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Optimum SIR balancing using extended 1-norm beamforming optimization

: Boche, H.; Schubert, M.

IEEE Signal Processing Society:
IEEE International Conference on Acoustics, Speech, and Signal Processing 2002. Proceedings. Vol.3: Signal processing for communications, sensor array and multichannel signal processing, design and implementation of signal processing systems : May 13 - 17, 2002, Renaissance Orlando Resort, Orlando, Florida, USA
Piscataway: IEEE Operations Center, 2002
ISBN: 0-7803-7402-9
International Conference on Acoustics, Speech, and Signal Processing (ICASSP) <2002, Orlando/Fla.>
Fraunhofer HHI ()
array signal processing; cellular radio; convergence of numerical methods; iterative methods; optimisation; power control; radio links; radiofrequency interference; telecommunication control; joint downlink beamforming; optimum sir balancing; extended 1-norm beamforming optimization; wireless cellular system; frequency band sharing; time slot sharing; iterative algorithm; 1-norm cost function; optimum infinity -norm solution; convergence

We 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.