An effective hybrid optimization algorithm for the synthesis of 4-D linear antenna arrays

Abstract

Some major global optimization algorithms, which involves all the optimized variables in one problem, were used to synthesize time-modulated linear antenna arrays (TMLAs) in the existing literature. In this work, a hybrid approach, combining differential evolution (DE) algorithm and convex optimization, is proposed. This hybrid method is performed to optimize the static excitations amplitude and the switch-on duration time of TMLAs in order to achieve ultralow sidelobe and low sideband radiation at the same time effectively. In one iteration, as long as a set of switch-on duration time is fixed by the DE algorithm, Then the problem with respect to the static excitation is convex. So a convex optimization programming can solve the static excitation which is best for the corresponding set of switch-on time. The approach makes full use of the convexity of the problem with respect to the static excitation variables. Consequently, DE algorithm is used to optimize the switch-on time variables only. Which means fewer optimized variables are needed and it is more likely to find the global optimal solution in a less iterations. So that faster convergence can be obtained compared to DE algorithm which includes all optimized variables, especially for larger arrays. Furthermore, some examples are presented to demonstrate the effectiveness of this hybrid approach. First is a 32-element broadside TMLAs, with half wavelength uniform spacing, which is concerned for synthesizing a ultralow sideband at the same time suppress the sideband radiation pattern. Second is to sparse a uniform spaced 30-element TMLAs with fewer element satisfies the requirement of pattern. The last is to synthesis shaped beams. For the first example, numerical results show that a −61.4 dB sidelobe pattern with a static excitation amplitude ratio 4 can be synthesized, while the sideband level (SBL) is suppressed to −32.1 dB. For the second example, we can only use 18-element to achieve a −23.8 dB sidelobe and −31.3 dB SBL pattern with a static excitation amplitude ratio 2.77.