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This paper considers the pilot contamination problem in multi-cell massive MIMO systems. We propose a novel cell-specific uplink training scheme along with a downlink pilot contamination elimination precoding (PCEP) scheme. In the uplink training phase, users in one cell apply the same pilot sequence, while orthogonal pilot sequences are employed in different cells. With time-division duplex operation, base stations (BSs) estimate downlink channels in uplink training phases. For downlink data transmissions, the PCEP scheme is introduced to cancel the intra-cell interference caused by pilot contamination. Analytical studies show that the downlink received signal-to-interference-plus-noise ratios (SINRs) of all users approach infinity simultaneously as the number of BS antennas tends to infinity. We also analytically investigate the performance of the proposed schemes in practical scenarios with a finite number …