Beampattern synthesis with minimal dynamic range ratio

The excitations with a small value of dynamic range ratio (DRR) are helpful to control the mutual coupling between array elements, reduce the output power loss, and simplify the feeding network design. Unlike the commonly specified DRR, this communication focuses on finding the minimal DRR of the excitations while synthesizing a desired beampattern. To address this issue, a nonconvex and nonlinear optimization problem is formulated to synthesize array pattern while minimizing the DRR of the excitations, which is solved by extending the penalty method. Firstly, violations of all the inequality constraints are augmented into the original objective function as penalty functions which are nonsmooth. Secondly, a new smooth function is introduced to replace the nonsmooth penalty functions. These operators convert the constrained optimization problem to a smooth unconstrained one which can be easily solved. Theoretical analysis on the approximation error between the constrained optimization problem and the transformed one is provided. Numerical results are also given to verify the proposed scheme in achieving the minimal DRR.