Modified MCP-Based Modeling and Performance Analysis of 3-D Cellular Networks

In this paper, we introduce a new stochastic geometry model, the ’Modified Matérn Cluster Process (MMCP),’ to provide an accurate representation of cell locations in a network. This model not only incorporates realistic constraints but also takes into account the clustered distribution of user equipment (UE). Specifically, UEs are assumed to cluster around small-cell base stations (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SCBs</i>), which adhere to a minimum separation distance and are organized according to a Matérn Hard-Core Process (MHCP) II, ensuring efficient spatial distribution and reduced interference. To further enhance network performance, we propose a novel transmission scheme specifically designed to mitigate interference. This innovative approach results in the development of a tractable analytical framework, which includes a detailed assessment of the non-interference probability, thereby optimizing resource allocation strategies across the network. Within this framework, we derive expressions for the successful transmission probabilities for both uplink and downlink communications. Additionally, we explore the average ergodic capacity, a crucial metric for evaluating the overall efficacy of the three-dimensional (3-D) MMCP. These derivations enable a deeper understanding of the model’s impact on network performance. To validate our theoretical findings, we conduct extensive Monte Carlo simulations, which demonstrate the accuracy of our proposed model. Our results highlight the critical importance of accounting for user distribution when evaluating dynamic system performance.