Multichannel RLS algorithms and FTF algorithms for active noise control and sound reproduction systems

Abstract

In the fields of active noise control (ANC) and transaural sound reproduction (TSR), multichannel FIR adaptive filters are extensively used. For the learning of such FIR adaptive filters, recursive-least-squares (RLS) algorithms are known to typically produce a faster convergence speed than stochastic gradient descent techniques, such as the basic least-mean-squares (LMS) algorithm or even the fast convergence Newton-LMS, gradient-adaptive-lattice (GAL) LMS and discrete-cosine-transform (DCT) LMS algorithms. In this presentation, multichannel RLS algorithms and multichannel fast-transversal-filter (FTF) algorithms are introduced, with the structures of some stochastic gradient descent algorithms used in ANC: the filtered-x LMS, the adjoint-LMS and the modified filtered-x LMS. The new algorithms can be used in ANC systems or for the deconvolution of sounds in TSR systems. Also, heuristic techniques are introduced, to compensate for the potential ill-conditioning of the correlation matrix in ANC or TSR systems, and for the potential numerical instability of the multichannel FTF-based algorithms. Simulations of ANC and TSR systems will compare the performance of the different multichannel LMS, RLS, and FTF-based algorithms.