The characterization of the antenna radiation pattern in 3D has a well established theory. The increasing complexity of radiating structures under test leads to significant field acquisition duration. Using the Vector Spherical Harmonics expansion of the field and harnessing the sparsity of the antenna spectrum, one is able to decrease the required number of field samples. Also, an electric field radiated by a structure can be described with a few harmonics, and this fact can be harnessed to reduce the problem to an underdetermined linear system. This approach implies the resolution of a sparse recovery problem that requires the proper tuning of key parameters in order to ensure qualitative pattern reconstructions. In particular, the required number of field samples and the field acquisition time savings are addressed. Additionnal means to further improve the field reconstruction are proposed: the automatic determination of the error tolerance parameter and the best antenna orientation. All proposed procedures are assessed and validated on far field measurements data. © 2020 AMTA.