We consider the problem of estimation of the node cardinality of each node type in a heterogeneous wireless network with $T$ types of nodes deployed over a large region, where $T \ge 2$ is an integer. A mobile base station (MBS), such as that mounted on an unmanned aerial vehicle, is used in such cases since a single static base station is not sufficient to cover such a large region. The MBS moves around in the region and makes multiple stops, and at the last stop, it is able to estimate the node cardinalities for the entire region. In this paper, we propose two schemes, viz., HSRC-M1 and HSRC-M2, to rapidly estimate the number of nodes of each type. Both schemes have two phases, and they are performed at each stop. We prove that the node cardinality estimates computed using our proposed schemes are equal to, and hence as accurate as, the estimates that would have been obtained if a well-known estimation protocol designed for homogeneous networks in prior work were separately executed $T$ times. We compute closed-form expressions for the expected number of slots required by HSRC-M1 to execute and the expected energy consumption of a node under HSRC-M1. We formulate the problem of finding the optimal tour of the MBS around the region, which covers all the nodes and minimizes the travel cost of the MBS, show that it is NP-complete, and provide a greedy algorithm to solve it. Using simulations, we show that the numbers of slots required by the proposed schemes, HSRC-M1 and HSRC-M2, for computing node cardinality estimates are significantly less than the number of slots required for $T$ separate executions of the above estimation protocol for homogeneous networks.

翻译：我们考虑在一个部署了$T$种节点类型（$T \ge 2$为整数）且覆盖大规模区域的异构无线网络中，估计每种节点类型节点基数的问题。由于单个静态基站无法覆盖如此广阔的区域，在此类场景下需采用移动基站（MBS），例如安装在无人机上的基站。MBS在区域内移动并多次停靠，在最后一次停靠时能够估计整个区域的节点基数。本文提出两种方案，即HSRC-M1和HSRC-M2，用于快速估计每种类型的节点数量。两种方案均包含两个阶段，并在每次停靠时执行。我们证明，所提方案计算得到的节点基数估计值与若将先前工作中为同构网络设计的成熟估计协议独立执行$T$次所得到的估计值相等，因此具有同等精度。我们推导出HSRC-M1执行所需预期时隙数量及单个节点在HSRC-M1下预期能耗的闭式表达式。我们构建了MBS在区域内覆盖所有节点且最小化旅行成本的最优路线规划问题，证明其为NP完全问题，并提供了贪心算法求解。仿真结果表明，所提方案HSRC-M1和HSRC-M2计算节点基数估计值所需的时隙数量显著少于上述同构网络估计协议独立执行$T$次所需的时隙数量。