Cognitive radio has emerged as a promising paradigm to improve the spectrum usage efficiency and to cope with the spectrum scarcity problem through dynamically detecting and re-allocating white spaces in licensed radio band to unlicensed users. However, cognitive radio may cause extra energy consumption because it relies on new and extra technologies and algorithms. The main objective of this work is to enhance the energy efficiency of proposed cellular cognitive radio network (CRN), which is defined as bits/Joule/Hz. In this paper, a typical frame structure of a secondary user (SU) is considered, which consists of sensing and data transmission slots. We analyze and derive the expression for energy efficiency for the proposed CRN as a function of sensing and data transmission duration. The optimal frame structure for maximum bits per joule is investigated under practical network traffic environments. he impact of optimal sensing time and frame length on the achievable energy efficiency, throughput and interference are investigated and verified by simulation results compared with relevant state of art. Our analytical results are in perfect agreement with the empirical results and provide useful insights on how to select sensing length and frame length subject to network environment and required network performance.