Quaternion-based polarimetric array manifold interpolation

Abstract

In order to do direction of arrival (DoA) estimation the array manifold is needed. However, in practical scenarios the available calibration data is sampled on a finite grid only. Hence, a suitable beam pattern interpolation scheme is essential to perform high precision DoA estimation. A reasonable interpolation algorithm is present via the Effective Aperture Distribution Function (EADF). The EADF basically relies on a two-dimensional Discrete Fourier Transform of each beam pattern.Since the EADF does not inherently incorporate polarization two separate EADFs are needed to describe a single array element. Hence, we propose to use a Quaternion EADF (QEADF) that jointly interpolates both patterns. Moreover, since the QEADF is based on a Discrete Quaternion Fourier Transform it opens up some degrees of freedom with respect to the Fourier basis functions.