Direction of Arrival Estimation Error vs. Signal-to-Noise Ratio Curve

The document specifies the following parameters: signal center wavelength = 2, antenna element spacing = 1 meter, number of snapshots = 2000, and four source signals with known frequencies and directions. The required tasks include: 1) Without adding noise, observe and calculate the eigenvalues of the covariance matrix, explaining their characteristics. In implementation, this involves constructing the signal covariance matrix from noise-free array measurements and performing eigenvalue decomposition to analyze signal subspace dimensions. 2) Apply MUSIC, CAPON, and ESPRIT algorithms to estimate the direction of arrival for the four sources under two conditions: - Case ①: Without adding noise - Case ②: With additive white Gaussian noise at 10dB SNR For each algorithm, plot the corresponding spatial spectrum. Implementation requires proper array manifold matrix construction, covariance matrix estimation, and algorithm-specific processing (e.g., peak searching for MUSIC, power minimization for CAPON, and rotational invariance for ESPRIT). 3) For SNR ranging from -20dB to +20dB, use MUSIC, CAPON, and ESPRIT algorithms to estimate the directions of arrival for the four sources. Plot the DOA estimation error versus SNR curve, with SNR as the x-axis and error values as the y-axis. This involves Monte Carlo simulations with noise variance adjustment and error calculation against ground truth directions.