  This paper considers the noncooperative maximization of mutual information in
the Gaussian interference channel in a fully distributed fashion via game
theory. This problem has been studied in a number of papers during the past
decade for the case of frequency-selective channels. A variety of conditions
guaranteeing the uniqueness of the Nash Equilibrium (NE) and convergence of
many different distributed algorithms have been derived. In this paper we
provide a unified view of the state-of-the-art results, showing that most of
the techniques proposed in the literature to study the game, even though
apparently different, can be unified using our recent interpretation of the
waterfilling operator as a projection onto a proper polyhedral set. Based on
this interpretation, we then provide a mathematical framework, useful to derive
a unified set of sufficient conditions guaranteeing the uniqueness of the NE
and the global convergence of waterfilling based asynchronous distributed
algorithms.
  The proposed mathematical framework is also instrumental to study the
extension of the game to the more general MIMO case, for which only few results
are available in the current literature. The resulting algorithm is, similarly
to the frequency-selective case, an iterative asynchronous MIMO waterfilling
algorithm. The proof of convergence hinges again on the interpretation of the
MIMO waterfilling as a matrix projection, which is the natural generalization
of our results obtained for the waterfilling mapping in the frequency-selective
case.
