Signal Detection Based on a Decreasing Exponential Function in Alpha-Stable Distributed Noise

Abstract

Signal detection in symmetric alpha-stable (S S α) distributed noise is a challenging problem. This paper proposes a detector based on a decreasing exponential function (DEF). The DEF detector can effectively suppress the impulsive noise and achieve good performance in the presence of S S α noise. The analytical expressions of the detection and false alarm probabilities of the DEF detector are derived, and the parameter optimization for the detector is discussed. A performance analysis shows that the DEF detector has much lower computational complexity than the Gaussian kernelized energy detector (GKED), and it performs better than the latter in S S α noise with small characteristic exponent values. In addition, the DEF detector outperforms the fractional lower order moment (FLOM)-based detector in S S α noise for most characteristic exponent values with the same order of magnitude of computational complexity.