Date of Award
Doctor of Philosophy (PhD)
Spectrum sharing allows the coexistence of heterogeneous wireless networks on the same frequency band. Managing the interference between such networks is critically important to ensure high spectrum efficiency, thus motivating the study of multiple-input-multiple-output (MIMO) interference channels (IC) in information theory. This dissertation studies three classes of such interference channels, namely, the MIMO one-to-three IC, the MIMO IC-ZIC, and the MIMO MAC-IC-MAC.
The MIMO one-to-three IC is a partially connected three-user IC with multiple antenna terminals, where one transmitter that causes interference is heard at all three receivers, whereas the other two transmitters are heard only by their intended receivers. We present inner and outer bounds on the capacity region of the MIMO one-to-three IC, quantify the gap between the two bounds, and show that the gap is independent of the channel signal-to-noise ratios (SNRs) and interference-to-noise ratios (INRs). In particular, the achievable scheme at the interfering transmitter involves three-level superposition coding with linear precoding based on the generalized singular value decomposition (GSVD) whereas the non-interfering transmitters perform single-user coding with Gaussian codebooks and scaled identity covariances. The outer bound is obtained using genie-aided arguments with various combinations of genie information provided to the receivers. The generalized degrees of freedom (GDoF) region, which can be seen as a high SNR approximation of the capacity region, of the MIMO one-to-three IC is then fully characterized. We study the achievability of the GDoF region and the sum GDoF curve using an analysis tool developed in this dissertation, which we refer to as multidimensional signal-level partitioning. This tool is tailored for demonstrating the achievability of GDoF-tuples of a MIMO network that can be achieved via multi-level superposition coding.
The MIMO IC-ZIC is also a partially connected three-user IC consisting of three transmitter-receiver pairs. In the IC-ZIC, the first and second pairs form a two-user IC, the first and third pairs form a one-sided or Z interference channel (ZIC) and the second and third transmitter-receiver pairs taken by themselves are two non-interfering point-to-point links. In this thesis, an explicit inner bound is obtained via a coding scheme is proposed in which the first transmitter employs three-level superposition coding (as in the MIMO one-to-three IC), the second one employs the previously proposed and well-known Karmakar-Varanasi coding scheme (which achieves a constant-gap-to-capacity region of the two-user MIMO IC), and the third transmitter employs single-user coding with a Gaussian codebook (with scaled identity covariance). An explicit single region outer bound based on genie-aided arguments is then obtained. The gap between the inner and outer bounds is then shown to be within a quantifiable gap to the capacity region and the gap is independent of channel SNRs and INRs. The GDoF region is then characterized and analyzed in a variety of channel settings. The difficulty in this part of the research lies in the quantification of the gap between the 28-inequality inner bound and the 33-inequality outer bound, which is characterized via a series of supporting lemmas that reveal the relationship between the entropy terms in the inner and outer bounds.
The MIMO MAC-IC-MAC consists of two interfering MACs in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous published work by Pang and Varanasi using inner and outer bounds that are unions of polytopes. In the dissertation, we obtain single region inner and outer bounds that characterize a constant-gap-to-capacity region of the MIMO MAC-IC-M
Pang, Yimin, "Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom" (2019). Electrical Engineering Graduate Theses & Dissertations. 39.