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This paper proposes a novel solution to the problem of beamforming and power control in the downlink of a multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system. This solution is developed in two steps. First, we describe an adaptive beamforming technique that, using a stochastic gradient method, maximizes the power delivered to a mobile terminal. In the proposed solution, perturbed precoding matrices are time multiplexed in the information signal transmitted to a mobile terminal; then, the mobile terminal informs the transmitter, via a single feedback bit, about the perturbation delivering the larger power. This approach does not need pilot symbols and uses quasi-Monte Carlo methods to generate the required perturbations with the relevant advantages of improving the downlink spectral efficiency and reducing the system complexity with respect to other competing solutions. Then, we propose a novel power-control algorithm that, selecting a proper transmission energy level from a set of possible values, aims to minimize the average bit error rate. This set of levels is generated on the basis of the channel statistics and a long-term constraint on the average transmission power. Numerical results evidence the robustness of the proposed algorithms in a dynamic fading environment.