CR-based technology aims to combat scarcity in the radio spectrum using Dynamic Spectrum Access (DSA). It improves the performance of spectrum efficiency by allowing secondary users to share the spectrum owned by primary users. In this paper, different techniques have been analyzed to improve the energy efficiency. Gradient based iteration algorithm is used to obtain the Stackelberg equilibrium solution. Water filling factors aided search method deals with the energy efficient optimization problem with multiple interference power constraint. Efficient barrier method is used to provide optimal solution with reasonable complexity. Extreme-value theory characterizes the impact of the multi-user diversity gain of both kinds of users.