Discretization of Planar Continuous Current Sources for Design of Planar Arrays Using Iterative Method of Least Squares

In this paper, a simple method for the discretization of planar continuous current sources is presented. First, the planar current distribution is determined by the Fourier and Inverse Hankel Transforms. Then it is discretized for the design of a planar array. The radiation pattern of the array of discrete elements will be quite different from that of the planar continuous current source. Therefore, for the improvement of its radiation characteristics, such as side-lobe level and ripple in the pattern, the iterative method of least squares is used. The desired radiation characteristics of the array, such as​​ the side-lobe level and ripple of pattern, are achieved by an iterative algorithm of the method of least squares together with the array element excitations. Indeed, first, in each iteration, in order to properly adjust the radiation pattern, the values of radiation pattern at the maximum points of the side-lobes and at the maximum and minimum points of the main-lobe, are replaced with the desired values. Then, by sampling of the adjusted radiation pattern, a linear equation system is obtained which by solving this linear equation system by using the method of least squares, the excitation currents of array elements are determined. The proposed method can be used to optimize any array with arbitrary configuration. Several examples of simulations have been presented to verify the efficacy of the proposed method.