Some new methodologies for multiobjective antenna design

Reflector antennas [1] are devices that are widely use for satellite communication. The life length of such devices depends highly on the fatigue due to the energy consumption for the signal emission. Thus, one of the goals of the optimal design of an antenna is to improve the productivity of systems designed for a given task, for a fixed input power. A reflector antenna is characterized by radiating surfaces whose geometry is the main parameter that can be controlled to fulfill the task. Based on the time-harmonic wave propagation simulation in free space, numerical procedures for the optimal design of the shape of radiating structures are examined. Usually, several concurrent criterions are considered, leading to a trade-off seeking rather than a pure minimization problem. Typically, such antennas are working over a frequency range, each frequency corresponding to a transmission channel. Hence the optimization problem reads as a multiobjective problem [2] to ensure that some performance are fulfilled for all frequencies. Such problems are referred to as multipoint optimization problem, a problem depending on a continuous physical parameter. To complete the task, objectives of different nature can be considered (multiobjective but not multipoint). For instance, a radiation criterion together with an energy loss criterion at the source are considered. New methodologies using multilevel techniques [3-6] and Nash Game theory [7-8] for the numerical treatment of such problems are proposed. Concrete numerical experiments are conducted for the multipoint design of a bi-criterion problem applied to a realistic reflector antenna.