|Angle of Arrival Estimation with a Polarization Diverse Array
William P. Ballance
Boeing North America
3370 Miraloma Avenue
Anaheim, CA 92803
tel: (310) 334-2726
Ralph A. Coan
Raytheon Systems Company
Abstract This paper investigates the problem of angle of arrival (AOA) estimation of a polarized signal source with a polarization diverse array. This type of array consists of elements with different orientations or polarization responses. AOA estimation for such diverse arrays requires that the source polarization be jointly estimated. In this paper, we derive the Cramer-Rao Bound (CRB) on AOA estimation performance for an arbitrary 3-dimensional array with arbitrarily polarized elements. In addition to the two AOA unknowns (azimuth and elevation), there are two unknown polarization-state parameters. An example is given for an array of dipoles with different orientations. The AOA performance is then compared to the performance achieved by the same array when the polarization is known, thus demonstrating the penalty associated with jointly estimating AOA and polarization. In addition, it is shown that, for a segmented array in which no isolated segment can estimate polarization itself (i.e., all elements have the same polarization response/orientation), AOA performance for unknown polarization is independent of the distance between array segments.
A derivation is given for the Maximum-Likelihood Estimator (MLE) that jointly estimates
AOA and polarization. Because polarization enters the model in a linear fashion, its
estimate can be expressed in a closed form and resubstituted into the performance index.
The MLE is shown to be equivalent to the BWE (Beamform, Whiten and Energy Detect)
technique developed by Allan Steinhardt at Lincoln Laboratory. An intuitive explanation
for the impact that unknown polarization has on the shape of the MLE performance index is
then provided. This explanation clarifies how polarization estimation has an adverse
effect on AOA estimation. In addition, the agreement between the CRB and the shape of the
MLE performance index is demonstrated. Finally, the effect of incorrectly assuming source
polarization and attempting "known polarization" AOA estimation is demonstrated.
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