Spatial limits on the performance of direction of arrival estimation

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 Cramér-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 reached.