Shaped Beam Directivity Maximization With Mainlobe Ripple Loss and Dynamic Range Ratio Constraints

The mainlobe directivity maximization problem for shaped beams of linear and planar arrays is addressed based on the framework of alternating direction method of multipliers (ADMMs). First, the optimization model with three constraints including the predefined mainlobe ripple loss (MRL), sidelobe level (SLL), and dynamic range ratio (DRR) is established. This model is nonconvex due to the constraints of directivity and excitations. To deal with the nonconvexity, several auxiliary variables and an augmented Lagrangian method are introduced to transform the original problem into a two-block problem. Then, the block coordinate descent (BCD) method is adapted to update the coupled variables in the first block, and the projection strategy is used to update the irrelevant variables in the second block. Following the above steps, satisfactory array excitations of lower DRR and higher directivity could be obtained with a shorter CPU time when compared with state-of-the-art methods. The effectiveness of the proposed method is verified via numerical and full-wave experiments.