Novel ${\rm S}\alpha{\rm S} $ PDF Approximations and Their Applications in Wireless Signal Detection

Three new approximations to the probability density function (PDF) of the symmetric alpha stable (SαS) distribution are proposed. The first two approximations use rational functions while the third approximation uses power functions. Using these approximations, new detectors for signals in symmetric alpha stable noise are also derived. Numerical results show that all these new approximations have good accuracies. Numerical results also show that the new detectors based on these approximations outperform the existing detectors, especially when the characteristic exponent of the symmetric alpha stable distribution is small.