<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The projection operator is a basic building block in the application of the alternating projections method to antenna synthesis. In general it is a non-linear operator that is repeatedly applied in the course of a single synthesis process, thus having a considerable impact on the convergence properties of the resulting algorithm. A novel approach to the computation of these projections is presented which exploits a simple definition of the relevant spaces (particularly that of radiated fields). Characterization of field mask specification as scale-invariant under this definition adds a further degree of freedom, namely reference level, which impacts on the (sensitive to scaling) projector. In order to compute the optimum reference level, an iterative procedure is proposed which is simple to implement, easily integrable in standard alternating projection routines, and adds negligible computational burden. Numerical tests confirm an improved performance with respect to the fixed-scaling projection operator in terms of convergence rate and robustness against the initial guess, supporting our approach as a valid aid in overcoming the drawbacks of the alternating projections-based antenna synthesis. </para>