Ultra-Dense Networks (UDNs) have been proposed to meet the ultra-high system capacity and ultra-high user experience rate requirements of sixth generation (6G) mobile networks. However, ultra-dense base stations (BSs) deployment poses challenges for cell-edge users such as BS selection, severe interference, resource allocation, and inter-cell handover. To tackle these obstacles, this paper formulates a joint BS clustering and resource allocation problem for cell-edge users in a 6G heterogeneous UDN system. For efficient resolution, this problem is decoupled into two sub-problems to be solved independently. We first propose a user-centric BS clustering algorithm based on many-to-many matching for the BS clustering problem in the heterogeneous UDN system; This algorithm considers the constraint of the system capacity. A many-to-many stable matching between users and small cell BSs is constructed under the optimization objective of maximizing the achievable user rate. Furthermore, we analyze the effectiveness, stability, convergence, and complexity of the BS clustering algorithm. Given established small cell BS clusters, we also propose a user-centric resource allocation algorithm based on network partitioning. This algorithm accounts for the interference of all users in the heterogeneous UDN system and maximizes intra-sub-network interference while minimizing inter-sub-network interference via a spectral clustering-based sub-network partitioning algorithm. Next, orthogonal allocation of resource blocks (RBs) is implemented within each sub-network, and RBs are spatially multiplexed between sub-networks. Numerical results confirm the benefits of the proposed methods: our algorithms outperform benchmark solutions in terms of the sum achievable system rate, average achievable user rate, and user spectral efficiency.
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