Comparison between Analytic Derivative and the Technique of Differential Contributions in Reflectarray Phase-Only Synthesis

Many algorithms for the optimization of array antennas need the calculation of a gradient to minimize a cost function. Usually, the best approach is to compute analytically the derivatives, since that way computations are faster. However, sometimes the derivatives are cumbersome to obtain or they cannot be calculated, such as when directly optimizing the layout in reflectarrays for cross-polarization improvement. In those cases, derivatives are evaluated using numerical techniques such as finite differences. In this work, we present the numerical technique of differential contributions (DFC) to accelerate gradient-based algorithms when the derivatives are calculated with finite differences, achieving a complexity time scaling of the same order as the analytical derivatives. The technique is applied to a far field phase-only synthesis for reflectarray antennas using the generalized Intersection Approach, and it is compared with the analytic derivatives and the use of finite differences with the FFT. The DFC technique shows superior performance in all cases, even than the analytic derivative.