In wireless communication scenarios, multipath propagation may cause angular spreading as seen from a base station antenna array. Environments where most energy incident on the array is from scatterers local to the mobile transmitters are considered, and the effects on direction of arrival (DOA) estimation with the MUSIC algorithm are studied. Previous work has studied rapidly time-varying channels and concluded that local scattering has a minor effect on DOA estimation in such scenarios. In this work, a channel that is time-invariant during the observation period is considered, and under the assumption of small angular spread, an approximate distribution for the DOA estimates is derived. The results show that local scattering has a significant impact on DOA estimation in the time invariant case. Numerical examples are included to illustrate the analysis and to demonstrate that the results may be used to formulate a simple estimator of angular spread. An extension to more general Rayleigh and Ricean fading channels is also included, In addition, results from processing experimental data collected in suburban environments are presented. Good agreement with the derived distributions is obtained.