# Joint Optimization of Scheduling and Power Control in Wireless Networks: Multi-Dimensional Modeling and Decomposition

## TL;DR

This paper presents a multi-dimensional optimization framework for wireless networks that jointly addresses scheduling, routing, power control, and resource assignment to enhance energy efficiency, overcoming complexity challenges with a novel decomposition algorithm.

## Contribution

It introduces a multi-dimensional network model and a decomposition algorithm that effectively solves joint scheduling and power control problems in complex wireless networks.

## Key findings

- The proposed algorithm effectively decomposes complex joint optimization problems.
- Numerical results show significant improvements in energy efficiency.
- Theoretical bounds demonstrate near-optimal performance of the method.

## Abstract

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.