Abstract

This work treats multi-cell (M-C) multi-user (M-U) massive MIMO (M-MIMO) systems taking into consideration pilot contamination (PC), where Rayleigh fading channels are correlated in the spatial domain. An appropriate exponential correlation (EC) is using as an approximation model for uniform-linear arrays (Un-LA). The statistics of minimum mean square error (MMSE), element-wise MMSE (EW-MMSE), approximate MMSE (Approx.MMSE), and least-squares (LS) estimators are evaluated and analyzed. The Approx.MMSE estimator uses an imperfect covariance matrix (CM), which relies on sample CM to estimate a true CM provided by the MMSE. Analytical NMSE formulas for idealistic and realistic CMs are presented and interpreted. An analytical normalized mean square error (NMSE) formula is also given for EW-MMSE.

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