On the Asymptotic Minimum Transporting Energy and Its Implication on the Wireless Network Capacity

In this paper we study the asymptotic minimum energy (which is defined as the
minimum

transporting

energy
) required to transport (via multiple hops) data packets from a source to a destination. Under the assumptions that nodes are distributed according to a Poisson point process with node density
n
in a unit-area square and the distance between a source and a destination is of constant order, we prove that the minimum transporting energy is Theta(
n

^(1-alpha)/2
) with probability approaching one as the node density goes to infinity, where alpha is the path loss exponent. We demonstrate use of the derived results to obtain the bounds of the capacity of wireless networks that operate in UWB. In particular, we prove the transport capacity of UWB-operated networks is Theta(
n

^(alpha-1)/2
) with high probability. We also carry out simulations to validate the derived results and to estimate the constant factor associated with the bounds on the minimum energy. The simulation results indicate that the constant associated with the minimum energy converges to the source-destination distance.