Structure and Performance Evaluation of Fractional Lower-Order Covariance Method in Alpha-Stable Noise Environments

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 alpha-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.