The Energy differentiated field theorem: a powerful tool to quantify wireless capacity limits
Résumé
This talk addresses the problem of quantifying the capacity limit in a wireless network all connected to a single access point. In the particular case when the network is made of independent wireless transmitters distributed in a uniform Poisson field in the infinite plan under a non-selective Rayleigh fading, it has been shown by numerous authors that the capacity limit in bit per Hertz is exactly equal to the ratio of the attenuation factor on the dimension of the Euclidian space embedding the network. However, this simple result is limited in scope and arrives after long and tedious computational steps.
In this talk we present a much more general result, called the “Energy differentiated field theorem”, which allows to derive the capacity limit in more general setting: general radio fading, general geographic distribution of transmitters, etc. It uses the differentiation of the average logarithm of the energy field around the base station. All The previous limit results which were obtained with lot of efforts, now very easily comes sometimes just via pure scaling comparison. We can generalize with the same ease to the cases where the geographical distribution of transmitters shows complicated patterns with fractal dimensions as we expect as we can expect in natural landscape and real urban deployments.
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