Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems

In the field of adaptive signal processing, it is well known that affine projection algorithms or their low-computational implementations fast affine projection algorithms can produce a good tradeoff between convergence speed and computational complexity. Although these algorithms typically do not provide the same convergence speed as recursive-least-squares algorithms, they can provide a much improved convergence speed compared to stochastic gradient descent algorithms, without the high increase of the computational load or the instability often found in recursive-least-squares algorithms. In this paper, multichannel affine and fast affine projection algorithms are introduced for active noise control or acoustic equalization. Multichannel fast affine projection algorithms have been previously published for acoustic echo cancellation, but the problem of active noise control or acoustic equalization is a very different one, leading to different structures, as explained in the paper. The computational complexity of the new algorithms is evaluated, and it is shown through simulations that not only can the new algorithms provide the expected tradeoff between convergence performance and computational complexity, they can also provide the best convergence performance (even over recursive-least-squares algorithms) when nonideal noisy acoustic plant models are used in the adaptive systems.