| In wireless communication networks, competition among users for channel resources can result in severe mutual interference. This is a bottleneck for obtaining higher communication rates. Recent advances in the network information theory, such as the idea of interference alignment, have greatly facilitated our understanding of signal dimensions or even exact capacity of wireless networks and produced a number of new transmission schemes to achieve higher rates. Usually, we are interested in the fundamental questions — what is the channel capacity of multiuser networks, and how to achieve higher communication rates, attractive for both theoretical researchers and engineers. Since finding the exact capacity of multiuser wireless networks is quite challenging, if not impossible, we are interested in the degrees of freedom (DoF) characterization, i.e., a coarse capacity approximation, of wireless networks. The number of DoF of a communication network is a metric of great significance as it provides a lens into the most essential aspects of the communication problem. DoF investigations have motivated many fundamental ideas such as interference alignment. In this dissertation, we investigate the DoF of a number of multiuser wireless networks using the idea of interference alignment. In particular, we start from the classical interference channels with global channel knowledge at each node. A number of scenarios will be studied, including networks with single antenna or multiple antennas at each node. Next, we consider the interference channel with local cooperation and local connectivity. Then we go beyond one-hop to multihop wireless networks where we find the DoF of multiple unicast for 2-source 2-sink layered networks with arbitrary topologies. Finally, we weaken the global channel knowledge assumption, to study broadcast channels with no channel state information at the transmitter. Several interesting tools, insights and surprising results are obtained in this work — including phase alignment, asymmetric complex signaling, subspace alignment chains, genie chains, the observation that removing interference-carrying links can reduce the channel capacity, and blind interference alignment. |
