This paper presents a synthesis of a volumetric ring antenna array for a terrestrial coverage pattern. This synthesis regards the spacing among the rings on the planes X-Y, the positions of the rings on the plane X-Z, and uniform and concentric excitations. The optimization is carried out by implementing the particle swarm optimization. The synthesis is compared with previous designs by resulting with proper performance of this geometry to provide an accurate coverage to be applied in satellite applications with a maximum reduction of the antenna hardware as well as the side lobe level reduction.