MUSIC Algorithm with Uniform Circular Array in Noise-Free Conditions

The MUSIC (Multiple Signal Classification) algorithm is a high-resolution Direction of Arrival (DOA) estimation method particularly suited for array signal processing. Under ideal noise-free conditions, the MUSIC algorithm can precisely estimate signal incident angles. A Uniform Circular Array (UCA) is a common array geometry configuration offering 360-degree omnidirectional coverage, making it suitable for multi-source signal direction estimation.

In a uniform circular array, all antenna elements are evenly distributed along a circumference, with element spacing typically set to half-wavelength to avoid spatial aliasing. However, in the scenario mentioned by the user, the element spacing equals the wavelength, which presents certain challenges. Larger element spacing may lead to higher sidelobe levels or grating lobe effects, but under noise-free conditions, the MUSIC algorithm can still achieve precise estimation by utilizing the orthogonality between signal subspace and noise subspace. In code implementation, this would require careful handling of the array manifold matrix calculation to account for the wavelength-spaced configuration.

The core steps of the MUSIC algorithm include computing the covariance matrix, performing eigenvalue decomposition to separate signal and noise subspaces, constructing the spatial spectrum function, and finally determining signal DOA through spectrum peak search. Under ideal noise-free conditions, the eigenvalues of the noise subspace theoretically become zero, resulting in sharper peaks in the MUSIC spectrum and more accurate estimation results. Programmatically, this involves implementing eigenvalue sorting algorithms and orthogonal projection calculations between subspaces.

The geometric symmetry of uniform circular arrays affects MUSIC algorithm implementation, typically requiring phase mode excitation or beamspace transformation to simplify computations. Additionally, larger element spacing may necessitate higher computational resolution to avoid angle ambiguity issues. Despite these considerations, under noise-free conditions, the MUSIC algorithm can still provide reliable direction estimation performance. Code implementation would benefit from incorporating resolution enhancement techniques and proper array calibration routines to handle the specific UCA geometry.