MUSIC Algorithm Simulation for Direction of Arrival Estimation

The MUSIC algorithm simulation represents a computational method for estimating the direction of arrival (DOA) of incoming waves. This high-resolution technique is widely employed in signal processing applications, demonstrating particular effectiveness in radar systems and wireless communications. The algorithm operates on the principle of eigenstructure analysis, where the covariance matrix of received signals undergoes eigenvalue decomposition to separate signal and noise subspaces. Key implementation steps include: - Collecting multiple snapshots of array sensor data - Computing the sample covariance matrix from received signals - Performing eigenvalue decomposition to identify noise eigenvectors - Constructing the MUSIC spectrum using the orthogonality between signal and noise subspaces - Peak detection in the spectrum to determine DOA estimates The algorithm transforms received signals into the frequency domain and utilizes eigenvalue decomposition to calculate the spectral correlation matrix. This matrix enables accurate estimation of both the number of signal sources and their respective directions of arrival. In practical implementations, developers often use singular value decomposition (SVD) as a numerically stable alternative for eigenvalue decomposition. The MUSIC algorithm simulation serves as a powerful tool for high-accuracy DOA estimation, with broad applications across various fields including sonar systems, radio astronomy, and smart antenna technology. Implementation typically involves MATLAB or Python programming, with critical functions focusing on covariance matrix computation, eigenvalue decomposition, and spatial spectrum peak identification.