| A communication environment with multiple transmitters and multiple receivers is inherently a competitive environment. The aim of this thesis is to illustrate the role of competition and the value of cooperation in a multi-user communication environment from an information-theoretical perspective. Various scenarios will be treated, including the multiple access channel where receivers cooperate, the broadcast channel where transmitters cooperate, and the interference channel where neither transmitters nor receivers cooperate.; There are three main results in this thesis: First, it is shown that in a Gaussian multiple access channel with multiple transmit and receive antennas, the optimum transmit strategy that maximizes the sum capacity can be found by an iterative water-filling procedure, where each user competitively maximizes its own rate while treating interference from other users as noise. Thus, a competitive optimum in a Gaussian multiple access channel is also a global optimum. Second, it is shown that in a Gaussian broadcast channel with multiple transmit and receive antennas, under a certain non-singularity condition, the sum-capacity can be achieved using a decision-feedback precoder. Further, the sum capacity can be interpreted as a saddle-point of a mutual information game, where the transmitter chooses a transmit strategy to maximize the mutual information, and “nature” chooses a fictitious noise correlation to minimize the mutual information. Thus, the sum capacity of a Gaussian broadcast channel corresponds to a competitive equilibrium. Third, it is shown that in a Gaussian interference channel, although a competitive optimum is not necessarily the global optimum, it leads to a desirable operating point. This suggests a distributed dynamic spectrum management scheme for digital subscriber line (DSL) applications. |
