Some useful approximations for calculation of directivities of multibeam power patterns of large planar arrays

In this paper, by adopting the superposition of terms with unequal coefficients, some useful closed-form formulas for the class of large planar arrays are presented for predicting the directivities of radiated beams. Despite the applied simplifying assumptions, the provided formulas may be used for designing a large multiple-beam planar array with a specified power pattern. Several illustrative examples are presented which are numerically demonstrate by the MATLAB software. The applicability of the proposed synthesis method verified by the achieved conformity between the simulations and theoretical predictions. Furthermore, the impact of quantization and array dimensions on the performance of power controlling as well as the limitations on the maximum scan angle are investigated. It is believed that the proposed straightforward approach for array synthesis provides a new opportunity for various applications such as multiple-target radar systems and beamforming array antenna.