On the convergence of iterative non-cooperative centralized power controllers for multiple adjacent asynchronous cellular networks

Transmit power control is used in cellular radio systems for reducing co-channel interference and increasing the capacity of system. To achieve the desired signal to interference ratio for all users in a cellular radio system, centralized power control (CPC) adjusts the transmit powers such that each user achieves the required quality of service. However, co-channel interfering signals are not only produced by users within the same network but also the users in adjacent cellular networks produce co-channel interfering signals. In this paper, the effect of interferer signals from other networks is taken into account. Each cellular radio network is assumed to have an independent central power controller that are not necessarily synchronized with each other. The convergence of the CPC algorithm to the optimum solution is proven using both analytical studies and computer simulations. Our results reveal that for static systems where the environment changes very slowly with time, non-cooperative and cooperative schemes perform similarly in the steady state and the complexity and communication overhead required for the cooperation makes the cooperative scheme unattractive. In contrast, for fast changing dynamical systems such as cognitive radios the cooperative schemeis more appreciated as the non-cooperative scheme is away from optimal during transitions.