Matrix analysis
Base station transmitting antenna arrays for multipath environments
Signal Processing
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Transmit beamforming and power control for cellular wireless systems
IEEE Journal on Selected Areas in Communications
QoS-based resource allocation and transceiver optimization
Communications and Information Theory
A general theory for SIR balancing
EURASIP Journal on Wireless Communications and Networking
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
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We address the problem of joint downlink beamforming and power control in an interference limited wireless system under hard fairness constraints. The transmitting base station is equipped with an antenna array, whereas the mobiles are equipped with single antennas. Transmit channel state information is available. The design goal: control the SIR levels in order to fulfill individual target thresholds. This leads to an l∞-norm minimization problem, which has no obvious solution. Thus, Gerlach and Paulraj (Signal Processing 54 (1996) 59) proposed an alternative optimization strategy that is based on l1-norm minimization. In this paper, we study whether or not this approach leads to the optimal solution. We provide necessary and sufficient conditions for the equivalence of l∞ and l1 optimization. These conditions are not always fulfilled, as can be shown by counterexamples. An exceptional case, however, is the 2-user scenario, for which both concepts are indeed equivalent and the solution can be given in closed form. For arbitrary numbers of users, we propose a modified optimization scheme that alternately performs power control and beamforming optimization based on the l1 cost function. We prove the convergence of this iterative algorithm by showing that the iteration is a monotonic sequence. Each local optimum is a global optimum of the l∞-norm minimization problem.