  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.
