Abstract: The fifth generation (5G) networks have been envisioned to support the explosive growth of data demand caused by the increasing traditional high-rate mobile users and the expected rise of interconnections between human and things. To accommodate the ever-growing data traffic with scarce spectrum resources, cognitive radio (CR) is considered a promising technology to improve spectrum utilization. We study the power control problem for secondary users in an underlay CR network. Unlike most existing studies which simplify the problem by considering only a single primary user or channel, we investigate a more realistic scenario where multiple primary users share multiple channels with secondary users. We formulate the power control problem as a non-cooperative game with coupled constraints, where the Pareto optimality and achievable total throughput can be obtained by a Nash equilibrium (NE) solution. To achieve NE of the game, we first propose a projected gradient based dynamic model whose equilibrium points are equivalent to the NE of the original game, and then derive a centralized algorithm to solve the problem. Simulation results show that the convergence and effectiveness of our proposed solution, emphasizing the proposed algorithm, are competitive. Moreover, we demonstrate the robustness of our proposed solution as the network size increases.

Key words: Cognitive radio networks, Multi-user power control, Non-cooperative game, Nash equilibrium, Projected gradient

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