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A beamforming algorithm for a macro cell base station (BS) is proposed. The method has the following three features. Firstly, each direction of arrival (DOA) of waves from mobile terminals to the BS is calculated by the modified Fourier beamformer using a real number correlation vector (RV-Fourier), which greatly reduces complexity. Secondly each DOA is estimated accurately even if there are high power interference waves, applying the technique to subtract the other user's correlation vector. Lastly, nulls in interference directions are formed using the modified directionally constrained minimization of power (DCMP) method, which does not need the derivation of the inverse correlation matrix. In comparison with the conventional recursive least-squares (RLS) method, the proposed method requires a much smaller computational load (about 10-20%). Simulation results show that the tracking performance of the proposed method excels RLS when the terminals are moving fast.