ThesisCommunications over the Broadcast Channel with Limited and Delayed Feedback: Fundamental Limits and Novel Encoders and Decoders
In many multiuser wireless communications scenarios, good feedback is a crucial ingredient that facilitates improved performance. While being useful, perfect feedback is also hard and time-consuming to obtain. With this challenge as a starting point, the main work seeks to address the simple yet elusive and fundamental question of ``HOW MUCH QUALITY of feedback, AND WHEN, must one send to achieve a certain degrees-of-freedom (DoF) performance in specific settings of multiuser communications''.
Emphasis is first placed on communications over the two-user multiple-input single-output (MISO) broadcast channel (BC) with imperfect and delayed channel state information at the transmitter (CSIT); a setting for which the work explores the tradeoff between performance, and feedback timeliness and quality. The work considers a broad setting where communication takes place in the presence of a random fading process, and in the presence of a feedback process that, at any point in time, provides CSIT estimates - of some arbitrary quality - for any past, current or future channel realization. Under standard assumptions, the work derives the DoF region, which is optimal for a large regime of sufficiently good (but potentially imperfect) delayed CSIT. This region concisely captures the effect of channel correlations, the quality of predicted, current, and delayed-CSIT, as well as concisely captures the effect of the quality of CSIT offered at any time, about any channel.
The bounds are met with novel schemes which - in the context of imperfect and delayed CSIT - introduce here for the first time, encoding and decoding with a phase-Markov structure. The results hold for a large class of block and non-block fading channel models, and they unify and extend many prior attempts to capture the effect of imperfect and delayed feedback. This generality also allows for consideration of novel pertinent settings, such as the new periodically evolving feedback setting, where a gradual accumulation of feedback bits progressively improves CSIT as time progresses across a finite coherence period. Then, the work considers the more general settings of the 2-user MIMO BC and IC, as well as the setting of the K-user MISO BC.
Further work also considers different aspects of communicating with delayed and limited CSIT, such as the aspect of global CSIR, i.e., with imperfect receiver estimates of the channel of the other receiver, and the aspect of diversity. In addition to the theoretical limits and novel encoders and decoders, the work applies towards gaining insights on practical questions on topics relating to communication with limited and delayed feedback.