Antenna pattern synthesis: a new general approach

The antenna pattern synthesis problem is of the utmost importance in almost every kind of antenna applications. Therefore, a very large number of contributions have appeared on this subject. But virtually all of them deal with simplified versions of the complete synthesis problem, wherein the degrees of freedom available in principle are strongly reduced, and/or idealized design criteria or requirements are considered. In this paper we present a formulation which allows us to overcome this fragmentation of the synthesis problem. A clear and direct description of the performance actually required by the antenna and a representation of the radiating properties of the antenna as a system allows us to formulate the synthesis problem as an intersections finding problem, i.e., to find a common element between a number of sets, each one containing elements fulfilling part of the requirements. This allows a completely general and flexible formulation of the problem, independent of the actual structure of the antenna. Then the practical implementation of this formulation is widely discussed, showing how an efficient solution procedure can be devised. The implications of the well-known ill-conditioning of the synthesis problem are also discussed. In order to show how the approach works and to assess its flexibility and power, a couple of significant examples are included, namely, a phase-only reconfigurable array and a shaped reflector synthesis. These examples are unconventional since no a priori choice of the intensity distribution (for the array case) or of the feed cluster (for the reflector case) is required. The method presented is able to exploit all the available degrees of freedom in order to fulfill the design requirements