In this paper, a novel beam shaping technique is developed to synthesize the array factor (AF) radiation pattern of linear, and planar antenna arrays. The proposed method is established based on the expanding of the AF using Legendre transform in conjunction with an integrand operator. A system of linear equations is derived and its solution is obtained using Least Square Method (LSM) for the required pattern. In addition, an iterative procedure is introduced to reduce the number of elements of the primary designed array for a specified Mean Square Error (MSE). Then, the proposed method is applied to synthesize the AF of planar and ring antenna arrays. To verify the performance of the proposed method, a few comprehensive well-known linear, planar and ring arrays are examined. The obtained results show that the introduced method can be used to design the AF pattern of many types of practical arrays with good accuracy.

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