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The authors consider a cognitive radio system with N Secondary User (SU) pairs and a pair of Primary Users (PU). The SU power allocation problem is formulated as a rate maximization problem under PU and SU quality of service and SU peak power constraints. They show their problem formulation is a geometric program and can be solved with convex optimization techniques. They examine the effect of PU transmissions in their formulations. Solutions for both low and high Signal-to-Interference-and-Noise Ratio (SINR) scenarios are provided. They show that including the PU rate in the optimization problem leads to increased PU performance while not significantly degrading SU rate.
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