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An array beampattern synthesis method which use a set of new constraints on magnitude response combined with an compensation method for the mutual coupling effect among array elements is investigated in this paper. The beampattern synthesis problem was solved by two different optimization methods. The proposed method can provide much improved flexibility in the design and has been demonstrated to be effective for the design of various array patterns including superdirective, null forming, and shaped-beam pattern. The non-convex problem of the constraints on magnitude response is solved by using a relaxed linear constraint. With the proposed method, the number of the DOFs consumed for beampattern control is small, so that the synthesized array has an attractive performance on interference cancelation. Simulation results show the effectiveness of the proposed methods.