Multichannel recursive-least-squares algorithms and fast-transversal-filter algorithms for active noise control and sound reproduction systems

In the last ten years, there has been much research on active noise control (ANC) systems and transaural sound reproduction (TSR) systems. In those fields, multichannel FIR adaptive filters are extensively used. For the learning of FIR adaptive filters, recursive-least-squares (RLS) algorithms are known to 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, the gradient-adaptive-lattice (GAL) LMS and the discrete-cosine-transform (DCT) LMS algorithms. In this paper, 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 modified filtered-x LMS and the adjoint-LMS. The new algorithms can be used in ANC systems or for the deconvolution of sounds in TSR systems. Simulation results comparing the convergence speed, the numerical stability and the performance using noisy plant models for the different multichannel algorithms will be presented, showing the large gain of convergence speed that can be achieved by using some of the introduced algorithms.