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In this paper, the authors propose a power control algorithm incorporating distributed beam-forming via multi-relay structure with underlay cognitive radio architecture. This problem is modeled as a non-cooperative game and a novel distributed algorithm is designed to achieve Nash Equilibrium (NE). At each iteration, power and beam forming weights are determined while Quality of Service (QoS) of primary and secondary users are guaranteed in terms of interference threshold and Signal to Interference and Noise Ratio (SINR) threshold levels, respectively. Convergence of the proposed algorithm to a unique and suboptimal fixed point for any given initial resource allocation has been proved.
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