On the optimal synthesis of sum or difference patterns of centrosymmetric arrays under arbitrary sidelobe constraints

This paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry. The aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem, extending and completing previous results regarding uniformly spaced (linear and planar) arrays. It is shown that such a class consists of the centrosymmetric arrays, whose element patterns are either equal or Hermitian symmetric with respect to the center of symmetry. The optimal solutions are also Hermitian symmetric and the corresponding patterns are real. Furthermore, it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns. Some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage.