On the introduction of an extended coupling matrix for a 2D bearing estimation with an experimental RF system

Narrow-band DOA (direction of arrival) estimation methods need an accurate modeling of the array manifold (response of the array of antennas to one source in all directions). In radio frequency (RF) systems, electromagnetic perturbations arising from the neighborhood of the array will bring differences between the ideal and the true or measured response. If the model of the array response used in the algorithms does not take this modeling error into account, the performance of the bearing estimation methods may degrade dramatically. Usually, either a data collection of true steering vectors or a mutual-coupling model are used to perform DOA estimation in an experimental setup. The purpose of this paper is to propose an alternative to the mutual-coupling model by deriving a more accurate analytic expression of the true response. We present a model using a new extending coupling matrix, which includes the polarization and the scattering elements of the array in addition to mutual-coupling effects. An estimation of these extended and mutual coupling matrices is also originally proposed when measurements of the true steering vectors are available. The true steering vectors are measured in an experimental setup. Based on these new analytical expressions of the steering vectors of the array response, we extend the MUSIC DOA estimation algorithm to polarization diversity.