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In this paper, a novel adaptive linearly constrained minimum variance (LCMV) beam former is proposed based on frequency response constraints. With frequency response constrained optimization criteria, the new constraint vector and thus the new weight vector are designed to improve the output signal to interference plus noise ratio (SINR), compared to the conventional distortion less constraint. The proposed methods flexibly control tradeoff between the output SINR performance and signal distortion. Simulation results are presented to demonstrate that the optimized beam former has higher overall performance about the SINR performance and signal distortion.