A near optimum detection in alpha-stable impulsive noise

Alpha stable distribution has gained much attention due to its generality to represent heavy-tailed and impulsive interference. In such non-Gaussian interference, the detection key is to evaluate the zero-memory nonlinearity (ZMNL) function of locally optimal (LO) detector. Unfortunately, there is no closed form expression for the probability density function (PDF) of alpha-stable distributions. Hereby, sub-optimum ZMNL function is adopted as an unavoidable approximation, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). In this paper, an algebraic-tailed ZMNL (AZMNL) with a concise form is proposed. Based on such ZMNL, derived detector has near optimal performance in various impulsive noise environments. Furthermore, using Bi-parameter CGM (BCGM), a concise approximate expression for PDF of symmetric alpha-stable (SalphaS) distribution, the test threshold can be evaluated according with preset false alarm ratio easily.