# 2008 Research Summary

## A Deterministic Model for Wireless Networks

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David Tse

The multiuser Gaussian channel model is the standard one used in information theory to capture these two effects: signals get attenuated by complex gains and added together with Gaussian noise at each receiver (the Gaussian noises at different receivers being independent of each other.). Unfortunately, except for the simplest networks such as the one-to-many Gaussian broadcast channel and the many-to-one Gaussian multiple access channel, the capacity region of most Gaussian networks is unknown. For example, even the capacity of the simplest Gaussian relay network, with a single source, single destination and single relay, is open.

To make further progress, in this project we present a new multiuser channel model which is analytically simpler than Gaussian models but still captures the two key features of wireless communication of broadcast and superposition. The key feature of this model is that the channels are {\em deterministic}: the signal received at a node in the network is a (deterministic) function of the transmitted signals. This model is a good approximation of the corresponding multiuser Gaussian model under two assumptions that are quite common in many wireless communication scenarios:

(1) The additive noise at each receiver is small compared to the strength of the signals received from the transmitters (high SNR regime); and

(2) The signals from different nodes in the network can be received at very different power at a given receiver (high dynamic range of received signals).