Efficient, Accurate and Scalable Reflectarray Phase-Only Synthesis Based on the Levenberg-Marquardt Algorithm

Abstract

The Levenberg-Marquardt algorithm is used to perform an efficient phase-only synthesis for shapedbeam reflectarray antennas. A thorough analysis of the problem and algorithm allows to improve greatly its performance and its results with regard to those in the literature. Specifically, several optimizations in the Jacobian matrix computation are detailed, including its fully parallelization thanks to the fact that each column of the Jacobian can be independently computed. A Cholesky factorization based solver is used to obtain the updating vector at each iteration of the algorithm, which is the fastest exact solver for linear equation systems. Finally, some guidelines to choose proper values for the algorithm parameters are presented. Due to the high dimensionality of the problem, a good control in the algorithm evolution is important to guarantee good convergence and avoid non-desired local minima. The synthesis of a LMDS shaped beam for a dual-polarized reflectarray is proposed to test the developed algorithm and the results are compared with others in the literature, showing improvements in accuracy and time efficiency. The framework established for the phase-only synthesis can be used in a broader problem to directly optimize the geometry of the reflectarray through full wave analysis of the unit cell.