Convergence theorem for a general class of power control algorithms

We consider the convergence issues of distributed power control algorithms for mobile cellular systems. A convergence theorem for power control algorithms of canonical type is proven. Our result generalizes Yates´ (1995) framework and provides a new outlook on the problem. The general applicability of the theorem is demonstrated by showing that all the well-known algorithms are canonical. Furthermore, by devising a new discrete algorithm, we exemplify how the theorem can be used to aid new design