An advanced digital beam forming technique is achieved that is capable of simultaneously forming multiple beams and attenuating the cross-pol component at multiple locations. The proposed invention, comprising a series of signal inputs, optimization loops and weighting processes, successfully eliminates the side effect of an increase of the cross-pol in the process of beam-forming, thus reducing potential interference. This technique utilizes the orthogonally polarized signal component which is already available and can minimize both the horizontally polarized and vertically polarized cross-pol at the same time. The complexity of computation can be reduced by using only part of the orthogonal polarized components in the optimization.