Lower Bounds on Lifetime of Clustering Extended Ultra Wide Band Sensor Network

A fundamental challenge for wireless sensor networks lies in energy constraint, hence the network lifetime becomes a critical concern in the design of wireless sensor networks under energy constraint. Considering time hopping impulse radio ultra wide band(TH-IR UWB) sensor networks with n sensor nodes randomly located on a disk of area S\-n=λn and a base station, the asymptotic lower bounds on the lifetime of complete clustering and ordinary clustering extended TH-IR UWB sensor networks are derived respectively. The results indicate that the lower bound on the lifetime of complete clustering static extended network is λn/(log(λn))\+2 times longer than that of ordinary clustering static network, and that the lower bound on the lifetime of complete clustering extended network in the ideal case is (λn)=\+{1/2}/(log(λn))\+{3/2} times longer than that of ordinary clustering network in the ideal case, and thus complete clustering can significantly improve the network lifetime. The results also reveal that for ordinary clustering extended TH-IR UWB sensor network the lower bound on the lifetime in the ideal case is longer than that of static network by a factor of(λn/log(λn))\+{1/2}, therefore, sensor nodes or base station moving randomly in the deployment area can improve the lifetime of ordinary clustering sensor network. The formulas for lower bounds also reveal that the network lifetime is in inverse proportion to the node number n or the size of deployment area, and thus the large-scale extended TH-IR UWB sensor network is not practical.