Adaptive locally optimum processing and fuzzy sets

Adaptive locally optimum processing can be used to effectively cancel interference from bandspread communication signals. One way to obtain practical algorithms is to use Gaussian kernels associated with complex sample amplitudes and symmetric phase-differences to represent the probability density functions of the amplitudes and symmetric phase-differences. These lead to adaptively locally optimum processing algorithms that can be used in military receivers to provide anti-jam and interference suppression. We show how the algorithms can be interpreted in a natural way in terms of a fuzzy set model for the interference. This viewpoint suggests that the algorithm performance for a particular interference depends on how well that interference can be modeled by a finite state model consisting of a few states that are easily distinguishable. We proceed to illustrate the usefulness of this idea by simulation results. From these results, it emerges that the fuzzy set viewpoint provides a way to assess the likely performance of the algorithms against interference depending on how well the interferer sample components of amplitude and symmetric phase-differences can be modeled by a finite state model. This is important because the supposition principle basic to predicting the performance of linear filters does not hold for non-linear adaptive processing algorithms