A robust algorithm for adaptive FIR filtering and its performance analysis with additive contaminated-Gaussian noise

We introduce a steepest descent linear adaptive algorithm, the proportion-sign algorithm (PSA), to make the least mean square (LMS) algorithm robust to impulsive interference occurring in the desired response. Its performance analysis is presented when the signals are from zero-mean jointly stationary Gaussian processes and the additive noise to the desired response is from a zero-mean stationary contaminated-Gaussian (CG) process which is usually used to represent impulsive interference. Since a special case of the PSA becomes the LMS algorithm, the analysis of the LMS is also obtained as a by-product. By adding a minimal amount of computational complexity, the PSA improves to some degree the convergence speed over the LMS algorithm without overly degrading the steady-state error performance for Gaussian noise. In addition, since the first derivative of its cost function with respect to estimation error is bounded, it has the properties of robustness to impulsive interference occurring in the desired response while the LMS algorithm is vulnerable to it. Computer simulations are used to demonstrate the validity of our analysis and the robustness of the PSA compared with the LMS algorithm