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A simple gradient algorithm for adaptation of complex base band beamspace weights of the transmit antenna at the base station by feedback from the mobile is presented. In order to converge to the optimal beamspace weights this beamspace beamformer relies on a single feedback bit from the mobile user. Here the ingenious idea is that the feedback bit indicates which of the two normalized perturbed beamspace weights of the base station array delivers more power to the mobile. Utilizing this feedback, our algorithm at the base station updates the complex beam space weights of the transmit beamformer. It converges to the optimum beam space weights for a static channel, which is confirmed by simulations.