Proportionate-type hard thresholding adaptive filter for sparse system identification

Recently proposed Hard Thresholding based Adaptive Filtering (HTAF) algorithm provides an on-line counterpart of a compressed sensing based greedy sparse recovery algorithm called iterative hard thresholding (IHT) by constructing a sliding-window based cost function. This leads to an adaptive algorithm with data reuse gradient term (i.e. with multi-regressors) followed by a fixed hard thresholding operator. The HTAF algorithm achieves both robustness against colored input (due to the data reuse in gradient update) and smaller steady state error (due to hard thresholding operator) while identifying a sparse system. In this paper, we propose a new sparse adaptive technique called Proportionate type Hard Thresholding Adaptive Filter (PtHTAF) using a proportionate-type gradient update followed by a variable hard thresholding operator. The proposed PtHTAF algorithm enjoys faster initial convergence rate (due to proportionate type gradient update) while maintaining low steady-state excess mean square error like the HTAF. Simulation results establish superiority of the proposed algorithm over existing sparse adaptive algorithms.