MUSIC Algorithm for Signal and Noise Subspace Separation using Covariance Matrix

The MUSIC algorithm is a high-resolution parameter estimation technique that utilizes the covariance matrix (Rx) of received data to separate signal and noise subspaces. Through eigendecomposition of the covariance matrix, the algorithm identifies signal eigenvectors corresponding to larger eigenvalues and noise eigenvectors from smaller eigenvalues. By leveraging the orthogonality between signal steering vectors and the noise subspace, the algorithm constructs a spatial spectrum function. Peak searching in this spectrum domain enables accurate estimation of signal parameters such as direction of arrival (DOA). In practical implementation, key steps include computing the sample covariance matrix, performing eigenvalue decomposition using functions like eig() or svd(), and applying peak detection algorithms to identify signal sources. This method effectively extracts signal characteristics and enables precise analysis, providing valuable insights for advanced signal processing applications and research.