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.
