Abstract:  A pattern synthesis of the circular array with the constraint of minimal arrays is proposed. This method firstly analyzes the reason why the synthesis with the norm constraint of is non-convex. And then the optimal model can be slack as a design problem with mixed norm constraints of and . It can not only enlarge the feasible region but also can enhance the accuracy of the optimal results in comparison with the traditional method. Lastly this method makes the location of the array element and the coefficient as joint variables for its optimization model, which can overcome the bad effects to the synthesis of the circular arrays caused by the constant grid point. The experimental results show that much reduction of the arrays and the peak side lobe can be obtained when applying the method presented in this paper.