Synthesis of Low-Sidelobe 4-D Heterogeneous Antenna Arrays Including Mutual Coupling Using Iterative Convex Optimization

A novel iterative convex optimization approach is proposed for the synthesis of low-sidelobe 4-D heterogeneous arrays in the presence of mutual coupling effect. To realize wide bandwidth and wide-angle scanning, a tightly coupled dipole element (TCDE) is selected as the basic element. Due to the strong coupling between antenna elements, the active element pattern (AEP) and active reflection coefficient (ARC) are included in the proposed approach in order to evaluate the overall mutual coupling and port matching. Specifically, a nonconvex programming problem in terms of the given maximum sidelobe level (SLL), the ARC or reflected power at the center frequency, and the given maximum sideband level (SBL) at sidebands is established. After the application of some mathematical transformations, the nonconvex programming problem is decomposed into a convex optimization problem at the center frequency and an iterative convex problem (ICP) at sidebands. Owing to the efficiency of the convex optimization, the two problems can be efficiently solved. The proposed approach is applied to synthesize low-sidelobe patterns while minimizing the SBL in a 32-element cone-shaped 4-D heterogeneous array. The simulated and measured results verify the effectiveness of the proposed approach and show the advantages (improved gain) of the heterogeneous array.