Combined block sparse PNLMS/NLMS algorithms

In some applications of adaptive filtering, such as echo cancellation and active noise reduction, an adaptive filter may be required to have a large number of coefficients in order to model unknown systems with a sufficient accuracy. The computational complexity of adaptive filtering algorithms is proportional to the number of filter coefficients being adapted. The main purpose of partial coefficient updating is to reduce high computational complexity associated with long echo paths. So as to reach computational savings, only a subset of the filter coefficients rather than the entire filter is updated. The filter weights to be updated are usually chosen in accordance with the amplitudes of input signal. However, this approach does not achieve similar performance comparing to the fully updated counterpart. There are opinions that for sparse impulse responses the convergence speed can be improved, if the coefficients amplitudes are used in selection criterion. This paper presents a study on proportionate, partially and sparse partial updated algorithms, and provides their generalization to the Proportionate Normalized Least Mean Squares algorithm. Computer simulations show a reasonable performance of the algorithm with applications, which require an identification of sparse regions within long echo paths.