Analysis of stochastic coverage and connectivity in three-dimensional heterogeneous directional wireless sensor networks

Coverage and connectivity are important factors that determine the quality of service of three-dimensional wireless sensor networks (3D WSNs) monitoring a field of interest (FoI). Most of the literature on the analysis of coverage and connectivity in 3D WSNs assumes the use of omni-directional sensors with spherical sensing regions. In this paper, we assume that the sensors are deployed uniformly at random in a FoI. We also consider a case when the sensors have only directional sensing capability and may have heterogeneity in terms of the sensing range, communication range, and/or probability of being alive. For such 3D heterogeneous directional WSNs, we derive probabilistic expressions for kk-coverage and mm-connectivity that are useful to optimize the cost of random deployment. We validate our analysis and demonstrate its benefits with numerical results. We also illustrate the application of this work for optimal design of a 3D heterogeneous directional WSN.