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SIR balancing for multiuser downlink beamforming - a convergence analysis

: Boche, H.; Schubert, M.


IEEE Communications Society:
IEEE International Conference on Communications 2002. Conference proceedings. Vol.2 : 28 April - 2 May 2002, New York, NY, USA
Piscataway: IEEE Operations Center, 2002
ISBN: 0-7803-7400-2
ISBN: 0-7803-7401-0
International Conference on Communications (ICC) <2002, New York/NY>
Fraunhofer HHI ()
antenna arrays; antenna radiation patterns; array signal processing; convergence of numerical methods; eigenvalues and eigenfunctions; iterative methods; matrix algebra; minimax techniques; minimisation; mobile radio; quality of service; multiuser downlink beamforming; sir balancing; spectral efficiency; transmit beamforming; optimization; minimization; maximum eigenvalue; system coupling matrix; iterative scheme; minmax problem; qos requirements; convergence analysis; signal-to-interference ratio; resource assignment; antenna array; mobiles; radiation patterns

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, 5, 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.