Frame decomposition has been introduced into Gaussian Beam Shooting (GBS) algorithms to perform decompositions of fields radiated by large planar apertures into a half plane in a rigorous and stable way. This work proposes a generalization of frame-based GBS to situations when fields are radiated into all directions in 3d space. Frame decomposition is applied in six planes in the spectral domain, starting from the knowledge of the radiated far field, which is partitioned through a "partition of unity" procedure. The formulation is presented, as well as numerical results which illustrate its validity and its accuracy versus frame decomposition and beam launching parameters.