Near‐optimal detection with constant false alarm ratio in varying impulsive interference

Abstract

As an important class of non-Gaussian statistic model, α -stable distribution has received much attention because of its generality to represent impulsive interference. Unfortunately, it does not have a closed-form probability density function (PDF) except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α -stable. In particular, a simplified version of Cauchy–Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form. Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and achieves near-optimal performance in varying impulsive interference.