## 1 Introduction  
The demand for ubiquitous wireless broadband data access and multimedia services is constantly growing in the crowded consumer radio bands while wider spectral ranges of already licensed frequency bands are barely used. To cope with this unequal spectrum access and usage, spectrum pooling is identified as one of the potential techniques that enables public access to licensed frequency bands. The key idea of spectrum pooling is to merge spectral ranges from different spectrum owners into a common pool and the cognitive or secondary users may borrow/rent spectrum from the pool. The coexistence of both the licensed users and cognitive users are realized by filling the time-frequency gaps of the primary network when they are idle. Orthogonal frequency division multiplexing (OFDM) has been identified as a feasible modulation technique due to its flexible spectral shape that can adaptively fill the idle gaps for such a co-existence scenario. However, due to the non-orthogonality of the transmit signals, both primary and secondary systems introduce mutual interference and it is crucial that the sum of the interference from all the subcarriers does not exceed acceptable limits. In this paper, our goal is to greenhouse design a cognitive radio (CR) system that optimizes energy efficiency under probabilistic interference quality of service (QoS) constraints for primary users (PUs), and throughput and power QoS constraints for secondary users (SUs). We assume that each PU has its own statistical interference limits depending on its own QoS requirements. The SU sharing the spectrum has knowledge of all these individual statistical interference limit of the PUs. OFDM has already been deployed in different broadband broadcast wireless standards, such as, Digital Video Broadcasting (DVB), Digital Audio Broadcast (DAB), _etc._ because of its many desirable features, such as high spectral efficiency, multipath delay spread tolerance, immunity to the frequency selective fading channels and power efficiency. However, in a downlink broadcasting network most of the power is consumed in the transmitter. Therefore, it is very crucial to design an energy-efficient broadcasting transmission strategy. Below we discuss some works in broadcasting situations that deals with OFDM. In [1], the authors presented an overview of peak-to-average power ratio (PAPR) reduction techniques for multiuser OFDM broadband communication systems. The mutual interference issues for OFDM-based spectrum pooling techniques between the primary and cognitive systems are studied in [2]. The authors in [3] studied an mutual interference minimization and subcarrier power allocation technique for OFDM-based CR. Different mutual interference suppression techniques are compared using laboratory test on real OFDM signals for spectrum pooling CR systems in [4]. In [5], the authors developed a dynamic subcarrier allocation algorithm for multi-user downlink communications using OFDM technique. Their algorithm attempts to allocate group of subcarriers to the user that have highest average channel gain. Conflict resolution technique is also studied to avoid the case when two or more users attempt to select the same channel partition. The authors also employed adaptive modulation techniques for each user on the allocated channel partitions. While accessing PU's spectrum, it is crucial to limit interference so that PU's operation is not hampered. Different form of interference limit has been used in the literature, such as, instantaneous hard interference limit, average interference limit, PU outage limit, or soft statistical interference limit. The authors in [6] proposed a distributed power control framework that satisfy tight QoS constraints for SUand interference level threshold constraints for PUs. In [7], cross-layer tradeoff of power, sensing time and throughput is studied under a PU interference threshold constraint. Peak and average interference power constraints for protecting PUs in cognitive radio networks is studied in [8].