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This paper studies transmission power control algorithms for cellular networks. One of the challenges in commonly used iterative mechanisms to achieve this is to identify if the iteration will converge since convergence indicates feasibility of transmit power allocation under prevailing network conditions. The convergence criterion should also be simple to calculate given the time constraints in a real-time wireless network. Towards this goal, this paper derives simple sufficient conditions for convergence of an iterative power control algorithm using existing bounds from matrix theory. With the help of suitable numerical examples, it is shown that the allocated transmit powers of the nodes converge when sufficient conditions are satisfied, and diverge when they are not satisfied. This forms the basis for an efficient link data-rate based admission control mechanism for wireless networks. The mechanism considers parameters such as signal strength requirement, link datarate requirement, and number of nodes in the system. Simulation based analysis shows that existing links are able to maintain their desired datarates despite the addition of new wireless links.
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