Pixel Antenna Optimization using the Adjoint Method and the Method of Moving Asymptotes

The pixel concept offers a convenient and efficient method for antenna design. To meet the given specified antenna requirements or constraints, heuristic algorithms are often used to optimize the connection states for the hardwires between pixels, which are usually assumed to have the binary states, "short" or "open". An alternative optimization strategy is proposed in this work, where the Boolean constraints on the hardwires are first relaxed to continuously tunable resistances and the globally convergent method of moving asymptotes (GCMMA) is applied to optimize the resistances. To speed up the computation, the adjoint method is used to simplify the calculation of the gradient information required in GCMMA. Resistances that are found as being above or below a certain threshold are then judged as "open" or "short", respectively. Finally, the remaining intermediate resistance states are binarized using the successive exhaustive Boolean optimization (SEBO) method. Four different optimization strategies are proposed in terms of the objective function implemented in GCMMA and whether the second-stage SEBO is iterative or not. Two broadband endfire pixel antennas having horizontal linear polarization and high radiation efficiency are designed and fabricated correspondingly to demonstrate the feasibility of our proposed methods.