An efficient algorithm for optimum joint downlink beamforming and power control

We address the problem of joint downlink beamforming and power control in a frequency flat multi-antenna broadcast channel. In this context, a common optimization strategy is to maximize the system throughput under a certain power constraint. This, however, does not guarantee a fair sharing of throughput among the users, which is required in case that the receivers cannot cooperate. Thus, we propose a different approach, which always assumes optimally balanced data rates. If the problem is feasible, i.e., desired target rates can be reached, spare degrees of freedom can be used in order to minimize the total transmission power. This strategy can even be applied if only spatial covariance channel information is available. The authors have developed a theoretical framework based upon uplink/downlink durability, feasibility considerations, and bounds on the maximal eigenvalue of the resulting coupling matrix. In this paper an overview of the results is given and they are discussed in the context of existing literature. Finally, a theoretical benchmark is provided for the case of perfect channel knowledge. Then, beamforming can be combined with Costa pre-coding, as proposed by Caire and Shamai [1,2]. This leads to a closed-form solution of the problem.