Abstract: In this paper, the optimal and suboptimal nonlinear processing for correlation-based signal detection is addressed in symmetric alpha-stable noise. By the equivalent proprecessing function of quantizer-array and Gaussian approximation of the correlator’s output, a constrained functional optimization problem is established by maximizing the correlator output signal-to-noise ratio. However, it is hard to get the analytical solution of this problem. We further apply finite discretization to this functional optimization problem, and prove that the approximation problem is a convex quadratic programming problem. Therefore, the resulting problem can be solved by convex optimization. We propose a novel adaptive threshold for the soft limiter detector based on sorting, which only need to estimate alpha-stable noise parameter α when comparing with other detectors. The proposed equivalent preprocessing function of quantizer-array approximates the maximum likelihood detector. Simulation results show that the proposed soft limiter achieves near-optimal performance, benefitting the real-time processing of symmetric alpha-stable signal.