In wireless communication scenarios, multipath propagation from local scatterers in the vicinity of mobile sources may cause angular spreading as seen from a base station antenna array. This paper studies the effects of suchlocal scattering on direction of arrival (DOA) estimation with the MUSIC and ESPRIT algorithms. Previous work has considered rapidly time-varying scenarios, and concluded that local scattering has a minor effect on DOAestimation in such scenarios. This work considers the case in which the channel is time-invariant during theobservation period. The distribution of the DOA estimates is derived, and the results show that local scatteringhas a significant impact on DOA estimation in the time-invariant case. In addition, numerical examples are included to illustrate the analysis, and to demonstrate that the results may be used to formulate simple estimators of angular spread.