Traditional MUSIC Algorithm and Fractional Lower-Order Moment-Based MUSIC Algorithm

This article discusses two different MUSIC algorithms implemented in our program: the traditional MUSIC algorithm and the fractional lower-order moment-based MUSIC algorithm. We conduct detailed simulations and analysis of both algorithms' performance under alpha-stable distribution environments to better understand their strengths, limitations, and applicable scenarios. The implementation includes covariance matrix computation for the conventional approach and fractional lower-order moment estimation for robust signal processing in impulsive noise environments. Additionally, we provide code implementation details and examples covering key functions such as signal subspace estimation, eigenvalue decomposition, and spatial spectrum calculation. Through pseudospectrum computation and direction-of-arrival estimation techniques, readers will gain deeper insights into MUSIC algorithms, enabling better application in research and practical implementations. The code structure demonstrates proper handling of array signal processing and statistical characterization for non-Gaussian noise conditions.