A spacing weighted antenna array

This paper considers a non-uniformaly spaced array. By starting with a continuous aperture distribution, the pattern function is formulated from a Lesbegue-Stieltjes integral point of view. A spacing weighting function can thus be generated. Based upon the methods of mechanical quadrature, the integral is reduced to a summation which represents the pattern function of a corresponding array. As an examples a symmetric linear array of 74 isotropic sources at an average spacing of 1.82 wavelengths is considered. The side lobe level is found to be less than -14 db for|u| < 0.98and below -10 db for|u| \leq 2. If these elements were uniformly spaced, secondary beams of 0-db level would occur atu = \pm 0.552, \pm 1.10, and\pm 1.66. A systematic optimization in a certain sense by a high speed computer has also been carried out. It indicates that a slight improvement in performance is possible. Based upon Legendre-Gaussian quadrature, two other linear arrays, both spacing and amplitude weighted: are studied. For relatively small u, their patterns are practically identical to that due to the corresponding continuous distribution.