Inverse QRD BEACON Algorithm

Jose Apolinario Jr., Mobien Shoaib, Stefan Werner

DOI: 10.14209/sbrt.2007.31320

Evento: XXV Simpósio Brasileiro de Telecomunicações (SBrT2007)

Keywords: Filtragem adaptativa Filtragem SetMembership filtering Algoritmos com decomposição QR

Abstract

This paper derives the inverse QR-decomposition (IQRD) version of the Bounding Ellipsoidal Adaptive CONstrained least-squares (BEACON) algorithm. The BEACON algorithm belongs to the family of set-membership filtering (SMF) algorithms that feature sparse updating in time and good tracking capability. The prominent characteristic of sparse updating in SMF arises from a predefined bounded error-constraint specified in the filter design. As a consequence, a set of valid coefficient vector estimates will conform to the constraint rather than a single point-estimate. The choice of the error constraint appears naturally in various signal processing applications, e.g., when model-order is unknown or distance between constellation points is a priori known in a decision-feedback equalizer. The new algorithm, the IQRD-BEACON, implements the same objective function as BEACON and will, therefore, in infinite-precision environment present identical results in terms of learning curves and update frequency. The advantage of the IQRD-BEACON comes with the use of numerically stable rotations in the update equations, thus avoiding the use of the ill-conditioned recursions associated with the matrix-inversion lemma employed in the conventional BEACON. Our claims regarding the performance of the IQRD-BEACON are verified through computer simulations.

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