We analyze the coverage probability of multi-user uplink cellular networkswith fractional power control. We use a stochastic geometry approach where themobile users are distributed as a Poisson Point Process (PPP), whereas theserving base station (BS) is placed at the origin. Using conditional thinning,we are able to calculate the coverage probability of $k$ users which areallocated a set of orthogonal resources in the cell of interest, obtaininganalytical expressions for this probability considering their respectivedistances to the serving BS. These expressions give useful insights on theinterplay between the power control policy, the interference level and thedegree of fairness among different users in the system.
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机译：我们用分数功率控制分析了多用户上行蜂窝网络的覆盖概率。我们使用随机几何方法，其中移动用户以泊松点过程（PPP）进行分布，而服务基站（BS）则位于原点。使用条件稀疏，我们能够计算在感兴趣的小区中分配了一组正交资源的$ k $个用户的覆盖概率，并考虑到用户到服务BS的各自距离，获得该概率的解析表达式。这些表达式为系统中不同用户之间的功率控制策略，干扰级别和公平程度之间的相互作用提供了有用的见解。
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