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In this paper, joint resource allocation and power control for energy-efficient device-to-device (D2D) communications underlaying cellular networks are investigated. The resource and power are optimized for maximization of the energy efficiency (EE) of D2D communications. Exploiting the properties of fractional programming, we transform the original nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form. Then, an efficient iterative resource allocation and power control scheme is proposed. In each iteration, part of the constraints of the EE optimization problem are removed by exploiting the penalty function approach. We further propose a novel two-layer approach, which allows finding the optimum at each iteration by decoupling the EE optimization problem of joint resource allocation and power control into two separate steps. In the first layer, the optimal …