Our activity has to do with the design of Direct Radiating Arrays (DRA) for satellite communications. The objective is to have a reduced number of controls in order to minimize the manufacturing and operating complexity. The DRAs will create a set of simultaneously overlapped multi-beams in the frequency range of 20 GHz and will satisfy certain specifications (End of Coverage (EOC) gain, grating and side lobe levels). Radio-Communications Laboratory (RCL) shall consider the DRA design and shall mainly optimize the geometry of the array and develop the appropriate software tool. The design methods which are going to be used are the Fractal Technique and the Orthogonal Method(OM) in conjunction with the Orthogonal Perturbation Method (OPM). Some preliminary examples are presented and show the effectiveness of the design methods.