Optimum scattering from an array of half-wave dipoles

Optimization of the field scattered by an antenna has important applications in radar systems and as elements in passive communication links. A method is presented of optimizing the scattering from a linear array of half-wavelength dipoles at a prescribed bistatic angle. The array is excited by a plane wave incident at an arbitrarily specified angle. The field scattered by the array is maximized or minimized as a function of the parameters of a network connected to the accessible antenna terminals. The result is a matrix eigenvalue equation of order N = \frac{1}{2}M(M + 1) for the optimum parameters of an M -element array. It is known that N - 1 solutions of this equation exist, which yield a prescribed zero in the bistatic scattering pattern but they do not correspond to physical networks. Using linear combinations of these, we construct a family of optimum admittance matrices that satisfy necessary and sufficient conditions that they be admittance matrices of passive networks. The form of the matrices is such that the corresponding passive regions in the bistatic plane are easily determined. The corresponding network can then be realized using existing network synthesis procedures. The essential features of the theory are illustrated by synthesizing an optimum network for a two-element array. It is also shown that backscatter at any angle can be minimized independently of the receiving pattern of the array.