Cram&-Rao Bound for Location Systems in

We study the Cram&-Rao lower bound for source localization in the context of multiple stochastic sources, mul- tipath propagation, and observations in an array of sensors. We derive a general expression which is then specialized to sim- pler configurations and related to results previously reported in the literature. The special case of a single stochastic source in a multipath environment is treated in detail. We assess the relative importance for source localization of the temporal (multipath) and spatial (array baseline) structures of the in- coming wavefield. We show that for an array of K sensors the multipath contribution to the Fisher information matrix can be interpreted as the contribution of K independent arrays whose size depends on the number of spatially resolved replicas. We analyze the degradation due to unknown source spectra. When the source spectrum is completely arbitrary, source location is not possible with a single sensor. If a parametric form of the source spectrum is available, we show that the multipath struc- ture can be used to locate the source. In particular, localization with a single sensor may then be possible.