A Memory Sparse Proportionate Affine Projection Algorithm for Echo Cancellation: Analysis and Simulations

The cluster-sparse proportionate affine projection algorithm (CS-PAPA) exhibits a good solution for estimating the unknown echo path in network echo cancellation. However, the algorithm does not take into account the past proportionate factors for updating the filter coefficients. In this paper, a modification to the CS-PAPA is proposed in the context of echo cancellation. The proposed algorithm named memory cluster-sparse proportionate affine projection algorithm (MCS-PAPA) incorporates the history of proportionate factors into the CS-PAPA. Based on the energy conservation arguments, a rigorous performance analysis of the proposed algorithm is presented, which expresses the steady-state mean square error in terms of the projection order and other parameters. Moreover, the condition for the mean stability is derived. Experimental results for the steady-state mean square error corroborate with the theoretical expressions. Simulation experiments show that the proposed algorithm outperforms some existing algorithms in terms of normalised misalignment, convergence rate, and tracking. As the history of proportionate gain elements is included recursively, the proposed algorithm also exhibits a reduction in computational complexity in terms of the number of multiplications required.