Boche, H.H.BocheSchubert, M.M.Schubert2022-03-092022-03-092002https://publica.fraunhofer.de/handle/publica/340940We address the problem of joint downlink beamforming and power control in a wireless cellular system, where several users share the same time slot and the same frequency band. In order to enable a fair sharing of resources among all users, the SIR levels should be balanced by minimizing the infinity -norm of a certain vector. To this end, Gerlach and Paulraj (1996) proposed an iterative algorithm, which is based on a 1-norm cost function. It has been observed that this algorithm approximates the optimum infinity -norm solution. In this paper we characterize the case where this algorithm is optimal. The analytical results are used to develop a new algorithm, which always converges to the optimum infinity -norm solution, regardless of the chosen initialization. A proof of convergence is given.enarray signal processingcellular radioconvergence of numerical methodsiterative methodsoptimisationpower controlradio linksradiofrequency interferencetelecommunication controljoint downlink beamformingoptimum sir balancingextended 1-norm beamforming optimizationwireless cellular systemfrequency band sharingtime slot sharingiterative algorithm1-norm cost functionoptimum infinity -norm solutionconvergence621conference paper