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In wireless communication scenarios, local scattering in the mobile vicinity causes angular spreading which leads to MUSIC performances degradation. In this paper, we study the performance of MUSIC algorithm in presence of scattering under the assumption of time-invariant channel during the observation period. To this aim, an approximate distribution of the direction of arrival (DOA) estimates is derived. Additionally a statistical analysis is carried out where a formulas for the bias and root mean square error (RMSE) of the DOA estimates are given. Simulation results of MUSIC algorithm are carried in different scenarios and compared to the theoretical study.