PDF approximations to estimation and detection in time-correlated alpha-stable channels

This paper considers the estimation and detection problems for statistically dependent heavy-tailed signals with no closed-form probability density function (PDF). We propose two parametric PDF approximations for symmetric α-stable (SαS) distribution to be utilized in approaches based on the Maximum likelihood (ML) criterion. The nonlinear least square (LS) and curve fitting are used to compute parameters of the new formulations which are functions of the characteristic exponent. Moreover, we study binary signal detection in channels with time-dependent heavy-tailed noise modeled by SαS distribution and first order autoregressive (AR(1)) process. Using the novel PDF approximations in the ML estimator, an algorithm for model parameters estimation of the noise is initially developed. Then, new suboptimal receivers are designed through the use of the new PDF formulations and parameter estimates. Numerical results demonstrate the superiority of the proposed approximations over the existing formulations, and also good accuracy for the estimation algorithm. Additionally, it is shown that the proposed detectors operate near optimal receiver and also outperform the other suboptimal detectors, especially when α is small.