The objective of this study is to analyze the statistics of the data rate and of the incident power density (IPD) in user-centric cell-free networks (UCCFNs). To this purpose, our analysis proposes a number of performance metrics derived using stochastic geometry (SG). On the one hand, the first moments and the marginal distribution of the IPD are calculated. On the other hand, bounds on the joint distributions of rate and IPD are provided for two scenarios: when it is relevant to obtain IPD values above a given threshold (for energy harvesting purposes), and when these values should instead remain below the threshold (for public health reasons). In addition to deriving these metrics, this work incorporates features related to UCCFNs which are new in SG models: a power allocation based on collective channel statistics, as well as the presence of potential overlaps between adjacent clusters. Our numerical results illustrate the achievable trade-offs between the rate and IPD performance. For the considered system, these results also highlight the existence of an optimal node density maximizing the joint distributions. (This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.)

翻译：本研究旨在分析以用户为中心的无小区网络（UCCFNs）中数据速率和入射功率密度（IPD）的统计特性。为此，分析提出了基于随机几何（SG）推导的若干性能指标。一方面，计算了IPD的一阶矩和边缘分布；另一方面，给出了两种场景下速率与IPD联合分布的边界：当需要获取高于给定阈值的IPD值（用于能量收集）时，以及当这些值应保持在阈值以下（出于公共健康原因）时。除推导这些指标外，本研究还引入了UCCFNs在SG模型中的新特征：基于集体信道统计的功率分配，以及相邻簇之间潜在重叠的存在。数值结果展示了速率与IPD性能之间可实现的权衡。对于所考虑的系统，这些结果还揭示了存在一个可最大化联合分布的最优节点密度。（本文已提交至IEEE期刊审稿，可能未经通知即转让版权，此后该版本可能不再公开。）