Classic MUSIC Algorithm: High-Resolution DOA Estimation Technique

The classic MUSIC (Multiple Signal Classification) algorithm is a high-resolution direction of arrival (DOA) estimation method widely used in radar, sonar, and wireless communication systems. This algorithm analyzes the covariance matrix of received signals and leverages the orthogonality between signal subspace and noise subspace to achieve precise estimation of multiple signal source directions. The core concept of the MUSIC algorithm is based on eigenvalue decomposition. In implementation, the algorithm first computes the covariance matrix from array received signals, followed by eigenvalue decomposition to obtain signal and noise subspaces. The spatial spectrum function is then constructed, where the angles corresponding to peak values represent the estimated DOA of signal sources. Due to its utilization of noise subspace orthogonality, MUSIC maintains superior resolution capability even under low signal-to-noise ratio (SNR) conditions. For simulation implementation, a Uniform Linear Array (ULA) is typically employed as the receiving array model. The implementation involves generating received data matrices by simulating multiple signal sources incident on the array. After computing the covariance matrix, eigenvalue decomposition is performed to extract eigenvectors corresponding to the noise subspace. Finally, the spatial spectrum function is plotted to generate direction-finding patterns, where peaks indicate true signal source directions. To evaluate MUSIC algorithm performance, Root Mean Square Error (RMSE) is commonly calculated. This metric quantifies the deviation between estimated and true angles, directly reflecting the algorithm's robustness and accuracy. Through Monte Carlo simulations, multiple algorithm runs with error statistics can validate MUSIC's performance across varying SNR conditions. The MUSIC algorithm's advantage lies in its super-resolution characteristics, enabling it to surpass the Rayleigh limit of conventional beamforming. However, its performance is constrained by array calibration accuracy and signal coherence. For coherent signals, preprocessing techniques like spatial smoothing are typically incorporated. Additionally, high computational complexity presents challenges for real-time applications, requiring optimization in practical implementations through efficient matrix operations and parallel processing techniques.