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We consider the downlink of a cellular network with cooperating multiple antenna base stations. On the one hand, each base stations tries to serve its associated mobile devices optimally, on the other hand, they try to minimize the interference they cause. Both goals could be achieved, if the interference channels would be zero. An adaptive beamforming based interference mitigation can only be performed for measured interference channels. To find an unachievable, but relatively tight upper bound we set the measured interference channels to zero. For such a limited cooperation, we show that the rates can be improved by predicting the interference over the unknown channels.