Investigations on performance enhancement of proportionate affine projection algorithms for sparse system identification

Abstract

Cluster-sparse or block-sparse system identification has gained newlinemuch attention in the domain of adaptive signal processing and the adaptive newlinefilters that improve the performance of identifying cluster-sparse systems are newlinebeing studied intensively. As sparse systems have only a few significant newlinecoefficients amidst large number of insignificant coefficients, the newlineproportionate algorithms exploit sparsity by assigning step-sizes that are newlineproportional to the individual coefficients. The objective of this research is to newlinepropose new algorithms for cluster-sparse or block-sparse system newlineidentification that exhibit improvement in terms of normalised misalignment, newlinetracking, and convergence rate over the existing algorithms in literature. newlineFirstly, a set of algorithms for the Cluster-Sparse Proportionate newlineAffine Projection Algorithm (CS-PAPA) or Cluster-Sparse Improved newlineProportionate Affine Projection Algorithm (CS-IPAPA) is proposed in the newlinecontext of echo cancellation. The algorithms are named Memory Cluster- newlineSparse Proportionate Affine Projection Algorithm (MCS-PAPA) and Memory newlineCluster-Sparse Improved Proportionate Affine Projection Algorithm (MCSIPAPA), newlinewhich incorporate the history of proportionate factors into the CSPAPA newlineand CS-IPAPA, respectively. The update equation is derived from the newlinecost function of the CS-PAPA or CS-IPAPA. Based on the energy newlineconservation arguments, a rigorous performance analysis of the proposed newlineMCS-PAPA is presented. Experimental results for the steady-state mean newlinesquare error corroborate with the theoretical expressions. Moreover, the newlinecondition for the mean stability is derived. Through simulations, the transient newlineperformance of MCS-PAPA is analyzed. newline