MUSIC Algorithm Source Code

In signal processing, the MUSIC algorithm employs matrix eigenspace decomposition by separating the observation space into signal and noise subspaces. These orthogonal subspaces consist of signal-related eigenvectors from the data covariance matrix and noise-associated eigenvectors corresponding to minimal eigenvalues (noise variance). The algorithm's core implementation involves: 1) Computing the sample covariance matrix using array reception data, 2) Performing eigenvalue decomposition to identify signal/noise subspace boundaries, 3) Constructing the MUSIC pseudospectrum through noise subspace vectors. Spectral peaks in the pseudospectrum correspond to signal directions, significantly enhancing direction-finding resolution for arbitrary antenna arrays. Note: The prototype MUSIC algorithm requires incoherent incoming signals.

Practical applications include radar/sonar localization systems where MUSIC processes echo signals for target positioning. Key implementation steps involve: - Array manifold vector calculation based on sensor geometry - Threshold-based eigenvalue separation for subspace identification - Peak detection algorithms for direction estimation. Additional applications span wireless communications for spectrum sensing and multi-channel estimation, demonstrating MUSIC's versatility as a fundamental signal processing technique.