Networks of randomly distributed nodes appear in various fields, including forestry and wireless communications, and can often be modeled, using stochastic geometry theory, as Poisson point processs (PPPs). In these contexts, estimation of nodes density is important for monitoring and optimizing the network. Originally, this problem has been addressed in forestry where the trees are the nodes and, assuming these are distributed according to an infinite two-dimensional homogeneous PPP, the spatial density can be estimated by measuring the distances from one reference tree to its neighbors. However, in many other scenarios, nodes could result invisible with some probability, for example depending on distance. In this paper, we derive the Cramér-Rao bounds and new estimators for the node spatial density, taking into account a limited capability in sensing neighbors. As an example, we provide estimators of the spatial density of transmitting devices in wireless networks with links affected by thermal noise, path loss, and shadowing.

中文翻译：

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随机分布无线网络中的密度估计


随机分布节点的网络出现在各个领域，包括林业和无线通信，并且通常可以使用随机几何理论将其建模为泊松点过程（PPP）。在这些情况下，节点密度的估计对于监控和优化网络非常重要。最初，这个问题已经在林业中得到解决，其中树木是节点，假设它们根据无限二维同质 PPP 分布，则可以通过测量从一棵参考树到其邻居的距离来估计空间密度。然而，在许多其他场景中，节点可能以某种概率导致不可见，例如取决于距离。在本文中，我们推导了 Cramér-Rao 界限和节点空间密度的新估计量，同时考虑到感知邻居的能力有限。例如，我们提供无线网络中传输设备空间密度的估计器，其链路受热噪声、路径损耗和阴影影响。