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Energy conservation of bidirectional cellular relay network over Rayleigh fading channel

In this paper, we investigate the energy minimization problem while satisfying the transmission rate requirements in a bidirectional cellular relay network, where a group of mobile users communicate with a base station (BS) across a relay node. We consider a comprehensive power consumption model which includes the power of all components in the radio frequency (RF) transmission, and adopt the Rayleigh fading channel model. We show that the energy minimization problem of the bidirectional cellular relay network can be formulated as a sum of fractional programming problem. Furthermore, we derive the sufficient condition that guarantees the problem to be convex. In the case that the energy minimizing problem is not convex, we decompose it into several sub-problems, and propose an iterative algorithm to solve it. Simulation results show that the iterative algorithm is fast and can achieve an average energy reduction of 65%, compared with the maximum power transmission policy.