Asymptotic Signal Bandwidth of Impulse Radio UWB Communication Networks

The asymptotic signal bandwidth of various kinds of large-scale asynchronous Time Hopping Impulse Radio Ultra-Wide Band (TH-IR UWB) communication networks such that multiple access interference can be negligible with respect to output noise with high probability is derived. The asynchronous TH-IR UWB communication networks consist of n nodes distributed in a cube (three-dimension) or on a square (two-dimension) according to a Poisson point process. The theoretic results indicate that the obtained asymptotic bandwidth of IR-UWB signal is in proportion to the number of nodes, and that the asymptotic bandwidth of IR-UWB signal of dense network is much more than that of extended network. The results also reveal that the asymptotic bandwidth of three-dimensional network is less than that of two-dimensional network assuming that the number of nodes in the networks and the distance loss exponent are the same. As the bandwidth of IR-UWB signal satisfies the obtained theoretic bandwidth, the expression of probability of error of multi-node network is simplified to that of single node network.