Improved array sectoral patterns by unequal element spacing

This paper presents a new method for synthesis of improved sectoral patterns by utilizing unequally spaced linear arrays. The new technique is presented in terms of four fundamental steps. Step 1 formulates the synthesis problem. In this step, the prescribed array factor is sampled at M uniformly spaced points over the observation range. Step 2 contains the key development in the synthesis technique, viz. the Legendre transformation of the array factor which leads to the generation of the recursive equations defined in step 3. In step 3, the limiting property of the Legendre polynomials is effected and this leads to the generation of the triangular system of equations. The actual design equations of the elements are obtained in step 4.