Downlink Pilots for Hybrid Massive MIMO Under Reciprocity Imperfections

In this letter, we study the performance of a time division duplex (TDD) hybrid massive multiple input multiple output (MIMO) system with imperfect calibration of the transmit and receive radio frequency chains. Using deterministic equivalent (DE) analysis, we establish the loss in the achievable rates due to calibration imperfections. We then discuss limited downlink training to estimate the effective downlink channel, and compare the relative merits of this method against frequency division duplexed (FDD) operation. Finally, via detailed numerical simulations, we evaluate the relative performance of no downlink training, limited downlink training, and FDD mode operation in the presence of reciprocity calibration errors.