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Weight Extraction of Fast QRD-RLS Algorithms

  • Stefan WernerEmail author
  • Mohammed Mobien
Chapter

Abstract

The main limitation of fast QR-decomposition recursive least-squares (FQRD-RLS) algorithms is that they lack an explicit weight vector term. Furthermore, they do not directly provide the variables allowing for a straightforward computation of the weight vector as is the case with the conventional QRD-RLS algorithm, where a back-substitution procedure can be used to compute the coefficients. Therefore, the applications of the FQRD-RLS algorithms are limited to certain output-error-based applications (e.g., noise cancelation), or to applications that can provide a decision-feedback estimate of the training signal (e.g., equalizers operating in decision-directed mode). This chapter presents some observations that allow us to apply the FQRD-RLS algorithms in applications that traditionally have required explicit knowledge of the transversal weights. Section 11:1 reviews the basic concepts of QRD-RLS and the particular FQRD-RLS algorithm that is used in the development of the new applications. Section 11.2 describes how to identify the implicit FQRD-RLS transversal weights. This allows us to use the FQRD-RLS algorithm in a system identification setup. Section 11.3 applies the FQRD-RLS algorithm to burst-trained systems, where the weight vector is updated during a training phase and then kept fixed and used for output filtering. Section 11.4 applies the FQRD-RLS algorithm for single-channel active noise control, where a copy of the adaptive filter is required for filtering a different input sequence than that of the adaptive filter. A discussion on multichannel and lattice extensions is provided in Section 11.5. Finally, conclusions are drawn in Section 11.6.

Keywords

Mean Square Error Weight Vector Adaptive Filter Primary Path Unknown System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Helsinki University of TechnologyEspooFinland

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