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AbstractCognitive radio (CR) is a cutting-edge wireless communication technology that adopts several existing communication concepts in order to efficiently utilize the spectrum and meet the users demands of high throughput and real-time systems. Conventionally, high throughput demands are met through adopting broadband and multi-antenna technologies such as, orthogonal frequency division multiplexing (OFDM) and Multi-Input Multi-Output (MIMO). Whereas, real-time application demands are met by analyzing metrics which characterize the delay limited channels, such as, outage probability over block-fading channels. Being an environmental friendly technology, energy efficiency metrics should be considered in the design of a CR application. This thesis tackles the energy efficiency of CR system from different aspects, utilizing different measuring metrics and constrains. Under the single-input single-output (SISO) OFDM we minimized the energy per goodbit (EPG) metric subject to several power and Quality of Service (QoS) constraints. In this approach, the minimum EPG metric is optimized via proposing two optimal and sub-optimal resource allocation schemes. We consider several parameters as optimization variables, such as, power policy, sensing threshold, and channel quality threshold. We also captured the impact of involving the media access control (MAC) layers parameters, such as, frame length, in the minimization of a modified EPG metric. Also, a MAC protocol, i.e., hybrid automatic repeat request (HARQ), and the associated power consumption of the retransmission mechanism is considered in the formulation of the problem. In this context, the optimal power and frame length are derived to minimize the modified EPG while considering several spectrum-sharing scenarios, which depend on sensing information. In MIMO based CR system, we maximized capacity to power ratio (CPR) (as an energy efficiency (EE) metric) subject to several power and QoS constraints. In this context, the impact of sensing information with imperfect channel state information (CSI) of the secondary channel has been considered. To realize a CR system with real-time applications we minimized the outage probability over M block-fading channel with several long-term and short-term energy constrains. We derive the minimum outage region and the associated optimal power. Tractable expressions to lower and upper bound the outage probability are derived. We then analyze the impact of utilizing the sensing process of primary user activity.