Upper Bound on Operational Lifetime of Ultra Wide Band Sensor Network

Juan Xu, Yongfa Hong, Changjun Jiang, Lin Chen

Abstract: The asymptotic upper bound on operational lifetime of time hopping ultra wide band (TH-UWB) wireless sensor network is derived using percolation theory arguments. The operational lifetime is defined as the maximum number of times the task of delivering certain data to the sink node can be repeated before some node runs out of energy under an initial energy of each sensor node is given. It is shown that for such a static TH-UWB sensor network, which sensor nodes are distributed in a square \([0, \sqrt{S}] \times [0, \sqrt{S}]\) according to a Poisson point process of intensity n and each sensor node transmitting R bits data packet to the sink node, the upper bound on the operational lifetime is O ( R − 1 S − α/2 n (α− 1)/2 ) , where α is the path loss exponent. The upper bound shows the operational lifetime increases with node density n/S, thus the large-scale dense TH-UWB wireless sensor network is preferable.