Convergence behavior of matrix-based iterative transceiver optimization

We analyze and compare two iterative algorithms for the joint optimization of powers and receive strategies in a multiuser network. The design goal is to minimize the total power while fulfilling individual QoS requirements. This problem can be solved by the fixed-point iteration proposed by Yates [1] as well as by a recently proposed matrix-based iteration [2, 3]. It was observed in the literature that the matrix-based iteration has an excellent convergence speed. 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 performs better than the fixed-point iteration in each step, given the same initialization. The resulting sequence of power vectors is component-wise monotonic decreasing. We also show that the matrix-based iteration has super-linear convergence. If the underlying interference functions are smooth, then the algorithm even has quadratic convergence, whereas the convergence of the fixed-point iteration is only linear, and depends on the system load. This explains the convergence behavior observed from simulations.