A novel two-step synthesis method of sparse nonuniform-amplitude concentric ring arrays (SNACRAs) to maximize the beam collection efficiency (BCE) for microwave power transmission (MPT) is proposed in this paper. In the first step, beetle antennae search (BAS) algorithm is used to optimize the radius of each ring of the SNACRA, to obtain the maximum BCE and the equivalent continuous excitation of each ring. In the second step, we find the least array element on each ring to discretize the continuous excitation on each ring by using the binary search (BS) algorithm directly under the restriction conditions and then find the excitation of each element. Through the above two steps of optimization, the optimal synthesized parameters of the SNACRA, including the maximum BCE, layout, excitation and power pattern, can be obtained highly efficiently. Many representative numerical results under different ring numbers, apertures, and receiving areas are presented. Comparing these numerical results with those of other three arrays for MPT, it is proved that the SNACRA synthesized by the two-step method can get higher BCE with less elements and have a relatively simple feed network.
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