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In this paper, the joint power and subcarrier allocation problem is solved in the context of maximizing the energy-efficiency (EE) of a multi-user, multi-relay orthogonal frequency division multiple access (OFDMA) cellular network, where the objective function is formulated as the ratio of the spectral-efficiency (SE) over the total power dissipation. It is proven that the fractional programming problem considered is quasi-concave so that Dinkelbach's method may be employed for finding the optimal solution at a low complexity. This method solves the above-mentioned master problem by solving a series of parameterized concave secondary problems. These secondary problems are solved using a dual decomposition approach, where each secondary problem is further decomposed into a number of similar subproblems. The impact of various system parameters on the attainable EE and SE of the system employing both EE maximization (EEM) and SE maximization (SEM) algorithms is characterized. In particular, it is observed that increasing the number of relays for a range of cell sizes, although marginally increases the attainable SE, reduces the EE significantly. It is noted that the highest SE and EE are achieved, when the relays are placed closer to the BS to take advantage of the resultant line-of-sight link. Furthermore, increasing both the number of available subcarriers and the number of active user equipment (UE) increases both the EE and the total SE of the system as a benefit of the increased frequency and multi-user diversity, respectively. Finally, it is demonstrated that as expected, increasing the available power tends to improve the SE, when using the SEM algorithm. By contrast, given a sufficiently high available power, the EEM algorithm attains the maximum achievable EE and a suboptimal SE.

Achieving Maximum Energy-Efficiency in Multi-Relay OFDMA Cellular Networks: A Fractional Programming Approach