Semi-blind Channel Estimation for Multiuser Massive MIMO Systems

Abstract

Motivated by recent developments in time-division duplex massive multiple-input multiple-output (MIMO) systems, this paper investigates semi-blind channel estimation for multiuser MIMO systems. An expectation-maximization (EM) algorithm is derived for semi-blind channel estimation and a tractable EM algorithm is obtained by assuming a Gaussian distribution for the unknown data symbols, which improves channel estimates even when the data symbols are drawn from a finite constellation, such as quadrature phase-shift keying. An alternate EM algorithm is also derived by employing suitable priors on the channel coefficients and it is shown to outperform the EM algorithm with no priors in the low signal-to-noise ratio regime. To analytically understand the performance of the semi-blind scheme, Cramer–Rao bounds (CRBs) for semi-blind channel estimation are derived for deterministic and stochastic (Gaussian) data symbol models. To get insight into the behavior of a massive MIMO system, the asymptotic behavior of the CRBs as the number of antennas at the base station grows is analyzed. The numerical results show the benefits of semi-blind estimation algorithm as measured by the mean squared error. In particular, the performance of the EM algorithm becomes closer to the genie-aided maximum likelihood estimator based on known data symbols as the number of antennas increases. This result is consistent with the asymptotic analysis of the two CRBs indicating that semi-blind channel estimation for massive MIMO systems is very promising.