Matrix analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
IEEE/ACM Transactions on Networking (TON)
Handbook of Antennas in Wireless Communications
Handbook of Antennas in Wireless Communications
Radio Resource Management for Wireless Networks
Radio Resource Management for Wireless Networks
A utility-based power-control scheme in wireless cellular systems
IEEE/ACM Transactions on Networking (TON)
A Nash game algorithm for SIR-based power control in 3G wireless CDMA networks
IEEE/ACM Transactions on Networking (TON)
QoS-based resource allocation and transceiver optimization
Communications and Information Theory
Log-convexity of the minimum total power in CDMA systems with certain quality-of-service guaranteed
IEEE Transactions on Information Theory
IEEE Journal on Selected Areas in Communications
A framework for uplink power control in cellular radio systems
IEEE Journal on Selected Areas in Communications
Perron-root minimization for interference-coupled systems with adaptive receive strategies
IEEE Transactions on Communications
A unified framework for interference modeling for multi-user wireless networks
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
A unifying approach to interference modeling for wireless networks
IEEE Transactions on Signal Processing
Pareto boundary of utility sets for multiuser wireless systems
IEEE/ACM Transactions on Networking (TON)
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In wireless networks, users are typically coupled by interference. Hence, resource allocation can strongly depend on receive strategies, such as beamforming, CDMA receivers, etc. We study the problem of minimizing the total transmission power while maintaining individual quality-of-service (QoS) values for all users. This problem can be solved by the fixed-point iteration proposed by Yates (1995) as well as by a recently proposed matrix-based iteration (Schubert and Boche, 2007). It was observed by numerical simulations that the matrix-based iteration has interesting numerical properties, and achieves the global optimum in only a few steps. However, an analytical investigation of the convergence behavior has been an open problem so far. In this paper, we show that the matrix-based iteration can be reformulated as a Newton-type iteration of a convex function, which is not guaranteed to be continuously differentiable. Such a behavior can be caused by ambiguous representations of the interference functions, depending on the choice of the receive strategy. Nevertheless, superlinear convergence can be shown by exploiting the special structure of the problem. Namely, the function is convex, locally Lipschitz continuous, and an invertible directional derivative exists for all points of interest.