Optimal Energy-Efficient Beamforming Designs for Cloud-RANs With Rate-Dependent Fronthaul Power

We study the downlink of a limited fronthaul capacity cloud-radio access networks (C-RANs). Three energy efficiency metrics, namely, global energy efficiency (GEE), weighted sum energy efficiency (WSEE), and energy efficiency fairness (EEF) are maximized by jointly designing transmit beamforming, remote radio head (RRH) selection, and RRH-user association. Furthermore, we incorporate a rate-dependent fronthaul power model, in which the fronthaul power consumption is proportional to the user sum rate. The formulated problems are difficult to solve. Our first contribution is to customize a branch and reduce and bound (BRB) method based on monotonic optimization to find globally optimal solutions for the three energy efficiency maximization problems. Subsequently, for a more practical approach, we propose a unified framework based on successive convex approximation (SCA) method that can be applied to all the considered problems. Our novelty lies in the equivalent transformations leading to more tractable problems that are amenable to the SCA. Specifically, appropriate continuous relaxation and convex approximation techniques are employed to arrive at a sequence of second-order cone programs (SOCPs) for which dedicated solvers are available. Then, a post-processing algorithm is devised to obtain a high-performance feasible solution from the continuous relaxation. The numerical results demonstrate that the proposed SCA-based algorithms converge rapidly and achieve near-optimal performance as well as outperform the known methods. They also highlight the importance of the rate dependent fronthaul power model in designing the energy efficient C-RANs.