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The authors present adaptive algorithms for the array antenna system to generate the weight vector which provides the beampattern having its main lobe along the direction of the mobile target subscriber at each snapshot. Three algorithms are introduced, i.e., the CGM (conjugate gradient method), Lagrange multiplier-method, and power series method. Each algorithm has been modified in such a way that the suboptimal weight vector can be produced with a reasonably small computational load for the real-time processing of signals with an off the shelf DSP (digital signal processor). The performance of each algorithm is demonstrated in terms of the improvements in SINR (signal to interference+noise ratio) for a given number of antenna elements.