Preconditioning multichannel adaptive filtering algorithms using EVD- and SVD-based signal prewhitening and system decoupling

It is well known that the convergence rate of multichannel LMS-based algorithms is limited by the correlation properties of the reference signals and the cross-coupling within the plant dynamics. These factors give rise to excessive eigenvalue spread and slow convergence rate of a gradient descent algorithm. A preconditioning technique is developed in this study for the multichannel LMS algorithm so as to improve its convergence rate. Signal prewhitening and system decoupling are the two key elements of the proposed techniques. Preconditioning filters are first formulated in the frequency domain by using eigenvalue decomposition and singular value decomposition. These filters are then transformed into the time domain with causality taken into account. The preconditioning filters are incorporated into a multichannel LMS algorithm, where the reference signals are prewhitened and the plants are decoupled prior to the adaptation process. Simulations for a two-channel/one listener cross-talk cancellation problem illustrate the effectiveness of the preconditioning technique in improving the convergence rate of the adaptive algorithms.