Optimal Synthesis of Array Focused Power Pattern With Arbitrary Polarization and Low Sidelobe Based on Nullspace

A novel method based on the nullspace is presented for the optimal synthesis of focused power patterns with arbitrary polarizations and low sidelobe levels (SLLs). For the first time, we construct a nullspace according to the desired polarization characteristics by determining the relative amplitude and phase differences of the two orthogonal components of the radiation pattern. Within the nullspace, the required polarization characteristics can always be guaranteed and the focused polarized pattern synthesis problem can consequently return to a traditional power pattern synthesis problem. Given the convex nature of the problem, it can then be effectively solved through a single execution of the second-order cone program (SOCP), which enables us to obtain optimal low SLLs under the preplaced polarization constraints. Three representative examples of synthesizing focused patterns with arbitrary polarization requirements are provided to verify the effectiveness and advantages of the proposed method, which involves the synthesis of planar array, linear array, and conformal array comprising different antennas as the radiating elements.