In this paper we propose an energy efficient cognitive radio system. Our design considers an underlaying resource allocation combined with soft sensing information to achieve a sub-optimum energy efficient system. The sub-optimality is achieved by optimizing over a channel inversion power policy instead of considering a water-filling power policy. We consider an Energy per Goodbit (EPG) metric to express the energy efficient objective function of the system and as an evaluation metric to our system performance. Since our optimization problem is not a known convex problem, we prove its convexity to guarantee its feasibility. We evaluate the proposed scheme comparing to a benchmark system through both analytical and numerical results.