Capacity Regions for General Ad Hoc Networks

In this paper, a new general ad hoc wireless network model where each node may transmit and receive simultaneously in the difference frequency band is proposed, which is different from the Toumpis-Goldsmith´s ad hoc network model where nodes cannot transmit and receive at the same time. Based on this new model, a new expansion expression of the capacity region for the ad hoc wireless networks with arbitrary number of nodes and arbitrary topology are derived. It is shown that any point in the convex hull of basic matrices associated with an ad hoc wireless network with nodes can be represented as the convex combination of n²+1 elements of basic matrices. In general, the capacity of the general ad hoc wireless network is higher than that of the Toumpis-Goldsmith´s ad hoc wireless network.