Formulation of optimization problems with radiation field phases as design variables for pattern synthesis of linear antenna arrays

Pattern synthesise of antenna arrays is usually complicated optimization problems, while evolutionary algorithms (EAs) are promising in solving these problems. This paper does not propose a new EA, but does construct a new form of optimization problems. The new optimization formulation has two differences from the common ones. One is the objective function is the field error between the desired and the designed, not the usual amplitude error between the desired and the designed. This difference is beneficial to decrease complexity in some sense. The second difference is that the design variables are changed as phases of desired radiation field within shaped-region, instead of excitation parameters. This difference leads to the reduction of the number of design variables. A series of synthesis experiments including equally and unequally spaced linear arrays with different pattern shape requirements are applied, and the effectiveness and advantages of the proposed new optimization problems are validated. The results show that the proposing a new optimization formulation with less complexity is as significant as proposing a new algorithm.