Classical MUSIC Algorithm Spectral Peak Search

The spectral peak search in the classical MUSIC algorithm is a critical step for achieving high-resolution Direction of Arrival (DOA) estimation. This algorithm utilizes the orthogonality principle between signal and noise subspaces to locate signal source directions by constructing a spatial spectrum function.

The spectral peak search process typically involves three core stages: First, compute the covariance matrix from received data and perform eigenvalue decomposition to partition eigenvectors into signal and noise subspaces. Then construct the MUSIC spatial spectrum function, which exhibits distinct peaks at the true signal arrival directions. Finally, scan through all possible azimuth angles to identify extremum points of the spatial spectrum function for precise source direction determination.

In practical implementation, the accuracy and efficiency of spectral peak search depend on several key factors: angle search range configuration, search step size selection, and peak detection algorithms. Finer step sizes improve estimation precision but increase computational load, requiring careful trade-offs. Common peak detection methods include simple local maximum searches or more sophisticated curve-fitting techniques.

Compared to conventional beamforming methods, the MUSIC algorithm's spectral peak search achieves superior resolution, enabling separation of multiple signal sources with angular spacing smaller than the beamwidth. However, this high performance requires precise knowledge of the number of signal sources and sufficient snapshot data for reliable covariance matrix estimation.

Code Implementation Insight: The MUSIC spectrum can be computed using matrix operations where the denominator contains the product of steering vectors and noise subspace eigenvectors. Peak detection typically involves implementing argmax functions with thresholding or polynomial fitting around local maxima for sub-degree precision.