Phase optimization of antenna array gain with constrained amplitude excitation

The formulation of antenna array optimization with variable phase and constant amplitude excitation is presented. The method shown using steepest ascents is general in that a nonlinear performance index expressible as a ratio of Hermitian quadratic forms can be optimized. Directive gain optimization of a linear array of isotropic elements is illustrated and compared with gain optimization using variable excitation. Endfire gain is emphasized and compared to the Hansen-Woodyard condition showing that the Hansen-Woodyard condition is not optimum in the directive gain sense for a discrete endfire array. In addition a
0.4\lambda
spaced linear array is optimized using phase only for scanning from endfire to broadside.