MUSIC Algorithm for DOA Estimation with 8-Element Linear Array

The MUSIC (Multiple Signal Classification) algorithm is a classical method for Direction of Arrival (DOA) estimation, particularly suitable for high-resolution angle estimation in multi-signal environments. It leverages the orthogonality between signal subspace and noise subspace to identify incident signal directions through spectral peak searching.

In an 8-element uniform linear array implementation, the MUSIC algorithm follows these key steps: First, compute the covariance matrix from array received data and perform eigenvalue decomposition to separate signal and noise subspaces. This can be implemented using MATLAB's eig() function or svd() for singular value decomposition. Then, construct the spatial spectrum function using the noise subspace eigenvectors, and determine signal arrival angles by searching for peak positions in the spectrum through angular scanning.

The algorithm offers high resolution capability, enabling discrimination between multiple signal sources with closely spaced angles. At the 36-degree direction, performance can be optimized by adjusting antenna weights. Different weight configurations affect beamforming directivity and sidelobe levels - rectangular weights provide uniform weighting while Hanning or Chebyshev weights can suppress sidelobes. Users can experiment with various weighting schemes (weights = hanning(8)) to achieve optimal estimation results for specific scenarios.

Although MUSIC algorithm has relatively high computational complexity due to eigenvalue decomposition and spectrum search operations, it demonstrates significant advantages in estimation accuracy and resolution under good signal-to-noise ratio conditions. It is widely applicable for DOA estimation tasks in radar systems, sonar applications, and wireless communication systems.