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This paper aims at solving two classes of energy efficiency (EE) maximization problems in multiple channels wireless communication systems. First, the EE maximization problem with sum power constraint is solved based on the geometric water-filling approach; and second, the approach is extended into the EE maximization problem with additional least throughput requirement constraint. Our proposed algorithms make use of the water-filling structure of the optimal solution and provide exact and computation efficient solution to the energy-efficient power allocation problems. The proposed algorithms also have excellent scalability, which is applicable for large-scale wireless communication systems. Optimality of the proposed algorithms is strictly proved, and the proposed algorithms only require low-degree polynomial computational complexity. Numerical results are presented to demonstrate the efficiency of the proposed algorithms. To the best of our knowledge, no prior algorithms in the existing literature could provide such solutions to the EE maximization problems under the merit of exactness and the efficiency. [ABSTRACT FROM AUTHOR]