The synthesis of antenna arrays in presence of mutual coupling using generalized scattering matrices in terms of characteristic modes is proposed. For the synthesis, the array is built of synthetic elements that are described by their modal scattering and radiation behavior. In particular, the question of how to describe the degrees of freedom of such elements is addressed. The eigenvalues of the characteristic modes of the element geometry and the modal radiation behavior of the antenna are thereby selected as degrees of freedom for the model of the synthetic elements. Using this model and a modal coupling matrix, an approach to optimize the modal configuration of the elements within an array is proposed. Finally, a close to reality example shows how the proposed theory can be used to enhance the cross-polarization rejection of a circularly polarized patch antenna array with a fixed beam.