Interference Alignment : Beyond Generic Channels

OF THE DISSERTATION Interference Alignment : Beyond Generic Channels By Sundar Rajan Krishnamurthy Doctor of Philosophy in Electrical and Computer Engineering University of California, Irvine, 2014 Professor Syed Ali Jafar, Chair Capacity characterization of communication networks is the most fundamental problem in Information Theory, that underlies the design of various wireless and wired networks. The radical idea of “Interference alignment” has enabled Capacity or Degrees of Freedom characterization (DoF, a first order approximation) for many interference networks. Various alignment schemes developed have provided new and fundamental insights into the number of accessible signal dimensions in communication networks where the output signals are linear functions of the input signals. Most of the prior art deal with generic channels wherein the channel coefficients are assumed to be independent and drawn from a continuous distribution, continuous alphabet with infinite diversity, and the network is often single-hop. These assumptions are challenged due to the following reasons : 1) In MIMO systems, poor scattering environment and network topology lead to spatial dependencies that are manifested as rank deficient channels, 2) Multi-hop dependencies arise due to the presence of relays, and 3) Linear network coding applications (as in wired networks) act as finite field counterparts of wireless networks, with limited diversity. In this thesis, Capacity / DoF of linear communication networks are characterized for “Non-generic channels”. One of the significant problems considered is the DoF of the K-user MIMO rank deficient interference channel, with different ranks for the direct and the cross channels. For this rank deficient interference channel, it is shown that the rank deficiency of direct channels does not help