| Currently, we are witnessing a veritable explosion in the number of mobile devices with network connectivity. This explosion in the number of mobile devices which guzzle data is resulting in bandwidth becoming an increasingly scarce resource. The surge in the demand for data calls for new techniques to understand and improve the capacity (data rates) of wireless networks. In this thesis, I will describe and explore the benefits of interference alignment - a recently discovered technique to manage interference, which is the primary bottleneck of rates of communication in wireless communication networks.;A primary object of study of this thesis is a communication network with K wireless transmitter-receiver pairs mutually interfering with each other, also known as the K user interference network. In this thesis, we study a high SNR approximation to its capacity known as the degrees of freedom. A widely held belief that influences design of most, if not all wireless networks is the following: in the K user interference network it is optimal from a network degrees of freedom perspective to divide the spectrum among the users like cutting a cake. This cake cutting view of spectrum access also known as orthogonalization enables each user in the interference network to get a fraction of 1/K degrees of freedom, i.e., 1/K of the spectrum free of interference. In this thesis, we will show that, from a degrees of freedom perspective, the belief in the optimality of the cake cutting view of spectrum access (i.e., orthogonalization) is flawed. We show that if the network is frequency-selective or time-varying, then each of the K users of an interference network can essentially get half the degrees of freedom of a single user (i.e., half the spectrum at high signal-to-noise ratios) simultaneously. In other words, each user can get "half the cake" rather than merely a fraction 1/K. The key to achieving this is the powerful interference management strategy of interference alignment.;The thesis will study and develop various aspects of interference alignment. First, we develop an asymptotic alignment scheme to achieve "half the cake" in frequency-selective/time-varying interference channels. We then extend the idea of interference alignment to channels that are not frequency-selective or time-varying (i.e., channels which are constant) via three approaches: asymmetric complex signaling, a deterministic approach, and a distributed (numerical) alignment algorithm. In each of these cases, we will demonstrate degrees of freedom and capacity benefits of interference alignment in wireless interference networks. We also demonstrate practical benefits of the third approach - distributed alignment - in terms of rates at moderate signal-to-noise ratios and distributed implementations.;Finally, we show that the impact of interference alignment extends beyond the context of just wireless systems. In particular, we explore an alternate application of the idea of alignment - erasure codes for distributed storage systems. |
