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Multichannel fast QR-decomposition RLS algorithms with explicit weight extraction

Multichannel fast QR decomposition recursive least-squares (MC-FQRD-RLS) algorithms are well known for their good numerical properties and low computational complexity. However, these algorithms have been restricted to problems seeking an estimate of the output error signal. This is because their transversal weights are embedded in the algorithm variables and are not explicitly available. In this paper we present a novel technique that can extract the filter weights associated with the MC-FQRD-RLS algorithm at any time instant. As a consequence, the range of applications is extended to include problems where explicit knowledge of the filter weights is required. The proposed weight extraction technique is used to identify the beampattern of a broadband adaptive beamformer implemented with an MC-FQRD-RLS algorithm. The results confirm that the extracted coefficients of the MC-FQRD-RLS algorithm are identical to those obtained by any RLS algorithm such as the inverse QRD-RLS algorithm.