The existing spatial smoothing (SS) technique, although it is effective in decorrelating coherent signals, is considered applicable only to uniformly spaced linear arrays which are very sensitive to the directions-of-arrival (DOAs) and can be used to estimate azimuth angles only. To significantly improve the robustness of DOA estimation and of beamforming and to estimate both azimuth and elevation angles in a 3D multipath mobile radio environment, we developed techniques for applying SS to arrays of nonlinear geometry. We found and proved the necessary and sufficient conditions on an array configuration for applying SS. This array must have an orientational invariance structure with an ambiguity free center array, and the number of subarrays must be larger than or equal to the size of the largest group of coherent signals. We also studied the cause of ambiguities in a multipath environment. We found the necessary and sufficient conditions for a three-sensor array manifold to be ambiguity free and identified several higher order ambiguity situations. If an array is also central symmetric, the forward/backward spatial smoothing can be used to improve the resolution. Finally, we expanded the application of our technique not only to MUSIC and adaptive beamforming algorithms but also to ESPRIT algorithms. All the predicted results are verified by simulations.