  A numerically effective description of the total active reflection
coefficient and realized gain are studied for multi-port antennas. Material
losses are fully considered. The description is based on operators represented
in an entire-domain port-mode basis, i.e., on matrices with favorably small
dimensions. Optimal performance is investigated and conditions on optimal
excitation and matching are derived. The solution to the combinatorial problem
of optimal ports' placement and optimal feeding synthesis is also accomplished.
Four examples of various complexity are numerically studied, demonstrating the
advantages of the proposed method. The final formulas can easily be implemented
in existing electromagnetic simulators using integral equation solver.
