A Comparative Survey of Convex Combination of Adaptive Filters

Abstract

Over the last twenty years, combination of adaptive filters has emerged to provide a potential solution in the development of advanced applications, such as channel equalization, active noise control, acoustic echo cancelation, adaptive beamforming, among others. Several authors have demonstrated that the combination of two filters with complementary capabilities improves the overall filter performance in comparison when a single filter is used. Commonly, these combinations employ a fast filter and slow filter to guarantee fast convergence speed and low steady-state mean square error (MSE), respectively, at the cost of increasing their computational complexity. However, those combinations have not been well analysed and compared. Currently, this aspect is crucial since most of the current convex combination of adaptive filters could be implemented in advanced embedded digital devices to be used in real-time signal processing applications. In this work, we evaluate the convex combination of adaptive filters, mainly including those based on least mean square (LMS) algorithm, the affine projection (AP) algorithm and the recursive least mean square (RLS) algorithm. We carry out an extensive performance evaluation to demonstrate the advantages and disadvantages of each approach. Specifically, we simulate them in fixed point, which makes feasible the rapid development of advanced prototypes. This aspect could be potentially valuable to the signal processing engineering communities.

KEYWORDS:

• Adaptive filters
• Adaptation term
• Affine projection algorithm
• Convex combination
• Least mean square algorithm
• Recursive least mean square algorithm

Acknowledgement

The authors would like to thank the Consejo Nacional de Ciencia y Tecnología (CONACyT) and the IPN for the financial support to realize this work.

Additional information

Notes on contributors

Ángel A. Vázquez

Ángel A Vázquez received the BS degree at Instituto Politécnico Nacional, Mexico, in 2018. Currently, he is a master's student at the Instituto Politecnico Nacional, Mexico. His research interest is signal processing applications. Email: [email protected]

J. Gerardo Avalos

J Gerardo Avalos received the BSc and the PhD degrees in electronics and communications engineering from the Instituto Politécnico Nacional, Mexico, in 2008 and 2014, respectively. He is currently working as a professor in the Department of Computer Engineering, at the National Polytechnic Institute. His current research interests are: signal processing, early auditory processing and neuromorphic systems.

Giovanny Sánchez

Giovanny Sánchez received the MS degree at Instituto Politecnico Nacional, Mexico, in 2008, and the PhD degree at Universitat Politécnica de Catalunya, Spain, in 2014. Currently, he is an associate professor in the Instituto Politécnico Nacional, Mexico. His main research interests include development of neuromorphic systems, cryptosystems, MEMs, signal processing and image processing. Email: [email protected]

Juan C. Sánchez

Juan Carlos Sánchez-García received electronic engineering and Doctor of Science degrees from the Universidad Autonoma Metropolitana, at Mexico City, in 1987 and 2000, respectively. Since 1997 he is a researcher at the Graduate Studies and Research Section at ESIME Culhuacan, of Instituto Politécnico Nacional (IPN) in Mexico. His areas of interest are signal processing and the development of analog and digital circuits for telecommunications, medicine and control. Email: [email protected]

Héctor Pérez

Hector Perez-Meana received the MS degree from the University of Electro-Communications, Tokyo Japan, a PhD degree in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1989. In 1981 he joined the Electrical Engineering Department of the Metropolitan University, Mexico City, where he was a professor. His principal research interests are adaptive systems, image processing, pattern recognition, information security and related fields. Dr Perez-Meana is a member of the IEEE, IEICE, the National Researchers System of Mexico and the Mexican Academy of Science. Email: [email protected]