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In this paper, we formulate and solve two Energy Efficiency (EE) problems, namely the Power Minimization Problem (PMP) and the Maximization of Energy Efficiency Problem (MEEP), for a wireless system using power and frequency resource allocation considering Quality of Service (QoS) requirements and multiple services. Despite those problems are nonlinear, they can be converted into Integer Linear Problems (ILPs). Therefore, the optimal solution for both PMP and MEEP can be obtained by well-known methods. Additionally, we propose two fast suboptimal algorithms as to avoid the high computational complexity of obtaining optimal solution for MEEP. Our results show that the MEEP has a better trade-off between transmitted data rate and power saving than the PMP solution. Moreover, the suboptimal algorithms present good performance compared to the optimal solution for moderated loads but with a much lower computational complexity, thus achieving a remarkable trade-off between performance and computational complexity.
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