The energy efficiency of future networks is becoming a significant and urgentissue, calling for greener network designs. At the same time, rapid developmentof wireless networks shows a trend of increasing complexity in networkstructure and resource space, leading to that optimizing the energy efficiencyof such networks requires a joint solution over multi-dimensional resourcespace. However, the coupled resource dimensions and growing problem scalesbring great challenges in obtaining the optimal solutions. In this paper, wedevelop a multi-dimensional network model on the basis of tuple-linksassociated with transmission patterns (TPs) and formulate the optimizationproblem as a TP based scheduling problem which jointly solves transmissionscheduling, routing, power control, radio and channel assignment. In order totackle the complexity issues raised from coupled resource dimensions, wepropose a novel algorithm that decomposes the coupling scheduling and powercontrol by exploiting the delay column generation technique to recursivelysolve a master problem for scheduling and a sub-problem for power allocation.Further, we theoretically prove that the performance gap between the proposedalgorithm and the optimum is upper bounded by that for the sub-problemsolution, where the latter is derived by solving a relaxed version of thesub-problem. Numerical results demonstrate the effectiveness of themulti-dimensional framework and the benefit of the proposed joint optimizationin improving network energy efficiency.
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