Efficient Two-Dimensional Direction Finding via Auxiliary-Variable Manifold Separation Technique for Arbitrary Array Structure

A polynomial rooting direction of arrival (DOA) algorithm for multiple plane waves incident on an arbitrary array structure that combines the multipolynomial resultants and matrix computations is proposed in this paper. Firstly, a new auxiliary-variable manifold separation technique (AV-MST) is used to model the steering vector of arbitrary array structure as the product of a sampling matrix (dependent only on the array structure) and two Vandermonde-structured wavefield coefficient vectors (dependent on the wavefield). Then the propagator operator is calculated and used to form a system of bivariate polynomial equations. Finally, the automatically paired azimuth and elevation estimates are derived by polynomial rooting. The presented algorithm employs the concept of auxiliary-variable manifold separation technique which requires no sector by sector array interpolation and thus does not suffer from any mapping errors. In addition, the new algorithm does not need any eigenvalue decomposition of the covariance matrix and exhausted search over the two-dimensional parameter space. Moreover, the algorithm gives automatically paired estimates, thus avoiding the complex pairing procedure. Therefore, the proposed algorithm shows low computational complexity and high robustness performance. Simulation results are shown to validate the effectiveness of the proposed method

On calibration and direction finding with uniform circular arrays

Antenna array calibration methods and narrowband direction finding (DF) techniques will be outlined and compared for a uniform circular array. DF is stated as an inverse problem, which solution requires a parametric model of the array itself. Because real arrays suffer from mechanical and electrical imperfections, analytic array models are per se not applicable. Mitigation of such disturbances by a global calibration matrix will be addressed, and methods to estimate this calibration matrix will be recapped from literature. Also, a novel method will be presented, which circumvents the problem of a changed noise statistic due to calibration. Furthermore, local calibration, where array calibration measurements are incorporated in the DF algorithm, is considered as well. Common DF algorithms will be outlined, their assumptions regarding array properties will be addressed, and required preprocessing steps such as the beam-space transformation will be presented. Also, two novel DF techniques will be proposed, based on the Capon beamformer, but with reduced computational effort and higher resolution for bearing estimation. Simulations are used to exemplary compare calibration and DF methods in conjunction with each other. Furthermore, measurements with a single and two coherent sources are considered. It turns out that global calibration enables computational efficient DF algorithms but causes biased estimates. Furthermore, resolution of two coherent sources necessitates array calibration