Bayesian methods for sparse RLS adaptive filters

This work deals with an extension of the standard recursive least squares (RLS) algorithm. It allows to prune irrelevant coefficients of a linear adaptive filter with sparse impulse response and it provides a regularization method with automatic adjustment of the regularization parameter. New update equations for the inverse auto-correlation matrix estimate are derived that account for the continuing shrinkage of the matrix size. In case of densely populated impulse responses of length M, the computational complexity of the algorithm stays O(M²) as for standard RLS while for sparse impulse responses the new algorithm becomes much more efficient through the adaptive shrinkage of the dimension of the coefficient space. The algorithm has been successfully applied to the identification of sparse channel models (as in mobile radio or echo cancellation).