论文标题
关于$ k $ tier hetnets具有广义关联规则
On Exact Distribution of Poisson-Voronoi Area in $K$-tier HetNets with Generalized Association Rule
论文作者
论文摘要
这封信表征了$ k $ tier泊松网络中典型的Voronoi区域的确切分布功能。用户遵守广义协会（GA）规则，该规则是最接近的基站关联的超集，并且基于收到的功率关联（具有任意褪色）规则，这些规则是文献中通常采用的。将Robbins的定理与泊松点过程的概率生成功能相结合，我们获得了典型的$ k $ -th tier voronoi区域的确切矩，$ k \ in \ in \ {1，...，k \} $在GA规则下。我们在几种特殊情况下应用了此结果。例如，我们证明，在具有GA规则的多层网络中，$ k $ -th tier voronoi区域的平均值可以按封闭形式表达。我们还为平均和瞬时收到的基于功率的用户协会的高阶矩获得了简化的表达式。在具有指数褪色的单层网络中，后来的关联规则提供了典型Voronoi区域的二阶时刻的封闭形式表达。我们通过数值评估此精确表达，并将其与近似结果进行比较。
This letter characterizes the exact distribution function of a typical Voronoi area in a $K$-tier Poisson network. The users obey a generalized association (GA) rule, which is a superset of nearest base station association and maximum received power based association (with arbitrary fading) rules that are commonly adopted in the literature. Combining the Robbins' theorem and the probability generating functional of a Poisson point process, we obtain the exact moments of a typical $k$-th tier Voronoi area, $k \in \{1,...,K\}$ under the GA rule. We apply this result in several special cases. For example, we prove that in multi-tier networks with the GA rule, the mean of $k$-th tier Voronoi area can exactly be expressed in a closed-form. We also obtain simplified expressions of its higher-order moments for both average and instantaneous received power based user association. In single-tier networks with exponential fading, the later association rule provides closed-form expression of the second-order moment of a typical Voronoi area. We numerically evaluate this exact expression and compare it with an approximated result.
