DOA Estimation Using Uniform Circular Arrays

When employing Uniform Circular Arrays (UCA) for Direction of Arrival (DOA) estimation, the Multiple Signal Classification (MUSIC) algorithm serves as a classical high-resolution spatial spectrum estimation method. The algorithm's core principle involves performing eigenvalue decomposition on the received signal covariance matrix, then constructing a spatial spectrum function by leveraging the orthogonality between noise subspace and signal subspace to determine signal source azimuth angles. In code implementation, this typically requires computing the covariance matrix using matrix operations like R = X*X'/N where X is the received signal matrix and N is the number of snapshots.

For uniform circular arrays, antenna elements are uniformly distributed in a circular pattern, enabling 360-degree omnidirectional coverage that makes them suitable for multi-source azimuth estimation scenarios. The MUSIC algorithm implementation first calculates the covariance matrix of received signals, followed by eigenvalue decomposition to separate signal and noise subspaces. Peak detection through spatial spectrum scanning then identifies signal source azimuths. A typical implementation would use MATLAB's eig() function for eigenvalue decomposition and conduct angular scanning from 0 to 360 degrees with 1-degree increments.

In UCAs, the phase differences between array elements correlate with signal incidence angles, requiring steering vector construction that accounts for the circular geometry. Common approaches include transforming circular array responses into equivalent virtual uniform linear arrays to simplify calculations, or directly modeling phase relationships using polar coordinates. The steering vector for UCA can be computed using a = exp(-j*2*pi*r*cos(theta-theta_m)/lambda), where r is the array radius, theta_m are element angular positions, and lambda is the wavelength.

MUSIC algorithm performance depends on element count, signal-to-noise ratio, and angular separation between signal sources. The symmetrical nature of UCAs effectively avoids front-back ambiguity issues common in linear arrays, making them suitable for DOA estimation in complex multipath environments. Practical implementations must consider mutual coupling effects between elements and the algorithm's sensitivity to coherent signals, potentially incorporating preprocessing techniques like spatial smoothing to enhance robustness. The spatial smoothing technique can be implemented by dividing the array into overlapping subarrays and averaging their covariance matrices.