Simulation of Higher-Order Cumulant-Based MUSIC Algorithm in MATLAB Environment

Implementing higher-order cumulant-based MUSIC algorithm simulation in MATLAB environment provides an effective approach for Direction of Arrival (DOA) estimation in signal processing applications. The MUSIC algorithm itself is a high-resolution subspace decomposition method, and when combined with higher-order cumulants, it significantly improves performance in non-Gaussian noise environments. In MATLAB implementation, this typically involves using array processing toolbox functions and custom cumulant calculation routines.

The method begins by collecting array receiver signal data and computing higher-order cumulant matrices to suppress Gaussian noise while extracting non-Gaussian signal characteristics. The implementation requires calculating fourth-order cumulants using matrix operations like cumulant() or custom functions that handle multi-dimensional statistics. Subsequent eigenvalue decomposition of the cumulant matrix separates the signal subspace from noise subspace. The orthogonality between these two subspaces is then utilized to construct the spatial spectrum function, with peak searching algorithms (such as findpeaks() function) ultimately determining signal DOA through spectrum peak localization.

Compared to traditional MUSIC algorithms, the higher-order cumulant-based version demonstrates stronger noise resistance, particularly suitable for practical non-Gaussian noise scenarios commonly encountered in real-world environments. The algorithm also effectively addresses coherent signal source estimation problems. Simulation results are typically presented as spatial spectrum plots using MATLAB's plotting functions (plot() or surf()), visually displaying energy distribution across different arrival directions with clear peak identification for DOA determination.