Date of Award
Doctor of Philosophy (PhD)
Mahesh K. Varanasi
David R. Grant
Dejan S. Filipovic
The physical layer of a wireless network can be used in various settings distinguished by the specific set of messages transmitted in the network. In this thesis, rather than considering each setting in isolation as has been the traditional approach, we study the unified setting of general message sets in which any subset (including all) of messages can be transmitted simultaneously in a network. The total number of possible messages is exponential in the size of the network and the number of settings simultaneously studied is double-exponential. For this reason, the problem quickly would become difficult or even impossible to solve for large networks unless some structure is found in smaller network settings.
In this thesis, we begin this journey by settling the approximate capacity regions in the form of exact degrees of freedom (DoF) or the linear DoF regions of selected small, but representative, multiple-input multiple-output (MIMO) wireless broadcast and interference networks. The aim is to not only develop novel approaches to fully obtain the DoF-optimal solutions through tight inner and outer bounds but also to suggest approaches that could be potentially useful in generalizing the results herein to a broader class of problems that may include larger networks and/or channel uncertainty models.
In developing novel achievable schemes, we propose a methodology that combines the idea of message splitting and channel decomposition, which notably simplifies the construction of the achievable region for the network. Using channel decomposition, the transmitter beamformer space is partitioned into several linearly independent subspaces, each of which has special properties and is easier to analyze. Message splitting involves expanding the number of message types beyond the original ones by splitting each message into several independent types according to their different impacts to the receivers or which beamformer subspaces they are transmitted through. This enlarges the dimensions needed to specify the achievable DoF region in split-message space. Interestingly though, it also simplifies the analysis and provides what is effectively a high-dimensional description of the achievable DoF region. When projected to the desired dimensions, the achievable region is specified.
Wang, Yao, "Degrees of Freedom of MIMO Wireless Networks with General Message Sets: Channel Decomposition, Message Splitting and Beamformer Allocation" (2017). Electrical, Computer & Energy Engineering Graduate Theses & Dissertations. 185.