Theoretical and experimental comparison of optimisation criteria for downlink beamforming

We address the problem of joint downlink beamforming and power control in wireless communication systems. The goal is to minimise the overall transmission power radiated from the base station while satisfying individual signal-to-interference levels at the mobiles. Several iterative algorithms have been proposed for this non-linear optimisation task. One important problem in this context is that for certain scenarios the problem has no feasible solution. One of the main contributions of this paper is to derive a necessary and sufficient condition for the existence of a solution. This not only gives new insight into the analytical structure of the problem, but also provides a unifying framework by which several optimisation criteria known from literature can be compared. Finally, simulations are carried out using a deterministic multi-path channel model.