Multi - User Communication Systems : Capacity , Duality , and Cooperation

In this thesis we investigate the capacity of multi-user wireless communication channels. We first establish a duality relationship between the Gaussian broadcast and multiple-access channels. This relationship allows us to characterize the capacity region of the Gaussian broadcast channel in terms of the dual Gaussian multiple-access channel, and vice versa. This relationship holds for constant, fading, and multiple antenna channels. We also extend this duality to a class of deterministic, discrete memoryless channels. We then consider multiple-antenna multi-user channels, for which the capacity region is known only for the multiple-access channel. A duality is established between the dirty paper coding achievable region of the broadcast channel, which is a lower bound to the capacity region, and the true capacity region of the multiple-access channel. We use duality to prove that dirty paper coding achieves the sum rate capacity of the multiple-antenna broadcast channel. Next, we provide an efficient and provably convergent algorithm that computes the sum rate capacity. Finally, we analytically upper bound the advantage that dirty paper coding provides over the sub-optimal technique of time division. Next we consider power allocation for time-varying wireless channels. We propose the concept of minimum rate capacity, in which average rates are maximized subject to the constraint that a minimum rate must be maintained for each user in all fading states. We explicitly characterize the minimum rate capacity and the corresponding optimal power allocation policies for the fading broadcast channel. We then use duality to characterize the minimum rate capacity of the dual fading multiple-access channel. Finally, we find the optimal power allocation policies that maximize ergodic capacity of a fading broadcast channel with both independent messages and a common, or multicast, message. In the final chapter, we study the benefits of cooperative communication in an ad-hoc network. In such a network there are multiple transmitters and multiple receivers. We consider cooperation schemes within the transmitting and receiving clusters. Using our earlier work on multiple antenna multi-user channels, we compare achievable rates to those achievable without cooperation.