Downlink multiuser transmit beamforming under total transmit power constraint

We consider a wireless downlink multiuser multiple-input single-output (MISO) system and we investigate the problem of jointly optimal beamforming and power allocation. In particular, under a total transmit power budget constraint and either exact or second-order statistics knowledge of the channel of all users we find the optimum set of beam vectors and associated power values such that the sum-rate between the base station and the end users is maximized. Then, we formulate and solve two variations of the above optimization problem as a low and high signal-to-interference-plus-noise ratio (SINR) approximation, respectively. To solve all optimization problems, we invoke the theory of uplink-downlink duality and derive computationally simple, coupled iterative procedures with guaranteed convergence.