Background:
All existing time delay estimation methods, i.e. correlation and covariance,
depend on second or higher-order statistics which are inapplicable for the correlation of alpha-stable
noise signals. Therefore, fractional lower order covariance is the most appropriate method to measure
the similarity between the alpha-stable noise signals.
Methods:
In this paper, the effects of skewness and impulsiveness parameters of alpha-stable distributed
noise on fractional lower order covariance method have been analyzed.
Results:
It has been found that auto-correlation, i.e. auto fractional lower order covariance,\ of non
delayed alpha-stable noise signals follows a specific trend for specific ranges of impulsiveness and
skewness parameters of alpha-stable distributed noise. The results also depict that, by maintaining the
skewness and impulsiveness parameters of α-stable noise signals in a certain suggested range, better
auto-correlation can be obtained between the transmitted and the received alpha-stable noise signals in
the absence and presence of additive white Gaussian noise.
Conclusion:
The obtained results would improve signal processing in alpha-stable noise environment
which is used extensively to model impulsive noise in many noise-based systems. Mainly, it would
optimize the performance of random noise-based covert communication, i.e. random communication.
Role of Fractional Powers in Manuevering the Fractional Lower-Order Auto-Covariance of Symmetric Alpha-Stable Noise Signals
