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 (WSNs) 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 fusion center, 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 fusion center, 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.