Decomposition Methods for Cross-Layer Optimization in Wireless Networks

Cross-layer optimization (physical, data link and network layers) in wireless networks has been limited by its combinatorial complexity (Toumpis and Goldsmith, 2003). Existing literature has traditionally been able to provide numerical analysis only for networks with less than 8 nodes (Madan et al., 2005), limiting our ability to understand the benefits of cross-layer optimization for more realistic-sized networks. In Barreto (2004) and Johansson and Xiao (2006) the authors showed that column generation could be used to reduce the complexity of the problem, with Johansson and Xiao (2006) providing in-depth analysis for 10-node networks and limited results for 20-node networks - all with minimum SNR and transmission rate restrictions. In this paper we show how decomposition methods can be used for the joint optimization of the physical (rate and power control), data link (MAC/scheduling), and networking (routing) layers, increasing the size of networks that can be analyzed. We present exact numerical solutions for ad-hoc networks with up to 30 nodes and mesh networks with up to 40 nodes, a significant scalability improvement. We continue by showing how bounded solutions for larger networks can be obtained with decreased computational complexity and present to heuristic implementations that increase the analysis to arbitrary-sized networks (Barreto and Chiu, 2006). We show how decomposition methods effectively decouple routing from the MAC/physical layers and allow us to solve the problems independently while reaching a global optimal solution.