NONLINEAR ADAPTIVE SIGNAL-PROCESSING BASED ON RATIONAL-FUNCTION

While linear adaptive filters are useful in a large number of applications and relatively simple from the conceptual and implementational point of view, there are many practical situations that require nonlinear processing. This paper presents a novel adaptive nonlinear filter which derives its nonlinearity by using rational functions. The output of this nonlinear system is related to its inputs through a finite order rational function. The rational function structure is attractive in adaptive filtering since it is a universal approximator and the coefficients of the filter can be estimated using a linear adaptive algorithm. Two representative examples from signal processing, classification and prediction, are used to demonstrate capabilities of this nonlinear adaptive filter that are lacking in its linear counterpart. The potential uses for this nonlinear adaptive filter will be further demonstrated by discussing the problem that is often encountered in the real world, namely, the estimation of directions-of-arrival (DOA) of two closely spaced signals using a uniform array and time series modeling. For the first problem, a new high resolution method using a rational function is derived and standard simulation examples are given. For the latter, real-life radar data are used as a test for the rational function filter in the practical application. In both cases, the results that are obtained using this nonlinear adaptive filter are encouraging.