End-fire array synthesis using gradient-based numerical optimization with analytical derivatives

Endfire linear arrays comprising isotropic radiators are optimized for sidelobe level reduction. Our approach utilizes the sequential-quadratic programming algorithm exploiting analytical derivatives of the array directivity with respect to the designable parameters, as well as initialization through smart random search. The initial design, the reference, is the Hansen-Woodyard (HW) design. Several test cases varying in the number of design variables are considered with the goals to lower the SLL and additionally suppress the first side lobe. Depending on the number of design variables and optimization objectives/constrains, it is possible to significantly reduce the sidelobe level without compromising the directivity compared to the HW design and without shrinking the inter-element spacing.