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The maximization of a weighted sum of data rates is an essential point in cross-layer based resource allocation. Several algorithms have been proposed in the literature to solve this problem for the downlink of a multiple antenna system employing dirty paper preceding at the base station. However, they all suffer from a relatively slow convergence if the true number of objective function evaluations is taken into account. In this paper, an improved conjugate gradient method is presented, that takes the power constraint into account in the calculation of the search direction. Its superior convergence properties compared to existing approaches are verified by Monte-Carlo simulations for various scenarios.