Energy Efficiency in Two-Tiered Wireless Sensor Networks

We study a two-tiered wireless sensor network (WSN) consisting of $N$ access points (APs) and $M$ base stations (BSs). The sensing data, which is distributed on the sensing field according to a density function $f$, is first transmitted to the APs and then forwarded to the BSs. Our goal is to find an optimal deployment of APs and BSs to minimize the average weighted total, or Lagrangian, of sensor and AP powers. For $M=1$, 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 BS should be located at the geometric centroid of the sensing field. Also, for a one-dimensional network and uniform $f$, we determine the optimal deployment of APs and BSs for any $N$ and $M$. Moreover, to numerically optimize node deployment for general scenarios, we propose one- and two-tiered Lloyd algorithms and analyze their convergence properties. Simulation results show that, when compared to random deployment, our algorithms can save up to 79\% of the power on average.Comment: 11 pages, 7 figure

Optimal Deployments of UAVs With Directional Antennas for a Power-Efficient Coverage

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. 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

Quantizers with Parameterized Distortion Measures

In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are additively and multiplicatively weighted for each reproduction point resulting in a heterogeneous quantization problem, as used for example in deployment problems of sensor networks. Whereas, normally in such problems, the average distortion is minimized for given weights (parameters), we will optimize the quantization problem over all weights, i.e., we tune or control the distortion functions in our favor. For a uniform source distribution in one-dimension, we derive the unique minimizer, given as the uniform scalar quantizer with an optimal common weight. By numerical simulations, we demonstrate that this result extends to two-dimensions where asymptotically the parameter optimized quantizer is the hexagonal lattice with common weights. As an application, we will determine the optimal deployment of unmanned aerial vehicles (UAVs) to provide a wireless communication to ground terminals under a minimal communication power cost. Here, the optimal weights relate to the optimal flight heights of the UAVs.Comment: submitted to DCC 201