Energy efficiency has currently become one of the central issues in today's wireless communication industry. In this paper, we focus on the optimal energy efficiency in a multiuser cellular system and investigate its achievable upper bound from the perspective of radio resource available. Particularly, an optimization problem is formulated concerning radio resource scheduling, and an analytical optimal solution is obtained via mathematical analysis. Furthermore, an energy-efficient radio resource scheduling (EE-RRS) algorithm is proposed for numerical applications. Simulation results show that our proposed EE-RRS algorithm can realize significant improvements on energy efficiency with the optimal solution, and there is always a tradeoff between energy efficiency and transmission capacity.