In this paper, we consider the network power minimization problem in a downlink cloud radio access network (C-RAN), taking into account the power consumed at the baseband unit (BBU) for computation and the power consumed at the remote radio heads and fronthaul links for transmission. The power minimization problem for transmission is a fast time-scale issue whereas the power minimization problem for computation is a slow time-scale issue. Therefore, the joint network power minimization problem is a mixed time-scale problem. To tackle the time-scale challenge, we introduce large system analysis to turn the original fast time-scale problem into a slow time-scale one that only depends on the statistical channel information. In addition, we propose a bound improving branch-and-bound algorithm and a combinational algorithm to find the optimal and suboptimal solutions to the power minimization problem for computation, respectively, and propose an iterative coordinate descent algorithm to find the solutions to the power minimization problem for transmission. Finally, a distributed algorithm based on hierarchical decomposition is proposed to solve the joint network power minimization problem. In summary, this work provides a framework to investigate how execution efficiency and computing capability at BBU as well as delay constraint of tasks can affect the network power minimization problem in C-RANs.
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