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Mathematical Model and Algorithm of Fair Power and Rate Control in Wireless Ad Hoc Networks Based on Deflected Sub-gradient Method
Meiqin Tang, Shaoyan Sun, Tingzhi Cheng and Yalin Xin

Wireless ad hoc networks have a broad application prospect in providing connections for a large number of devices in the next generation network, which transmits data through complex data transmission channels. This paper proposes a new fair power and rate control algorithm based on the network utility maximization mathematical model for wireless ad hoc networks, which guarantees the fairness through the weight of the system. These weights allow system operators to place different levels of quality of service (QoS) or importance for each user, which enables the system to avoid selfish optima. In fact, the objective function is always nonconvex. In this paper, some progress has been made in solving this problem by a deflected sub-gradient method. The convergence analysis of the algorithm is also given. Simulation results show that the algorithm has better convergence than other algorithms and can ensure the fairness of the system.

Keywords: wireless ad hoc networks, network utility maximization, fairness, power and rate control, deflected sub-gradient method