# Signal subspace techniques for source localization with circular sensor arrays

#### Abstract

Estimating the directions-of-arrival (DOAs) of propagating plane waves is a problem of interest in a variety of applications including radar, mobile communications, sonar, and seismology. The widely studied uniform linear array (ULA) can only provide estimates of source bearings relative to the array axis. A planar array is required if estimates of source azimuth and elevation are required (2D angle estimation). Uniform circular arrays (UCAs) have several properties that make them attractive for 2D angle estimation; e.g., directional patterns synthesized with UCAs can be electronically rotated in the plane of the array without significant change of beam shape. Two signal subspace algorithms for 2D angle estimation with UCAs have been developed. Both algorithms operate in beamspace and employ phase mode excitation based beamformers. The first algorithm, UCA-RB-MUSIC, offers numerous advantages over element space MUSIC. These advantages include reduced computation due to the ability to compute subspace estimates via a real-valued eigenvalue decomposition and the applicability of ULA techniques such as Root-MUSIC. The second algorithm, UCA-ESPRIT, represents a significant advance in the area of 2D angle estimation. It is a novel closed-form algorithm that provides automatically paired source azimuth and elevation angle estimates via the eigenvalues of a matrix. The eigenvalues have the form $\mu$ = $\sin \theta e\sp{j\phi}$, where $\theta$ and $\phi$ are the elevation and azimuth angles, respectively. UCA-ESPRIT avoids expensive search procedures and is thus superior to existing 2D angle estimation algorithms with respect to computational complexity. The statistical performance of element space MUSIC, UCA-RB-MUSIC, and UCA-ESPRIT has been analyzed. Computer simulations that demonstrate the efficacy of the algorithms and validate the performance analysis results are presented.

#### Degree

Ph.D.

Zoltowski, Purdue University.

#### Subject Area

Electrical engineering

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