Nonlinear Processing for Correlation Detection in Symmetric Alpha-Stable Noise

In this letter, the optimal and suboptimal nonlinear processing for correlation-based signal detection is addressed in symmetric alpha-stable noise. By maximizing the correlator output signal-to-noise ratio, a constrained functional optimization problem is established. As this optimization problem is hard to get analytical solution, we apply finite discretization to it and prove that the resulting approximation problem is a convex quadratic programming problem. This optimal nonlinear processing provides performance bound and design criteria for correlator detection. Based on the noise parameter $\alpha$ and the order statistic of received data, we further propose an adaptive method to determine the optimal threshold of the commonly used soft limiter. Simulation results show that the proposed method achieves near-optimal performance.