Linearly Polarized Shaped Power Pattern Synthesis With Sidelobe and Cross-Polarization Control by Using Semidefinite Relaxation

In this communication, the problem of synthesizing a linearly polarized shaped power pattern with accurate control on both sidelobe and cross-polarization (XP) levels is considered. For a user-defined desired polarization direction, the definitions of realizable co-polarization (COP) and XP directions for an arbitrary propagation direction in the shaped pattern are presented. With the help of such definitions, the considered problem is formulated as finding appropriate excitations so as to produce a shaped power pattern in which the realizable COP component meets prescribed lower and upper bounds, the realizable XP component and the total power pattern are less than their upper bounds in the regions of interest. The semidefinite relaxation method in the literature is then extended to solve this vectorial pattern synthesis problem. The proposed method can include the mutual coupling and platform effects by using vectorial active element patterns of an antenna array. A set of synthesis examples with different array geometries and radiation requirements are conducted to validate the effectiveness and advantages of the proposed method.