Closed form evaluation of the antenna directivity via sampling expansion

A simple, fast and accurate closed form formula is proposed for determining the antenna directivity from the knowledge of the radiation intensity in a nonredundant number of points on the far-field sphere. The derivation of such a formula is based on the spatial bandlimitation properties of the electromagnetic field radiated by a transmitting system, so that a sampling representation and an interpolation expansion are adopted to reduce the integration of the radiation intensity on the far-field sphere in summations. Without loosing the accuracy, this allows a remarkable reduction of the computation time required by the evaluation of the total radiated power in the expression of the antenna directivity. Numerical simulations are used to show the performances of the solution in terms of accuracy and fastness.