SIR balancing for multiuser downlink beamforming - a convergence analysis

The downlink spectral efficiency of interference limited wireless systems can be drastically increased by employing multiuser transmit beamforming at the base station. The goal is the joint optimization of the user transmission powers and the beamforming weights. An important problem is to find the range where a feasible solution can be expected. Recently, it has been shown (see Boche, H. and Schubert, M., European Trans. on Telecom., vol.12, no.5, p.417-26, 2001) that this problem is equivalent to the minimization of the maximum eigenvalue of the system coupling matrix. An iterative scheme to solve this min-max type problem was proposed by G. Montalbano and D.T.M. Slock (see Proc. IEEE ICUPC, 1998), but no convergence analysis was given. We analyze the convergence behavior of the algorithm and extend the results to the more general case of individual QoS requirements. It is shown that the iteration sequence is strictly monotonically decreasing as long as the global optimum is not reached. This proves the optimality of the algorithm and provides valuable insight into the analytical structure of the problem.