On the Bounds of Feedback Rates for Pilot-Assisted MIMO Systems

For pilot-assisted multiple-input-multiple-output (MIMO) systems with imperfect feedback, we investigate the relationship between the feedback transmission rate and the resulting closed-loop capacity gain. Based on this relationship quantified via rate-distortion theory, we investigate the lower and upper bounds of the feedback rate that would effect positive closed-loop capacity gains without overly consuming feedback transmission resources. Extensive simulations are carried out to validate the analytic results and to shed light on the achievable closed-loop MIMO capacity given the system configuration parameterized by the number of antennas, transmit signal-to-noise ratio, pilot power allotment, and finite feedback rate. Such results provide guideline on the feedback channel for meaningful designs of practical pilot-assisted MIMO systems.