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In this paper, a lower bound on the capacity of wireless ad hoc erasurenetworks is derived in closed form in the canonical case where $n$ nodes areuniformly and independently distributed in the unit area square. The boundholds almost surely and is asymptotically tight. We assume all nodes have fixedtransmit power and hence two nodes should be within a specified distance $r_n$of each other to overcome noise. In this context, interference determinesoutages, so we model each transmitter-receiver pair as an erasure channel witha broadcast constraint, i.e. each node can transmit only one signal across allits outgoing links. A lower bound of $\Theta(n r_n)$ for the capacity of thisclass of networks is derived. If the broadcast constraint is relaxed and eachnode can send distinct signals on distinct outgoing links, we show that thegain is a function of $r_n$ and the link erasure probabilities, and is at mosta constant if the link erasure probabilities grow sufficiently large with $n$.Finally, the case where the erasure probabilities are themselves randomvariables, for example due to randomness in geometry or channels, is analyzed.We prove somewhat surprisingly that in this setting, variability in erasureprobabilities increases network capacity.

A Lower Bound on the Capacity of Wireless Erasure Networks with Random Node Locations