27, 2-5 pm

Presented by

Danilo P. Mandic, Scott C. Douglas


Numerous adaptive signal processing applications are enabled by a complex-valued signal framework. For the most part, these methods are driven by physical models that assume traditional complex-valued computations for input-output behavior and statistical assumptions that lead to proper (second-order circular) signal models. Recently, it has become recognized by numerous signal processing practitioners that a broader framework involving widely-linear input-output systems and improper or non-circular statistical models offers additional capabilities beyond the traditional complex-valued methods. Development of adaptive signal processing solutions in this broader framework can be challenging to get right, and the understanding of their advantages and limitations are non-obvious at first glance.

This tutorial brings together algorithms, analyses, and applications of widely-linear complex system models and non-circular signal statistics for adaptive signal processing. The approach taken offers new insights into well-known problems in beamforming, blind source separation, and adaptive frequency tracking and complex channel modeling, while enabling critical connections between real-valued and complex-valued adaptive signal processing methods to be made.

This tutorial will bring together the latest advances in augmented complex statistics and will introduce a suite of adaptive signal processing and blind source separation algorithms under the umbrella of widely linear modelling. In this tutorial, we will:

  • Provide a theoretical and computational platform for statistical signal processing of the generality of complex valued signals (both proper and improper);
  • Give an in-depth insight into widely linear estimation, the role of noise and eigenstructure of correlation matrices;
  • Revisit the complex gradient and Hessian, and introduce the CR calculus;
  • Present tests for the degree of noncircularity and use this information as an additional degree of freedom in detection and estimation problems;
  • Introduce a suite of adaptive signal processing algorithms suitable for the filtering of both second order circular and noncircular signals;
  • Illustrate the performance and convergence of widely linear adaptive filtering algorithms for both circular and noncircular data;
  • Introduce blind source separation and extraction algorithms in this context;
  • Provide simulation studies, including prediction, tracking, beamforming, and source separation in communications and renewable energy (smart grid) applications

Speaker Biography

Danilo P. Mandic

Danilo P. Mandic has been working in the area of nonlinear and adaptive signal processing for more than 15 years, and is a Professor at the Department of Electrical and Electronic Engineering, Imperial College London, UK. His work on complex valued and nonlinear adaptive signal processing has been widely published, and some of the concepts relevant to this tutorial can be found in his research monographs Recurrent Neural Networks for Prediction, Wiley 2001 (with J. Chambers) and Complex Valued Nonlinear Adaptive Filters, Wiley 2009 (with S. L. Goh). Dr. Mandic has been a Member of the IEEE Signal Processing Society Technical Committee on Signal Processing Theory and Methods and an Associate Editor for IEEE Signal Processing Magazine, IEEE Transactions on Neural Networks, IEEE Transactions on Signal Processing, and IEEE Transactions on Circuits and Systems. He has authored several award winning papers and has received awards for products arising from his collaboration with industry.

Scott C. Douglas

Scott C. Douglas received the B.S. (with distinction), M.S., and Ph.D. degrees in Electrical Engineering from Stanford University, Stanford, CA. He is a Professor in the Department of Electrical Engineering at Southern Methodist University, Dallas, TX. His research activities include adaptive filtering, active noise control, blind deconvolution and source separation, and VLSI/hardware implementations of digital signal processing systems. Dr. Douglas is the author or co-author of two books, seven book chapters, and more than 180 artices in journals and conference proceedings. He is a senior member of the IEEE and a past Associate Editor for the IEEE Transactions on Signal Processing (IEEE), the IEEE Signal Processing Letters (IEEE), and the Journal of Signal Processing Systems (Springer). He has served in numerous roles to the IEEE, including General Chair of ICASSP 2010, Chair of the Neural Networks for Signal Processing Technical Committee, and Secretary of the Signal Processing Education Technical Committee of the IEEE Signal Processing Society. He has played an integral role in developing and managing the Infinity Project, an effort among university faculty, high-tech industry, and civic educational leaders to bring an exciting and practical engineering curriculum to high school students both in the U.S. and internationally.