Toward the Performance vs. Feedback Tradeoff for the Two-User MISO Broadcast Channel

For the two-user MISO broadcast channel with imperfect and delayed channel state information at the transmitter (CSIT), the work explores the tradeoff between performance, and CSIT 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 degrees-offreedom (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.