ADAPTIVE ALGORITHMS FOR NON-GAUSSIAN NOISE ENVIRONMENTS - THE ORDER STATISTIC LEAST MEAN-SQUARE ALGORITHMS

In this paper, convergence properties are studied for a class of gradi ent-based adaptive filters known as order statistic least mean square (OSLMS) algorithms. These algorithms apply an order statistic filterin g operation to the gradient estimate of the standard least mean square (LMS) algorithm. The order statistic operation in OSLMS can reduce th e variance of the gradient estimate (relative to LMS) when operating i n non-Gaussian noise environments. A consequence is that in steady sta te, the excess mean square error can be reduced. It is shown that when the input signals are i.i.d, and symmetrically distributed, the coeff icient estimates for the OSLMS algorithms converge on average to a sma ll area around their optimal values. Simulations provide supporting ev idence for algorithm convergence. As a measurement of performance, the mean squared coefficient error of OSLMS has been evaluated under a ra nge of noise distributions and OS operators. Guidelines for selection of the OS operator are presented based on the expected noise environme nt.