MUSIC Algorithm Implementation for 2D Direction of Arrival (DOA) Estimation

The MUSIC (Multiple Signal Classification) algorithm is a classical spatial spectrum estimation method specifically designed for solving Direction of Arrival (DOA) estimation problems. Its core principle involves utilizing eigenvalue decomposition of the received signal's covariance matrix to separate the signal subspace from the noise subspace, thereby achieving precise localization of signal source directions. In two-dimensional DOA estimation scenarios, the MUSIC algorithm must handle angle information in two dimensions (such as azimuth and elevation angles). The implementation first requires constructing an array manifold matrix, which contains the array's response characteristics to signals from different directions. Through collecting multiple channels of received signals and computing their covariance matrix, eigenvalue decomposition enables discrimination between signal and noise subspaces. Key implementation steps in code include: estimating the covariance matrix from array reception data, performing eigenvalue decomposition to identify the noise subspace, and constructing the spatial spectrum function. The peaks in the spatial spectrum function correspond to the signal sources' directions of arrival. In the 2D case, spectrum peak search must be performed across both angular dimensions, increasing computational complexity compared to 1D scenarios. Practical implementation considerations include array geometry design, where different array configurations significantly impact algorithm performance. The algorithm exhibits sensitivity to signal-to-noise ratio (SNR) and signal coherence, often requiring preprocessing or algorithm modifications in low-SNR or strongly coherent signal environments. Code implementation typically involves functions for covariance matrix calculation, eigenvalue decomposition (using built-in functions like eig() or svd()), and spectrum peak search algorithms for 2D angle grids.