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Adaptive beamformers at the element level usually require a great number of training samples and the computational cost for calculating the weight vector for large phased array antennas is very high, which make it difficult for real-time applications. To address this problem, a two-dimensional (2-D) adaptive beamformer applicable to large planar array antennas that have low computational complexity and low training sample requirement is proposed. In the proposed method, the weight matrix is first reconstructed as a matrix that has the same or close columns and rows by utilising the special Kronecker property of the array steering matrix. Then, the weight vector is determined by adopting a bi-quadratic cost function and a bi-iterative algorithm. Experimental results show that the proposed method can achieve fairly good performance even when the training samples are small. [ABSTRACT FROM AUTHOR]