## 1 Introduction
A recent study shows that information and communication technology (ICT) is responsible for about \(3\%\)-\(5\%\) of the worldwide total energy consumptions [25]. Data-hungry applications, such as wireless cloud computing and wireless machine-to-machine communications, are getting increasingly more attention in emerging wireless networks. The increase in telecommunications data volume is found to be approximately \(10\) times every \(5\) years, and the corresponding increase in energy consumption is \(16\%\)-\(20\%\). As a result, the research attention to energy-efficient environment-friendly wireless communications networks and architecture design are increasing worldwide among telecommunication researchers, operators and government bodies. While most of research in the last decades deals with throughput maximization, little attention is paid on energy-efficiency issues. Future generation wireless networks need to be optimized using energy-efficiency metric as an objective [26]. Energy-efficiency in its simplest form is defined as the effective throughput per unit transmitted power. Some other research works that deals with energy aware communications using green cost functions discussed above can be found in [27; 28; 29; 30; 31; 32; 33; 34]. From the discussion above it can be seen that there are two streams of studies for cognitive radio networks in the literature: some authors studied the maximization of capacity with statistical interference constraint, and some authors addressed the maximization of EE without considering statistical interference model. In this paper, we address the deficiencies in both streams by combining them. We address a generalized formulation for green cognitive radio networks. Therefore, although downlink power allocation techniques for wireless broadcast channels exist in the literature, energy-efficient green power allocation technique with statistical interference constraint is not explored yet. Also, most of spectrum access techniques in cognitive radio networks deal with either throughput maximization or power minimization in interweave manner (cognitive user transmit when the primary user is off). In this paper, we addressed EE maximization problem considering three important constraints that are not addressed before together, but for cognitive radio scenario. The main contributions of this paper are as follows:  
1. We propose an energy-efficiency maximization framework in a cognitive radio scenario, where the transmitter judiciously allocates total power over multiple subcarriers. The transmitter maintains specified statistical interference limits for the individual PUs and minimum throughput for the SUs. We formulate the resulting problem as a fractional program;
2. Since the optimal solution of the formulated fractional program may be hard to obtain due to non-concavity of the objective function, we show using Charnes-Cooper Transformation (CCT) technique that the problem is equivalent to a concave optimization problem. Suitable concave optimization solution technique can be used to obtain optimal subcarrier powers for the equivalent concave optimization problem;
3. We discuss the special structure of the solution analytically and show that the power allocation follows a water-filling type distribution for the special case when the sum rate throughput is greater than the specified threshold;4. We propose and study an iterative technique based on Dinkelbach method to obtain \(\varepsilon\)-optimal solution of the problem, where the objective function is transformed into a parametric form. A comparison of both techniques is also studied;
5. With numerical analysis, we show the performance of the green cognitive radio network with different operational parameters. We also compare the convergence of iterative method with equivalent CCT problem. The rest of the paper is organized as follows. The system model and problem formulation are presented in Section 2.