Gibbs-Sampling-Based CRE Bias Optimization Algorithm for Ultradense Networks

Cell range expansion (CRE) is an effective technique in the ultradense network (UDN) to enlarge small cells' ranges and promote network utility such as system throughput, number of users lower than a rate threshold, and proportional fairness. Due to the coupled relationship of user association and scheduling in rate-related utility optimization, optimal cell-specific CRE bias is difficult to achieve. This paper first proposes a centralized CRE bias adjusting algorithm based on Gibbs sampling to achieve the optimal solution of cell-specific CRE bias based on global information. After that, a decentralized Gibbs-sampling-based CRE bias adjusting algorithm without the need for the entire knowledge of global channel gains is designed to deal with the computational complexity and message exchange overhead problem caused by scale expansion of UDN. Finally, to further reduce the increasing computational complexity, message exchange overhead, and time complexity caused by scale expansion of UDN, this paper constructs a neighbor graph based on the mutual bias influence among cells, develops a graph-coloring-based clustering algorithm to classify cells into groups, and proposes a central-aided distributed CRE bias adjusting algorithm to obtain the optimal solution to the rate-related utility optimization problem based on local information. In the central-aided distributed CRE bias adjusting algorithm, a central macrocell is used to collect the information from the small cells, and the small cells distributively determine their CRE bias based on shared central information. The optimality and complexity of the proposed algorithms are proven and analyzed. Numerical results show that, compared with existing schemes, the proposed Gibbs-sampling-based algorithms can achieve a larger utility function with less iteration time.