Given the growing concern over energy consumption and associated global warming, green communication is becoming more and more important. Lots of efforts have been put into investigating energy efficiency based design in wireless systems. Unfortunately, the maximum energy efficiency of a point-to-point link is normally achieved when the transmit power approaches zero, which, however, is not desirable in practical systems due to the low achievable data rate. In this paper, we consider the energy efficiency optimization with a practical power consumption model, where, besides a maximum transmit power constraint, we set a rate constraint (r 0) to guarantee an average throughput requirement (R th). Due to the possible outage in transmission, r 0 is in general different from R th, and determining r 0 for a given R th is not trivial. We shall derive a closed-form solution for the optimal transmit power that maximizes energy efficiency. We will also demonstrate that a carefully selected rate constraint r 0 can guarantee the required average throughput R th and provide the freedom to achieve different tradeoffs between energy efficiency and average throughput.