Compressive Sensing Implementation for Array Signal Processing: A Comparative Analysis with MUSIC Method

This article explores the implementation of compressive sensing technology for array signal processing and provides a comparative analysis with the MUSIC method. Compressive sensing represents an innovative approach to signal sampling and reconstruction that enables high-quality signal recovery while significantly reducing sampling rates. In array signal processing applications, compressive sensing algorithms leverage sparse signal representations to process signals more efficiently, minimizing energy loss and mitigating noise interference through optimization techniques like l1-norm minimization. The implementation typically involves constructing measurement matrices and solving convex optimization problems using MATLAB functions such as l1eq_pd or CVX toolbox. In contrast, the MUSIC (Multiple Signal Classification) method serves as a traditional approach for array signal processing, renowned for its high-resolution direction-of-arrival (DOA) estimation capabilities. The MUSIC algorithm operates by performing eigenvalue decomposition on the covariance matrix and utilizing the orthogonality between signal and noise subspaces, often implemented through MATLAB's pmusic function or custom covariance matrix calculations. While MUSIC remains effective in scenarios with high signal-to-noise ratios, compressive sensing demonstrates superior performance under conditions of significant noise contamination and sparse signal environments. The selection between these methods requires careful consideration of multiple factors including noise levels, sampling rate constraints, computational complexity, and sparsity characteristics of the target signals. Compressive sensing implementations typically involve trade-offs between reconstruction accuracy and computational efficiency, whereas MUSIC requires adequate snapshot numbers for covariance matrix estimation.