Optimal Decomposition for Large-Scale Infrastructure-Based Wireless Networks

The fundamental idea of network decomposition is to break a large-scale network into smaller parts such that the subnetworks can operate in parallel, each with a much lower dimensionality. For large-scale wireless networks, the cellular structure is based on the idea of network decomposition, where the network is decomposed into multiple subnetworks, i.e., cells, according to the coverage of each base-station (BS). Such a decomposition scheme, nevertheless, leads to strong interference among subnetworks, which becomes increasingly significant as the density of BSs grows. For the next-generation cellular network, where a massive amount of BSs need to be deployed to meet the ever-increasing demand of high data rate, it is of paramount importance to develop efficient network decomposition schemes to replace the current cellular structure. How to build such a decomposition framework, unfortunately, has remained largely unknown. This paper aims to establish a network decomposition theory for large-scale wireless networks from a graph-theoretic point of view. Specifically, we start from a novel bipartite graph representation of an infrastructure-based wireless network and show that in general the optimal network decomposition can be formulated as a graph partitioning problem. For demonstration, we focus on maximizing the number of subgraphs for a given cut ratio constraint and propose a binary search based spectral relaxation (BSSR) algorithm to solve it in two loops. The performance of the proposed BSSR algorithm is further examined and compared with the current cellular structure and BS clustering in various scenarios. Significant gains are shown to be achieved by the proposed BSSR algorithm, which corroborates that the optimal network decomposition of next-generation cellular networks should be performed based on a bipartite graph, where the geographical information of BSs and users are both included.