doa estimation with classic music algorithm using simple incident signals

DOA (Direction of Arrival) estimation represents a fundamental problem in array signal processing, and the MUSIC (Multiple Signal Classification) algorithm serves as a classical super-resolution DOA estimation method. It achieves high-precision direction estimation by analyzing the orthogonality between signal subspace and noise subspace.

When constructing simple incident signals, we typically assume far-field narrowband signals arriving at the antenna array from specific angles. For a 7-element antenna array, it can be arranged as a Uniform Linear Array (ULA) with element spacing typically set to half-wavelength to prevent spatial aliasing. The incident signals can be single-frequency sine waves or modulated signals, where the phase differences generated when wavefronts reach different antennas provide crucial information for DOA estimation. In code implementation, this involves generating steering vectors that represent phase shifts for different arrival angles.

The core steps of the MUSIC algorithm include: first computing the covariance matrix of received signals, then performing eigenvalue decomposition to separate signal subspace and noise subspace. By constructing a spatial spectrum function and searching for its peaks, we can determine the direction of arrival for incident signals. The algorithm demonstrates excellent resolution capability under high Signal-to-Noise Ratio (SNR) conditions but shows sensitivity to coherent signals, requiring preprocessing techniques like forward-backward smoothing. Implementation-wise, this involves using eigendecomposition functions (e.g., numpy.linalg.eig in Python) and peak detection algorithms for spectrum analysis.

Practical implementation must also consider factors such as array calibration, effects of limited snapshots, and computational complexity optimization. Through appropriate configuration of search step sizes and thresholds, we can balance estimation accuracy with computational efficiency. Code optimization techniques may include vectorization for faster spectrum computation and intelligent search range reduction based on prior knowledge.