MATLAB Implementation of MUSIC Algorithm for Direction of Arrival Estimation

The MUSIC algorithm is a classical signal processing technique primarily used for Direction of Arrival (DOA) estimation. It leverages the orthogonality principle between signal subspace and noise subspace to achieve high-precision estimation of multiple signal sources' azimuth angles. Implementing the MUSIC algorithm in MATLAB involves the following key steps.

Data Acquisition and Preprocessing First, signal data is collected through an antenna array, typically using Uniform Linear Array (ULA) or other array configurations. The received signal data requires preprocessing operations such as DC component removal and normalization to ensure accuracy in subsequent processing stages.

Computing Covariance Matrix Calculate the covariance matrix from the received signal data. This step is central to the MUSIC algorithm, as the covariance matrix reflects signal correlations and forms the foundation for subsequent eigenvalue decomposition. In MATLAB, this can be implemented using the cov() function or direct matrix multiplication with proper averaging.

Eigenvalue Decomposition Perform Eigenvalue Decomposition (EVD) on the covariance matrix to obtain eigenvalues and eigenvectors. The magnitude of eigenvalues helps distinguish between signal subspace and noise subspace. Larger eigenvalues correspond to eigenvectors belonging to the signal subspace, while smaller eigenvalues correspond to eigenvectors in the noise subspace. MATLAB's eig() function efficiently handles this decomposition.

Constructing MUSIC Spatial Spectrum Utilize the eigenvectors from the noise subspace to construct the MUSIC pseudospectrum. The core concept of MUSIC algorithm is that the noise subspace is orthogonal to steering vectors in signal directions. By searching for peaks in the pseudospectrum, the corresponding angles represent DOA estimates of signal sources.

Peak Search and DOA Estimation Perform peak search on the MUSIC pseudospectrum to identify angles corresponding to the highest peaks, which provide azimuth angle estimates of signal sources. Algorithm optimization techniques (such as interpolation methods) can be applied to enhance angular resolution. MATLAB's findpeaks() function combined with angle scanning provides efficient implementation.

In MATLAB, built-in matrix operation functions (like eig, svd) enable efficient eigenvalue decomposition, while plot functions facilitate visualization of MUSIC pseudospectrum results. By appropriately adjusting array parameters (such as element spacing, signal frequency), DOA estimation performance can be optimized through parameter sweep implementations.

Furthermore, the MUSIC algorithm can be extended to wideband signal processing and time-frequency analysis domains. Integration with Short-Time Fourier Transform (STFT) or wavelet transform enables DOA estimation in more complex signal scenarios, requiring additional MATLAB implementations for time-frequency distribution analysis.