  Massive multiple-input multiple-output (massive MIMO) can provide large
spectral and energy efficiency gains. Nevertheless, its potential is
conditioned on acquiring accurate channel state information (CSI). In time
division duplexing (TDD) systems, CSI is obtained through uplink training which
is hindered by pilot contamination. The impact of this phenomenon can be
relieved using spatial division multiplexing, which refers to partitioning
users based on their spatial information and processing their signals
accordingly. The performance of such schemes depend primarily on the
implemented grouping method. In this paper, we propose a novel spatial grouping
scheme that aims at managing pilot contamination while reducing the required
training overhead in TDD massive MIMO. Herein, user specific decoding matrices
are derived based on the columns of the discrete Fourier transform matrix
(DFT), taken as a spatial basis. Copilot user groups are then formed in order
to obtain the best coverage of the spatial basis with minimum overlapping
between decoding matrices. We provide two algorithms that achieve the desired
grouping and derive their respective performance guarantees. We also address
inter-cell copilot interference through efficient pilot sequence allocation,
leveraging the formed copilot groups. Various numerical results are provided to
showcase the efficiency of the proposed algorithms.
