On the achievable localization accuracy of multiple sources at high SNR

The Cramér-Rao Bound (CRB) for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated. It is shown that unlike in the case where the number of samples grows, wherein the CRB for the localization error always converges to zero, in the case where the number of snapshots is kept fixed and the signalto-noise ratio (SNR) grows,: the CRB converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension.