| Summary: | A network of n transmitters and n receivers is considered. We assume that transmitter
i aims to send data to its designated destination, receiver i. Communications occur in
a single-hop fashion and destination nodes are simple linear receivers without multi-user
detection. Therefore, in each time slot every source node can only talk to one other
destination node. Thus, there is a total of n communication links. An important question
now arises. How many links can be active in such a network so that each of them supports
a minimum rate Rmin? This dissertation is devoted to this problem and tries to solve it
in two di erent settings, dense and extended networks. In both settings our approach is
asymptotic, meaning, we only examine the behaviour of the network when the number
of nodes tends to in nity. We are also interested in the events that occur asymptotically
almost surely (a.a.s.), i.e., events that have probabilities approaching one as the size of
the networks gets large. In the rst part of the thesis, we consider a dense network where
fading is the dominant factor a ecting the quality of transmissions. Rayliegh channels are
used to model the impact of fading. It is shown that a.a.s. log(n)^2 links can simultaneously
maintain Rmin and thus be active. In the second part, an extended network is considered
where nodes are distant from each other and thus, a more complete model must take internode
distances into account. We will show that in this case, almost all of the links can be
active while maintaining the minimum rate.
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