A Source Coding Perspective on Node Deployment in Two-Tier Networks

Multi-tier networks have many applications in different fields. We define a novel two-tier quantizer that can be applied to different node deployment problems including the energy conservation in two-tier wireless sensor networks consisting of N access points (APs) and M fusion centers (FCs). We aim at finding an optimal deployment of APs and FCs to minimize the average weighted total, or Lagrangian, of sensor and AP powers. For one FC, M = 1, we show that the optimal deployment of APs is simply a linear transformation of the optimal N-level quantizer for density f, and the sole FC should be located at the geometric centroid of the sensing field. We also provide the exact expression of the AP-Sensor power function and prove its convexity. For more than one FC, M > 1, we provide a necessary condition for the optimal deployment. Furthermore, to numerically optimize the AP and FC deployment, we propose three Lloyd-like algorithms and analyze their convergence. Simulation results show that our algorithms outperform the existing algorithms.