A new method of fast pattern synthesis is presented in this paper.Under the framework of alternating projection (AP)

the amplitudes of desired pattern is firstly constrained.Then the method adopts an auxiliary phase function to obtain the optimized phases of desired pattern.Finally

the required excitations can be obtained from a constrained least mean squares (CLMS)

which is solved by the proximal splitting method.Compared with other methods based on AP

the optimization of pattern phase is helpful to improve the convergence speed and performance of the algorithm.The synthesized results show its high performance in the pattern synthesis with or without excitation constraints.The proposed method is suitable for the arbitrary arrays and has good generalization capability.