Noise-Free MUSIC Algorithm Implementation for Uniform Circular Arrays with Wavelength-Spaced Elements

This article explores the implementation details of the MUSIC algorithm applied to uniform circular arrays under noise-free conditions. The program operates by first constructing a uniform circular array configuration where sensors are equally spaced around a circle with inter-element distances precisely equal to the signal wavelength. This wavelength-matching ensures identical signal propagation paths between array elements, eliminating phase ambiguities and enhancing spatial resolution. The core algorithm implementation involves several key computational stages: First, the program collects signal snapshots from all array elements and constructs the covariance matrix. Since we're operating in noise-free conditions, the covariance matrix contains pure signal subspace components. The MUSIC algorithm then performs eigenvalue decomposition on this matrix to separate signal and noise subspaces - though in this idealized scenario, the noise subspace is theoretically zero. The algorithm computes the MUSIC spatial spectrum by projecting steering vectors onto the identified subspaces, with peak locations in the spectrum corresponding to source directions. In the code implementation, special attention is given to steering vector calculation for circular geometry. The program uses mathematical transformations to convert circular array coordinates into effective linear array equivalents, enabling standard MUSIC algorithm application. Key functions include array geometry initialization, covariance matrix computation, eigenvalue decomposition using numerical methods like SVD, and spatial spectrum peak detection. This implementation demonstrates how uniform circular arrays with wavelength spacing provide full 360-degree coverage with consistent resolution, unlike linear arrays that suffer from front-back ambiguity. The wavelength-matched spacing ensures optimal spatial sampling without aliasing effects, while the circular symmetry offers uniform performance across all azimuth angles. The program serves as an ideal benchmark for studying MUSIC algorithm performance under perfect conditions, providing insights into theoretical limits of direction-of-arrival estimation. It also offers a foundation for developing more robust versions that incorporate noise handling and real-world impairments. Through this implementation, researchers can better understand the fundamental principles of subspace-based signal processing and apply them effectively in practical array signal processing applications.