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In this paper, we propose a novel reformulation of the Mixed Integer Programming (MIP) problem for solving the Cloud Radio Access Network (Cloud-RAN) power consumption minimization problem, and present an l2-box technique to reformulate the MIP problem into an exact and continuous model for recasting the binary constraints into a box with an l2 sphere constraint. A Majorization-Minimization (MM) dual ascent algorithm is proposed for solving the reformulated problem, which leads to solving a sequence of Difference of Convex (DC) subproblems handled by an inexact MM algorithm. After obtaining the final solution, we use it as the initial result of the bi-section Group Sparse Beamforming (GSBF) algorithm to promote the group-sparsity of beamformers, rather than using the weighted l1/l2-norm. Simulation results indicate that the new method outperforms the bi-section GSBF algorithm in achieving smaller network power consumption, especially in sparser cases, i.e., Cloud-RANs with a lot of Remote Radio Heads (RRHs) but fewer users.

$L_{2}$-Box Optimization for Green Cloud-RAN via Network Adaptation