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A new class of adaptive beamforming algorithms is proposed based on a uniformly spaced linear array by constraining its weight vector to a specific conjugate symmetric form. The method is applied to the well-known reference signal based (RSB) beamformer and the linearly constrained minimum variance (LCMV) beamformer as two implementation examples. The effect of the additional constraint is equivalent to adding a second step in the derived adaptive algorithm. However, a difference arises for the RSB case since no direction-of-arrival (DOA) information of the desired signal is available, which leads to a two-stage structure for incorporating the imposed constraint. Compared to the traditional algorithms, the proposed ones can achieve a faster convergence speed and a higher steady state output signal-to-interference-plus-noise ratio, given the same stepsize.