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. (read more)