A Parametric Approach to Suboptimal Signal Detection in $\alpha$-Stable Noise

This paper deals with the detection of a known deterministic signal embedded in alpha-stable noise. The implementation of the optimal receiver requires the explicit expression of the probability density function (pdf) of the noise. Unfortunately, since there exists no closed-form for the pdf of alpha-stable distributed random variables, numerical integrations are required. To avoid such numerical approximations, we suggest a low-complexity parametric suboptimal detector well matched to essential properties of alpha-stable noises. This receiver does not require the explicit expression of the noise pdf. In addition, parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal Gaussian detector (matched filter) as well as the locally optimal detector in the Cauchy context. The performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given. The robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed