MATLAB Implementation of Uniform Linear Array with Fourth-Order Cumulant Virtual Array Extension for DOA Estimation

This paper presents a uniform linear array-based methodology for directional source localization. The approach generates virtual array elements using fourth-order cumulants, allowing estimation of more signal sources than the actual number of physical array elements for Direction of Arrival (DOA) estimation purposes. The implementation involves calculating fourth-order cumulant matrices from received array signals, which effectively expands the array aperture and enhances spatial resolution. Key algorithmic steps include: 1. Signal acquisition from physical array elements 2. Fourth-order cumulant matrix computation using MATLAB's statistical functions 3. Virtual array construction through cumulant matrix transformation 4. Spatial spectrum estimation using MUSIC or ESPRIT algorithms The method demonstrates excellent resolution capabilities for precise source localization. Additionally, this technique finds applications in environmental noise cancellation and speech enhancement systems, offering broad practical implementation prospects. MATLAB implementation typically involves functions from the Signal Processing Toolbox for array signal processing and custom routines for cumulant-based virtual array generation.