Parameter estimator based on the log-cumulant and its performance analysis for heavy-tailed-distributed impulsive interference}{Parameter estimator based on the log-cumulant and its performance analysis for heavy-tailed-distributed impulsive interference

Abstract

The impulsive interference in many wireless communication networks can be modeled as a symmetric $\alpha$-stable distribution noise. The probability density function of the interference needs to be obtained in advance in signal detection, channel decoding, wireless network outage probability, and bit error rate analysis application scenarios. The method of log-cumulant is used to estimate the characteristic exponent and dispersion of the interference. Furthermore, the probability distribution of the estimated parameters is derived in detail, which can be used for quantitative analysis to evaluate the estimation reliability. In addition, the noise in the receiver of the actual system is bivariate mixture noise including the independent Gaussian noise and S$\alpha$S interference. We suggest that the bivariate noise can be approximated from its univariate counterpart. We prove that this type of approximation is reasonable by means of simulation and numerical calculation. The relationship between the parameters of the mixture noise and the geometric power signal-to-noise ratio are provided in this paper based on this assumption. The estimator based on the log-cumulant and performance analysis is therefore still valid in the bivariate noise environment.