A Proportionate Adaptive Conjugate Gradient Algorithms for Sparse Systems with Impulsive Noise

Tukey's biweight M-estimate conjugate gradient method (TbMCG) is one of the best algorithms to identify the systems with colored input in an impulsive noise environment. In this algorithm, Tukey's biweight M-estimator function is used to im-prove convergence rate and steady-state error in an impulsive environment with less complexity. However, the TbMCG algorithm does not exploit sparse systems though in practice many systems are found to be sparse, such as network echo cancellation, hands-free telephony acoustic echo cancellation, HDTV, wireless multipath channels, underwater acoustic communication, etc. In this paper, proportionate idea is incorporated in the cost function of the TbMCG algorithm to provide proportionate gain to filter taps. The proposed algorithm, called as Tukey's biweight M-estimate proportionate conjugate gradient method (TbMPCG) improves the overall convergence rate by allowing active taps to converge faster. The proposed TbMPCG algorithm also reduces the excessive mean square error (EMSE). Simulation results show that, in particular, the proposed TbMPCG algorithm improves the performance of the TbMCG algorithm both in terms of convergence rate and steady-state error.