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We study a wireless ad-hoc sensor network (WASN) where N sensors gather data from the surrounding environment and transmit their sensed information to M fusion centers (FCs) via multi-hop wireless communications. This node deployment problem is formulated as an optimization problem to make a trade-off between the sensing uncertainty and energy consumption of the network. Our primary goal is to find an optimal deployment of sensors and FCs that minimizes a Lagrangian combination of sensing uncertainty and energy consumption. To support arbitrary routing protocols in WASNs, the routing dependent necessary conditions for the optimal deployment are explored. Based on these necessary conditions, we propose a routing-aware Lloyd-like algorithm to optimize node deployment. Simulation results show that our proposed algorithm outperforms the existing deployment algorithms, on average. 

To provide a reliable wireless uplink for users in a given ground area, one can deploy Unmanned Aerial Vehicles (UAVs) as base stations (BSs). In another application, one can use UAVs to collect data from sensors on the ground. For a power efficient and scalable deployment of such flying BSs, directional antennas can be utilized to efficiently cover arbitrary 2-D ground areas. We consider a large-scale wireless path-loss model with a realistic angle-dependent radiation pattern for the directional antennas. Based on such a model, we determine the optimal 3-D deployment of N UAVs to minimize the average transmit-power consumption of the users in a given target area. The users are assumed to have identical transmitters with ideal omnidirectional antennas and the UAVs have identical directional antennas with given half-power beamwidth (HPBW) and symmetric radiation pattern along the vertical axis. For uniformly distributed ground users, we show that the UAVs have to share a common flight height in an optimal power-efficient deployment, by simulations. We also derive in closed-form the asymptotic optimal common flight height of N UAVs in terms of the area size, data-rate, bandwidth, HPBW, and path-loss exponent. 

We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as a quantization problem with distortion defined as the total power consumption of the network. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi diagrams as the optimal cell partition for this network, and show that each AP should be placed between its connected FC and the geometric center of its cell partition. In addition, we propose a heterogeneous two-tier Lloyd-like algorithm to optimize the node deployment. Simulation results show that our proposed algorithm outperforms the existing methods like Minimum Energy Routing, Agglomerative Clustering, and Divisive Clustering, on average.