Lower Bounds on Lifetime of Three Dimensional UWB Sensor Networks

Considering three dimensional time hopping ultra wide band (TH-UWB) sensor networks with n sensor nodes uniformly and independently distributed in a cube of unit volume, the asymptotic lower bounds on the lifetime of non-cluster-based and cluster-based three dimensional TH-UWB sensor networks are derived irrespectively. For static three dimensional TH-UWB sensor networks, our finding is that the lower bound on the lifetime of cluster-based network is Omega((n/log n)^alpha/3) and that the lower bound on the lifetime of non-cluster-based network is Omega((n/log n)^(alpha-3)/3), thus clustering can significantly improve the lower bound on network lifetime. The results also indicate that for non-cluster-based three dimensional TH-UWB sensor network the lower bound on the lifetime in idea case is longer than that of static network by a factor of (n/log n)^2/3, thus sensor nodes or sink moving randomly in the sensor field can improve the lower bound on lifetime of network.