Downlink performance of massive-MIMO systems using EVD-based channel estimation

In this paper, we consider the downlink of multi-cell multiuser massive multiple-input-multiple-output (MIMO) systems employing the eigenvalue-decomposition-based channel estimation. The impacts of two errors are emphasized, namely, the error due to nonorthogonal channel vectors caused by a finite number of base station (BS) antennas and the error of the sample covariance matrix because of the received signal with a finite length. First, we derive the closed-form expressions for the achievable rate and the symbol error rate (SER). It is shown that no matter how large the number of BS antennas is, the rate loss due to finite BS antennas always exists. As the number of BS antennas increases, the rate loss converges to a constant, which only relates to the large-scale factors and transmit power. On the other hand, the rate loss caused by the sample covariance matrix could be zero when the number of received signal goes to infinity. We further investigate the asymptotic behaviors of the SER in the regimes of high signal-to-noise ratio (SNR), large number of received signals, and large number of BS antennas. It is demonstrated that the SER at high SNRs is interference limited instead of noise limited; the boundary of the SER in the limit of an infinite number of received signal is also derived. Although increasing the number of BS antennas can improve system performance, there is always a gap between the SER and that obtained without these two errors. More importantly, this gap enlarges as the number of BS antennas increases. Numerical results are presented to verify our analysis