Synthesis of antenna arrays with spatial and excitation constraints

Synthesis of antenna arrays subject to spatial and excitation constraints to yield arbitrarily prescribed patterns in both the mean-squared and minimax sense are discussed. The spatial constraints may require that the interelement spacings be greater than a prescribed value or that the element locations lie within a specified region. The excitation constraints are of the form where the current-taper ratio is constrained to be less than or equal to a prescribed value. The technique employed consists of reducing the constrained optimization problem into an unconstrained one by the use of simple transformations of the independent variables. In such cases where explicit transformations are not available, a created response surface technique (CRST) has been used to convert the constrained optimization problem into a series of unconstrained optimizations. The optimization has been carried out using a nonlinear simplex algorithm. Numerical examples are given wherein both the linear and circular arrays are synthesized subject to constraints.