Bounds on the Error in Estimating Redundancy in Randomly Deployed Wireless Sensor Networks

A challenging requirement in wireless sensor networks is the deployment of nodes in a wireless sensor network to satisfy continuous sensing with extended network lifetime while maintaining uniform coverage in the deployment region. While dense random deployments satisfy coverage and sensing requirements, constructing dense networks of sensor nodes poses economical constraints as well as the problem of redundancy. We provide an analytical framework for estimating the redundancy in a random deployment of nodes without the need of location information of nodes. We use an information theoretic approach to estimate the redundancy in a randomly deployed wireless sensor network and provide the Cramer-Rao bound on the error in estimating the redundancy in a wireless sensor network. We illustrate this redundancy estimation approach and calculate the bounds on the error in estimating the redundancy for a wireless sensor network with 1-redundancy. We also analytically show the interdependence between redundancy and network lifetime for random deployment.