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Energy consumption for mobile and wireless communication device, such as cell phones, has long been an important aspect for both designers and customers. This paper shows how a cognitive radio (CR) framework can help to reduce system energy consumption of a mobile and wireless communication device based on the application quality of service requirement, the channel condition, and the radio capabilities and characteristics. The CR framework enables not only adaptation of modulation, coding rate, coding gain, and radiated power as conventional adaptive modulation (AM) scheme, but also joint adjustment of radio component characteristics (e.g., power amplifier (PA) characteristics) to achieve high energy efficiency. A unified PA efficiency model characterizing theoretical Class A, Class B, and practical PAs is adopted and enables the analysis of the impact of different radio configurations and channel conditions on energy efficiency. Significant energy savings (up to 90%) using the proposed CR framework for systems with theoretical PAs and with a realistic PA can be achieved compared with the conventional AM approach in simulation. This framework can also be used to manage other radio resources.