Multi-input multi-output fast QR decomposition algorithm for active noise control

Fast QR-decomposition based recursive least-squares (FQRD-RLS) algorithms are known for their good numerical properties and low computational complexity. However, they have so far not been used in active noise control (ANC) because the general implementation would require multiple-input multiple-output (MIMO) FQRD-RLS algorithms, which are currently not available in the technical literature. Another reason is the lack of an explicit weight vector update equation in the FQRD-RLS algorithms, which prevents their use in structures where a copy of the coefficients is filtering a different input sequence than that of the adaptive filter, e.g., the modified filtered-x ANC (MFX-ANC) structure. In this paper, we derive a MIMO-FQRD-RLS algorithm based on backward prediction error updates. The proposed algorithm is applied to a multichannel MFX-ANC structure. We show how to avoid the explicit use of the weight vector in the MFX-ANC structure by reproducing the filtered-x signal from the internal variables of the proposed algorithm. Simulation results confirm that the learning curves of the MIMO-FQRD-RLS algorithm are identical to those obtained by the QRD-RLS algorithm.