Be´zier representations for the multiobjective optimization of conformal array amplitude weights

For conformal phased arrays, generally the excitation amplitude of the array elements must be adjusted in order to maintain low sidelobes as the array is scanned. While the desired phase weights for maximum gain are deterministically set by the array geometry and scan angle, the representation of optimum low sidelobe amplitude weights remains an open problem. Following up on prior work using the efficiency-constrained optimization of a modified Bernstein polynomial for low sidelobe conformal array synthesis, a Be´zier surface is shown to provide a good representation of the optimized amplitude weights with a reduced number of parameters, while demonstrating ε-constraint multi-objective optimization of conformal aperture efficiency versus sidelobe level. These results are extended to include a Be´zier volume representation for the multiobjective optimization of conformal aperture efficiency versus both sidelobe level and scan angle.