Abstract:

Because of the optimal detection under impulsive noise requiring nonlinear operation, the detection structure of zero memory nonlinear transformation followed by the matched filter is often used. In this paper, the nonlinear transformation design under impulsive noise is systematically reviewed, and the research work in the noise model, the nonlinear function and the design method at home and abroad is summarized. Firstly, the impulsive noise model usually uses the symmetric α stable distribution, the Class A distribution, the Gaussian mixture distribution and other mixture distributions. Secondly, characterized by the tailing function, the nonlinear function model can be divided into traditional clipping/blanking, multi-region combined tailing, single parameter-based specific tailing or non-piecewise function, and bi-parameter variable tailing. Thirdly, in the design method, the idea of analysis-based approximation and normalization-based transformation is intuitive, and the criteria of maximum signal to noise ratio and maximum efficacy are directly related to the detection performance. Then, the common research routes and the common laws of the main research results are summarized. Finally, the problems of unknown noise distribution and efficacy optimization are discussed, and the possible research points in the future are prospected.

Key words: impulsive noise, signal processing, nonlinear transformation, signal to noise ratio, optimization