Systems and methods are disclosed herein for providing full orthogonality between simultaneously used beams, e.g., in a Multi-User Multiple-Input-Multiple-Output (MU-MIMO) radio system. In some embodiments, a radio system comprises an antenna system and a processing unit. The processing unit is adapted to determine an initial set of null locations for a particular beam based on an initial set of beam weighting factors for the particular beam, and change one or more of the initial null locations based on one or more other beams to be used simultaneously with the particular beam, thereby providing a new set of null locations for the particular beam. The processing unit is further adapted to compute a new set of beam weighting factors for the particular beam based on the new set of null locations, and utilize the new set of beam weighting factors to transmit or receive on the particular beam.