Coverage and Lifetime Optimization of Wireless Sensor Networks with Gaussian Distribution

A wireless sensor network (WSN) has to maintain a desirable sensing coverage and periodically report sensed data to the administrative center (i.e., base station) and the reporting period may range from months to years. Coverage and lifetime are two paramount problems in a WSN due to constraint of associated battery power. All previous theoretical analysis on the coverage and lifetime is primarily focused on the random uniform distribution of sensors or some specific network scenarios (e.g., a controllable WSN). In this paper, we provide an analytical framework for the coverage and lifetime of a WSN that follows a two-dimensional Gaussian distribution. We also study the coverage and lifetime when the dimensions of Gaussian dispersion (i.e., x, y) admit different Gaussian parameters (i.e., standard deviation, $\sigma_x \neq\sigma_y$). We identify intrinsic properties of coverage/lifetime in terms of Gaussian distribution parameters, which is a fundamental issue in designing a WSN. Following the results obtained, we further determine the sensor deployment strategies for a WSN that could satisfy a predefined coverage and lifetime. Two deployment algorithms are developed based on using our analytical models and are shown to effectively increase the WSN lifetime.