The predominant game-theoretic solutions for distributed rate-maximization
algorithms in Gaussian interference channels through optimal power control
require perfect channel knowledge, which is not possible in practice due to
various reasons, such as estimation errors, feedback quantization and latency
between channel estimation and signal transmission. This thesis therefore
aims at addressing this issue through the design and analysis of robust gametheoretic
algorithms for rate-maximization in Gaussian interference channels
in the presence of bounded channel uncertainty.
A robust rate-maximization game is formulated for the single-antenna
frequency-selective Gaussian interference channel under bounded channel
uncertainty. The robust-optimization equilibrium solution for this game is
independent of the probability distribution of the channel uncertainty. The
existence and uniqueness of the equilibrium are studied and sufficient conditions
for the uniqueness of the equilibrium are provided. Distributed algorithms
to compute the equilibrium solution are presented and shown to have
guaranteed asymptotic convergence when the game has a unique equilibrium.
The sum-rate and the price of anarchy at the equilibrium of this game
are analyzed for the two-user scenario and shown to improve with increase in
channel uncertainty under certain conditions. These results indicate that the
robust solution moves closer to a frequency division multiple access (FDMA)
solution when uncertainty increases. This leads to a higher sum-rate and a
lower price of anarchy for systems where FDMA is globally optimal.
A robust rate-maximization game for multi-antenna Gaussian interference
channels in the presence of channel uncertainty is also developed along
similar principles. It is shown that this robust game is equivalent to the
nominal game with modified channel matrices. The robust-optimization
equilibrium for this game and a distributed algorithm for its computation
are presented and characterized. Sufficient conditions for the uniqueness of
the equilibrium and asymptotic convergence of the algorithm are presented.
Numerical simulations are used to confirm the behaviour of these algorithms.
The analytical and numerical results of this thesis indicate that
channel uncertainty is not necessarily detrimental, but can indeed result in
improvement of performance of networks in particular situations, where the
Nash equilibrium solution is quite inefficient and channel uncertainty leads
to reduced greediness of users.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.