Summary: Spatial Limits on the Performance of Direction of
Michael I. Y. Williams, Glenn Dickins, Rodney A. Kennedy, and Thushara D. Abhayapala
Abstract-- In this paper, we demonstrate that the performance
of a direction of arrival (DOA) estimator is fundamentally limited
by the size of the region over which we measure a wavefield.
That is, even assuming continuous field measurements across
the region, we still cannot achieve perfect performance. We
use an approach based on modal decomposition of a spatially
truncated field, and completely independent of sensor geometry,
to derive the Cram´er-Rao Bound (CRB) for spatially-limited
DOA estimators. The model is validated by comparison with
results from a uniform circular array (UCA) as the number of
sensors goes to infinity. Simulations of the spatial CRB show how
DOA performance improves as the measurement region expands.
Simulations of the bound also indicate that P sources can only
be effectively resolved once a certain threshold region size is
Index Terms-- Direction of arrival estimation, spatial limits on
resolution, sensor array processing.