On the Distribution of Subnetwork Size with Virtual-Cell-Based Optimal Decomposition for Next-Generation Wireless Networks

For large-scale wireless networks, the optimal network decomposition has been proposed from a graph theoretical perspective to maximize the number of decomposed subnetworks with an interference constraint. When each user is associated with multiple base-stations (BSs) to form its virtual cell, however, the optimal network decomposition may lead to highly unbalanced subnetwork sizes if the key system parameters are not properly set. In this paper, an analytical framework is proposed to characterize the distribution of subnetwork size in terms of the number of users in a randomly chosen subnetwork for virtual-cell-based optimal decomposition. The analysis reveals that the distribution of subnetwork size is crucially determined by the virtual cell size, i.e., the number of BSs associated with each user, and the ratio of the number of users to the number of BSs, both of which should be carefully tuned to produce balanced subnetworks. © 2025 IEEE.