The existing spatial smoothing (SS) technique, although it is effective in decorrelating coherent signals, can only be applied to uniformly spaced linear arrays which are very sensitive to the directions-of-arrival (DOA's) and can be used to estimate arimuth angles only. To significantly improve the robustness of DOA estimation and of beamforming and to estimate both arimuth and elevation angles, we developed techniques for applying SS to arrays of arbitrary geometry. We found that an array must have an orientational invariance structure with an ambiguity free center array for applying SS. We also study the cause of ambiguities in a multiple signal environment and find the necessary and sufficient conditions for an array manifold to be ambiguity free. If an array is also central symmetric, the forward/backward spatial smoothing can be used to improve the resolution. Finally, we expand the application of our technique not only to MUSIC and adaptive beamforming algorithms but also to ESPRIT algorithm. All the predicted results are verified by simulations.