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A fast-scanning phased array weather radar (PAWR) with a digital beam forming receiver is under development. It is important in beam forming for weather radar observation with temporally high resolution to form a stable and robust main lobe and adaptively suppress sidelobes with a small number of pulses in order to accurately estimate precipitation profiles (reflectivity, mean Doppler velocity, and spectral width). A minimum mean square error (MMSE) formulation with a power constraint, proposed in this paper, gives us adaptively formed beams that satisfy these demands. The MMSE beam-forming method is compared in various precipitation radar signal simulations with traditional beam-forming methods, Fourier and Capon methods, which have been applied in atmospheric research to observe distributed targets such as precipitation, and it is shown that the MMSE method is appropriate to this fast-scanning PAWR concept.