Direction of Arrival Estimation Using Uniform Linear Arrays

In DOA estimation using uniform linear arrays, the Multiple Signal Classification (MUSIC) algorithm provides an effective approach for accurately estimating signal source directions. This algorithm operates by analyzing phase differences between antenna elements to construct a covariance matrix from received signals. Through eigenvalue decomposition, MUSIC separates signal and noise subspaces, then uses orthogonality between these subspaces to generate a spatial spectrum where peaks indicate source directions. Implementation typically involves calculating the array covariance matrix R = X*X'/N where X is the received signal matrix and N is the number of snapshots. The noise subspace is obtained from eigenvectors corresponding to smallest eigenvalues, followed by spectrum computation P_MUSIC(θ) = 1/(a(θ)'*E_n*E_n'*a(θ)) where a(θ) is the steering vector. Additional signal processing techniques can further optimize DOA estimation results. Beamforming methods like Capon's minimum variance distortionless response (MVDR) can enhance resolution using adaptive weight vectors. Spatial smoothing techniques address coherent signal scenarios by dividing the array into overlapping subarrays to restore rank of the covariance matrix. These methods significantly improve estimation accuracy and robustness in complex real-world environments with multipath propagation and interfering sources.