On the performance of EVD-based channel estimations in MU-Massive-MIMO systems

This paper considers the conventional eigenvalue decomposition (EVD) based and widely linear (WL) channel estimations to alleviate inherent pilot contamination problems in multi-cell multi-user massive multiple-input multiple-output (MU-Massive-MIMO) systems. Both channel estimation schemes utilize the asymptotic orthogonality between the propagation vectors of different users which would be true only if the number of base station (BS) antennas goes to infinity. However, the limit on the number of BS antennas plus the error on the sample-based covariance matrix of the received signal deteriorate the channel estimate in practice. We derive therefore the closed-form mean-square-error (MSE) of both channel estimates characterizing two aforementioned error sources, which analytically demonstrates that the WL algorithm is superior to the EVD-based one in two folds: it applies more orthogonalized real representations of channel vectors and reduces a typical phase shift in EVD-based estimate to a sign ambiguity. The performance analysis is verified by our numerical results.