Role of Fractional Powers in Manuevering the Fractional Lower-Order Auto-Covariance of Symmetric Alpha-Stable Noise Signals

Abstract

Since, Fractional Lower-Order Auto-Covariance (FLOAC) remains the only technique to quantify the similarity between alpha-stable ( ${\alpha}$ -stable) signals, therefore, the effects of impulsiveness and skewness parameters has also been analyzed before for better generation and detection in various applications. This paper includes the detailed analysis of the FLOAC of symmetric alpha-stable ( $\mathrm{S}\alpha\mathrm{S}$ ) noise signals in order to observe the possible involvement of the associated fractional powers. The two associated fractional powers of FLOAC has been maneuvered in three possible ways to observe the probable trend of $\mathrm{S}\alpha\mathrm{S}$ noise signals in the presence and absence of Gaussian noise. The observation depicts that the fractional powers largely and solely affect the FLOAC when they are maneuvered collaboratively or even individually where the obtained results can be useful in improving many $\mathrm{S}\alpha\mathrm{S}$ noise signal processing techniques, especially, in the detection of $\mathrm{S}\alpha\mathrm{S}$ noise carrier signals in Random Communication Systems.