Coverage Probability and Average Rate Analysis of Hybrid Cellular and Cell-Free Network

Collaborative access points (APs) enabled cell-free networks can provide stable and uniform communication services for all user locations, making them a promising network architecture for the sixth-generation (6G) mobile communication systems. While the performance of pure cell-free networks has been extensively studied, it remains unclear whether deploying large-scale cell-free APs in legacy cellular networks can effectively boost communication performance. Besides, the realization of a cell-free network is considered to be a gradual long-term evolutionary process in which APs will be incrementally introduced and form a hybrid communication network with the existing cellular base stations (BSs). Such a collaboration will bridge the gap between the established cellular network and the innovative cell-free network. Therefore, hybrid cellular and cell-free networks (HCCNs) emerge as a feasible solution for advancing cell-free network development, and it is worthwhile to further explore its performance limits. Different from heterogeneous networks or multipoint coordinated networks, the characterization of HCCNs needs to take both inter- and intra-layer collaboration into account. This paper presents a stochastic geometry-based HCCN model to analyze the distributions of signal and interference and reveal their mutual coupling. Specifically, in order to benefit the user equipments (UEs) from both the cellular BSs and the cell-free APs, a conjugate beamforming design is employed, and the aggregated signal is analyzed using moment matching. Then, the coverage probability of the hybrid network is characterized by deriving the Laplace transforms and their higher-order derivatives of interference components. Furthermore, the average achievable rate of the hybrid network over channel fading is derived based on the interference coupling analysis. Simulation results demonstrate that compared to traditional cellular networks, HCCN effectively narrows communication quality differences between different UEs and improves overall communication performance.