This paper focuses on energy-efficient coordinated multi-point (CoMP) downlink in multi-antenna multi-cell wireless communications systems. We provide an overview of transmit beamforming designs for various energy efficiency (EE) metrics including maximizing the overall network EE, sum weighted EE and fairness EE. Generally, an EE optimization problem is a nonconvex program for which finding the globally optimal solutions requires high computational effort. Consequently, several low-complexity suboptimal approaches have been proposed. Here we sum up the main concepts of the recently proposed algorithms based on the state-of-the-art successive convex approximation (SCA) framework. Moreover, we discuss the application to the newly posted EE problems including new EE metrics and power consumption models. Furthermore, distributed implementation developed based on alternating direction method of multipliers (ADMM) for the provided solutions is also discussed. For the sake of completeness, we provide numerical comparison of the SCA based approaches and the conventional solutions developed based on parametric transformations (PTs). We also demonstrate the differences and roles of different EE objectives and power consumption models.
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