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Pilot decontamination via Doppler PSD alignment

Pilot contamination in the uplink (UL) can severely degrade the channel estimation quality at the base station (BS) in a massive multi-input multi-output (MIMO) system. Thus, it is critical to explore all possible avenues to enable more orthogonal resources for the users to transmit non-interfering UL pilots. In conventional designs, pilot orthogonality typically assumes constant channel gains. To circumvent this constraint, in this paper, we show how to enable orthogonal multiplexing of pilots in the case of Doppler fading by aligning the power spectrum densities (PSD) of different users. From the derived PSD aligning rules, we can see multiple users can be sounded simultaneously without creating pilot contamination even when these users are experiencing time-varying channels. Furthermore, we provide analytical formulas characterizing the channel estimation mean square error (MSE) performance assuming ideal pilot orthogonality, which serve as the performance bounds for our proposed pilot designs. Computer simulations further confirm us the PSD alignment can serve as one important decontamination mechanism for the UL pilots in massive MIMO.