Power Spectral Estimation Using MUSIC Algorithm

This document discusses the MUSIC (Multiple Signal Classification) algorithm, which employs autocorrelation matrix decomposition to achieve power spectral estimation. The algorithm is widely applied in signal processing, particularly in antenna array applications. The core principle of MUSIC involves transforming signals into the frequency domain and performing eigenvalue decomposition on the autocorrelation matrix to separate signal and noise subspaces. A key implementation step involves constructing the pseudospectrum by projecting steering vectors onto the noise subspace, where spectral peaks correspond to estimated signal frequencies. The algorithm's advantages include high-resolution frequency and direction-of-arrival estimation capabilities, making it particularly effective for resolving closely spaced signals. However, its performance is sensitive to signal-to-noise ratio (SNR) conditions and requires accurate estimation of the source number. To address these limitations, researchers continue developing variants like Root-MUSIC and beamspace MUSIC, which improve robustness through polynomial rooting and dimensionality reduction techniques respectively. Practical implementations often involve forward-backward averaging for enhanced covariance matrix estimation and subspace tracking algorithms for real-time applications.