Source localization with isotropic arrays

We consider the effect of unknown signal propagation velocity on direction-of-arrival (DOA) estimation performance using an array of sensors. For general arrays, the DOA estimation variance, as measured by the Cramer-Rao bound (CRB), degrades when the propagation velocity is unknown. In this letter, we show that for both two- and three-dimensional arrays, the CRB on the DOA angle is independent of whether or not the propagation velocity is known if and only if the sensor locations satisfy the isotropy conditions given in earlier work. The results hold for both narrowband and wideband signals.