  The energy efficiency of future networks is becoming a significant and urgent
issue, calling for greener network designs. At the same time, rapid development
of wireless networks shows a trend of increasing complexity in network
structure and resource space, leading to that optimizing the energy efficiency
of such networks requires a joint solution over multi-dimensional resource
space. However, the coupled resource dimensions and growing problem scales
bring great challenges in obtaining the optimal solutions. In this paper, we
develop a multi-dimensional network model on the basis of tuple-links
associated with transmission patterns (TPs) and formulate the optimization
problem as a TP based scheduling problem which jointly solves transmission
scheduling, routing, power control, radio and channel assignment. In order to
tackle the complexity issues raised from coupled resource dimensions, we
propose a novel algorithm that decomposes the coupling scheduling and power
control by exploiting the delay column generation technique to recursively
solve a master problem for scheduling and a sub-problem for power allocation.
Further, we theoretically prove that the performance gap between the proposed
algorithm and the optimum is upper bounded by that for the sub-problem
solution, where the latter is derived by solving a relaxed version of the
sub-problem. Numerical results demonstrate the effectiveness of the
multi-dimensional framework and the benefit of the proposed joint optimization
in improving network energy efficiency.
