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A Novel Solution to the Optimum Transmit Beamforming Problem Ben Wild and

In this project we address the problem of optimum transmit beamforming. Transmit beamforming is a powerful means of increasing capacity in systems in which receive beamforming is not possible but the transmitter is equipped with an antenna array. This is typical of the base to mobile downlink channel in cellular communication systems. The problem is formulated as the minimization of the power used at the base station, subject to signal to interference constraints at the mobiles. Traditionally this problem has been formulated as a non-convex optimization problem. We attempt to transform the problem to a more tractable convex optimization problem through certain relaxations. We prove that even with these relaxations the optimal solution to the relaxed problem is the same as that of the original problem. We also perform simulations to show that the relaxed problem and the original problem converge to the exact same solution. Finally, we also solve the related case when the mean and covariance of the channel gains are known but not the exact values and show the advantages of using the relaxed formulation for this case.