We present a power allocation framework for spectrum sharing Cognitive Radio (CR) systems based on maximizing the energy efficiency (EE). First, we show that the relation between the EE and the spectral efficiency (SE) is strictly increasing in contrast with the SE-EE trade-off discussed in the literature. We also solve a non-convex problem and explicitly derive the optimal power for the proposed average EE under either a peak or an average power constraint. We apply our results to the underlay CR systems where the power is limited by an additional interference constraint. When the instantaneous channel is not available, we provide a necessary and sufficient condition for the optimal power and present a simple sub-optimal power. In the numerical results, we show that the proposed EE corresponds to a higher SE at mid-range and high power regime compared to the classical EE. We also show that the sup-optimal solution is very close to the optimal solution. In addition, we deduce that the absence of instantaneous CSI affects the EE and the SE at high power regime compared to full CSI. In the CR context, we show that the interference threshold has a minimal effect on the EE compared to the SE.
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