Weight Extraction of Fast QRD-RLS Algorithms

  • Stefan WernerEmail author
  • Mohammed Mobien


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.


Mean Square Error Weight Vector Adaptive Filter Primary Path Unknown System 
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© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Helsinki University of TechnologyEspooFinland

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