  In this paper, the problem of sequential beam construction and adaptive
channel estimation based on reduced rank (RR) Kalman filtering for
frequency-selective massive multiple-input multiple-output (MIMO) systems
employing single-carrier (SC) in time division duplex (TDD) mode are
considered. In two-stage beamforming, a new algorithm for statistical
pre-beamformer design is proposed for spatially correlated time-varying
wideband MIMO channels under the assumption that the channel is a stationary
Gauss-Markov random process. The proposed algorithm yields a nearly optimal
pre-beamformer whose beam pattern is designed sequentially with low complexity
by taking the user-grouping into account, and exploiting the properties of
Kalman filtering and associated prediction error covariance matrices. The
resulting design, based on the second order statistical properties of the
channel, generates beamspace on which the RR Kalman estimator can be realized
as accurately as possible. It is observed that the adaptive channel estimation
technique together with the proposed sequential beamspace construction shows
remarkable robustness to the pilot interference. This comes with significant
reduction in both pilot overhead and dimension of the pre-beamformer lowering
both hardware complexity and power consumption.
