A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in practice be acquired with multi-channel receivers. Due to the linearity of the formulation, a reliable phaseless transformation is achieved, which completely avoids the problem of local minima - the Achilles heel of most existing phase retrieval techniques. Furthermore, the necessary number of measurements are kept close to that of fully-coherent antenna measurements. Comparisons with an already existing approach exploiting local phase relations demonstrate the accuracy and reliability for synthetic data.