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Transmit-power control is a critical task in Cognitive Radio (CR) networks. In the present contribution, adherence to hierarchies between primary and secondary users in a peer-to-peer CR network is enabled through distributed power control. Hierarchies are effected by imposing minimum and maximum bounds on a Quality-of-Service (QoS) metric, such as communication rate. These bounds translate to Signal-to-Interference-plus-Noise Ratio (SINR) constraints. Furthermore, a utility function captures each user's satisfaction with the received SINR. The novel power control strategy-maximizes the total utility while respecting individual SINR constraints - a task recast as a convex optimization problem under a suitable relaxation.
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