Simulation and Performance Analysis of the MUSIC Algorithm

In the simulation and performance analysis of the MUSIC algorithm mentioned in this document, we employed the following parameters: number of sources N=3, arriving from angles of -10 degrees, 0 degrees, and 10 degrees; these sources are mutually independent and have equal amplitudes; noise is independent and follows a Gaussian distribution; we utilized a uniform linear array consisting of 8 elements with wavelength λ.

In addition to the parameter setup, we conducted a detailed analysis of the signals, including their spectral characteristics, time-domain properties, and spatial features. We observed the power spectral density distribution of the signals and analyzed their directivity patterns at different angles using array processing techniques. Furthermore, we examined the noise power spectral density to evaluate its impact on signal detection and estimation performance.

Through simulation and performance analysis of the MUSIC algorithm, we derived several important conclusions. First, we found that the beamforming characteristics of the signals vary significantly with different angles of arrival. The implementation involves computing the covariance matrix from the received signals and performing eigenvalue decomposition to separate signal and noise subspaces. Second, we observed that noise substantially affects the beamforming characteristics, potentially increasing localization errors in DOA estimation. Additionally, we evaluated the computational complexity of the algorithm through complexity analysis of the eigenvalue decomposition and spectral peak search processes, which helps in selecting appropriate algorithms for practical applications.

Overall, through comprehensive simulation and performance analysis of the MUSIC algorithm, we gained deeper insights into its working principle and performance characteristics, obtaining valuable conclusions. These results are significant for optimizing algorithm design and application in array signal processing systems.