Nonlinearity Design With Power-Law Tails for Correlation Detection in Impulsive Noise

Impulsive noise plays an important role in power line communication among other applications. To improve the communication performance, this paper proposes a novel design of nonlinear processing which improves the fundamental performance of signal detection in impulsive noise. Power-law tails are firstly introduced in nonlinearity design to provide adjustable decay factors for different distributions. Four modes of nonlinearity functions are developed and analyzed. By taking the exponent and the threshold as two arguments, we formulate the nonlinearity design as an optimization problem of maximizing the efficacy function, which is the fundamental measurement for detecting a deterministic signal in impulsive noise. Given that the efficacy function is differentiable, unimodal but without closed-form derivatives, we propose to solve the optimization problem by derivative-free methods, e.g. the Nelder-Mead simplex method. As concept demonstration, our method is used for three commonly-used distribution examples. Results show that our nonlinearity design can achieve almost the same efficacy and detection performance as the locally optimal detector, with the advantage of easy-to-apply closed form expressions.