Iterative Power Control and Resource Allocation for General Interference Functions - A Superlinearly Convergent Algorithm

We consider a multiuser wireless network, where users are coupled by interference. Thus, transmission powers should be optimized jointly with the receive strategy, like beamforming, CDMA, base station assignment, etc. We study the problem of minimizing the total transmission power while maintaining individual QoS values for all users. This problem can be solved by the fixed-point iteration proposed by R. D. Yates (1995) as well as by a recently proposed matrix-based iteration by the authors (2006). 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 continuously differentiable. This property is caused by ambiguous receive strategies, resulting in ambiguous representations of the interference functions. By exploiting the special structure of the problem, we show that the iteration has super-linear convergence