Probabilistic Analysis of Adaptive and Diversity Schemes in Mobile Ad Hoc
Networks
In spite of their inherently random topology, future wireless mobile
ad hoc networks are subject to fundamental laws (scaling laws,
conservation laws, etc.) which are yet to be discovered and
validated. These involve traffic, topology, throughput, quality of
service etc. The aim of this thesis will be to investigate these
fundamental laws using probabilistic tools stemming from random
graph theory, point process theory and stochastic geometry.
The thesis will go beyond the Gupta and Kumar capacity bounds for such
networks, which are based on Interference-aware Stochastic Geometry,
and which are clearly not the final word on the throughput of this
class of networks. New scenarios involving for instance mobility (as
first investigated by D. Tse and M. Grossglauser) or Multiple Input
Multiple Output (MIMO) channels, or cognitive radio schemes, show
that much throughput gain can be expected from innovative schemes.
The main challenge will be the development of an Information Theory-aware
Stochastic Geometry/Random Graph Theory leveraging these key paradigms,
which go way beyond point to point channels and SINR determined bit rates.
More specifically, we will explore
1) the potential of adaptive techniques: power control, adaptive antennas,
cognitive radio and more generally opportunism, which could leverage
fading,
locations or the randomness present in the MAC and variations in the
utilization of the radio spectrum.
2) the throughput gain offered by MIMO channels, by multiple antennas, by
successive interference cancellation techniques or by network coding etc.
This will require a deep interplay between Information Theory and
Stochastic
Geometry.