In wireless communication scenarios, local scatterers in the vicinity of the sources cause angular spreading. A parameterization of the spatial signature in the presence of local scattering is presented which applies to uniform linear arrays (ULAs). The spatial signature is shown to be approximately a Vandermonde vector for a ULA inenvironments with small angular spread. An estimator of the spatial signature is formulated based on ESPRIT. Fora simple signal waveform estimator the gain may be considerable in scenarios with multiple sources, as compared with using the ideal manifold parameterized by direction of arrival (DOA).