DOA Estimation Using MUSIC and Smooth MUSIC Algorithms in Pattern Space of Uniform Circular Array

In array signal processing, Uniform Circular Arrays (UCA) are widely used for Direction of Arrival (DOA) estimation due to their omnidirectional advantages. The MUSIC (Multiple Signal Classification) algorithm and its improved version (such as smoothed MUSIC) can effectively address the special geometrical structure of UCAs through pattern space transformation.

Core Implementation Approach Pattern Space Transformation: Since UCA elements are arranged non-linearly, the received data must be transformed into pattern space through phase mode excitation. This conversion creates virtual linear array characteristics, making it compatible with the subspace decomposition requirements of traditional MUSIC algorithms. In code implementation, this typically involves calculating pattern transformation matrices using Bessel function expansions. MUSIC Algorithm Application: The transformed covariance matrix undergoes eigenvalue decomposition to obtain the noise subspace. Spatial spectrum construction through peak search identifies signal directions where peaks correspond to arrival angles. Key functions would include covariance matrix calculation, eigenvalue decomposition, and spectrum peak detection algorithms. Smoothed MUSIC Improvement: For coherent signal scenarios, subarray smoothing is applied to restore the rank of the covariance matrix, enhancing algorithm robustness. Implementation requires partitioning the array into overlapping subarrays and averaging their covariance matrices.

Technical Implementation Details Pattern space transformation requires computation of Bessel function expansion coefficients, where the order is determined by the circular array radius and wavelength. Code implementation needs careful handling of Bessel function calculations and order truncation. Smoothed MUSIC suppresses coherent signal effects through block-averaged covariance matrices, but sacrifices some array aperture. Programmers must balance smoothing parameters against resolution requirements. DOA estimation accuracy is jointly affected by the number of array elements, signal-to-noise ratio, and pattern space order truncation errors. Optimal parameter selection is crucial in practical implementations.

This method combines UCA's omnidirectional detection capability with MUSIC algorithm's high-resolution advantages, making it suitable for scenarios requiring multi-target azimuth estimation in sonar, radar, and other applications. The implementation typically involves MATLAB or Python coding with signal processing toolboxes for matrix operations and spectral analysis.