  A technique of designing antenna excitation realizing orthogonal states is
presented. It is shown that a symmetric antenna geometry is required in order
to achieve orthogonality with respect to all physical quantities. A maximal
number of achievable orthogonal states and a minimal number of ports required
to excite them are rigorously determined from the knowledge of an antenna's
symmetries. The number of states and number of ports are summarized for
commonly used point groups (a rectangle, a square, etc.). The theory is applied
to an example of a rectangular rim where the positions of ports providing the
best total active reflection coefficient, an important metric in multi-port
systems, are determined. The described technique can easily be implemented in
existing solvers based on integral equations.
