A wireless cellular network with energy efficient is the important subject for research in recent years. Cognitive radio can play an important role in improving energy efficiency in wireless networks, because from the green perspective, spectrum is a scare natural resource which should not be wasted but be shared. In this paper we study energy efficiency aspect of imperfect spectrum sensing and power allocation in cognitive radio network. The optimization model is established in which the focus is on maximization of energy efficiency with different power level in transmission link and interference link in considered of error in sensing i.e. imperfect sensing. The problem has been studied out of average transmission power level of cognitive radio and optimum value of energy efficiency has been carried out. By search method of optimization plenty of numerical result is produced. Through numerical result the impact of sensing performance and transmit and interference power constraint on the energy efficiency is shown. Calculation shows that for every value of average transmitting power the energy efficiency will be optimum.

Keywords : Cognitive Radio Network, Energy Efficiency (EE), Imperfect Spectrum Sensing.