Pilot Contamination in Massive MIMO Induced by Timing and Frequency Errors

Pilot contamination in the uplink (UL) puts asymptotic limits on the downlink (DL) spectral efficiency in time-division duplex (TDD) massive multiple-input multiple-output (MIMO) systems relying on TDD channel reciprocity. Pilot contamination can be induced by the UL pilot reuse across different neighboring cells. In this paper, we show that receiver front-end impairments also contribute to pilot contamination. In particular, we consider a TDD multi-user (MU) massive MIMO orthogonal frequency-division multiplexing (OFDM) system, where either time-division multiplexed (TDM) pilots or frequency-division multiplexed (FDM) pilots are utilized for UL channel sounding. We endeavor to characterize the impacts of the residual timing offsets (TOs) and the carrier frequency offsets (CFOs) on the DL performance of the massive MIMO-OFDM system. Closed-form expressions of the asymptotic DL MU spectral efficiencies are derived in the presence of both TOs and CFOs under different scenarios. Our analytical results reveal how the residual TOs and CFOs destroy the orthogonality among the UL training sequences from different users and give rise to pilot contamination. Specifically, we show that the DL spectral efficiencies become bounded even when the number of antennas goes toward infinity. Furthermore, to alleviate the impacts of TOs and CFOs, we propose different pilot decontamination methods based on our analyses for both the TDM pilots and the FDM pilots. Numerical simulation results corroborate our analyses and designs.