Gradient-Based Aperiodic Array Synthesis of Real Arrays With Uniform Amplitude Excitation Including Mutual Coupling

This paper proposes the synthesis of aperiodic arrays of realistic antennas excited with uniform amplitude, where the mutual coupling between elements is rigorously taken into account. A cost function that involves the expression of the radiated field of the coupled array is obtained and its gradient is evaluated in order to move the elements in the corresponding direction at each iteration. The synthesis method involves the calculation of the gradient of the field radiated by the coupled array, which is obtained analytically by using a full-wave method based on the generalized scattering matrix, spherical mode expansions and rotation, and translation properties of spherical waves.